This paper describes work in progress on the Higher Education simulation project funded by the Alfred P. Sloan Foundation. Contents may not be used or cited without permission. Limited distribution is provided to obtain comments and criticisms, and to assist potential development partners. Copyright © 1997 by JHHEG.

1. Introduction

Higher Education is a computer-based simulation game under development that targets both the institutional professional and the interested layperson to participate in leadership challenges in a college or university setting. Players set, monitor, and modify a variety of institutional parameters and policies, allocate resources as they see fit, and watch as results continually unfold. The game provides an opportunity to experiment and succeed or fail in a safe and entertaining fantasy environment. While Higher Education is necessarily a caricature of real academic life, it is grounded in authentic data and will provide serious lessons in higher education. The game will be driven by a sophisticated simulation engine that models five broad areas:

• enrollment management
• academic operations
• resource allocation and finance
• physical plant activities
• performance indicators

This paper describes the model that simulates academic operations It is intended to provide an overview for technical readers, especially those who will be responsible for game development. The elements discussed herein pertain to the simulation engine, not to the player interface. Many will be transparent to the player.

• Overview

Working with input from the enrollment management model, the game database, and player-provided parameters, the academic operations model simulates behavior at the department level. The model generates output for student and faculty behavior as reflected in variables like student FTEs, course demand and supply, graduation and drop rates, faculty arrivals and departures, sponsored research funding, and the quality and quantity of publications. Each element of the academic operations model runs once per academic year, after the enrollment management model, in the order presented herein. Its results inform the resource allocation, physical plant, and institution-level performance models—which follow it in the engine sequence—and the enrollment management model when it is applied for the following year.

The academic operations model simulates the behavior of students as they select or change their major field, select courses, graduate, or leave the institution. It also simulates faculty behavior, including initial inhire, promotion, tenure, and departure, teaching load determination, discretionary time allocations, and sponsored research. begins by simulating students’ choice of major and movement toward graduation or exit. This student model produces figures for the number of majors in each department (and in an "undecided" category), and the number of graduates and other departures, for each student level. Then the course demand model determines students’ course choices as a function of major and student level. The faculty model determines the faculty resources that will be available to fulfill course demand and other departmental obligations: it simulates faculty additions, promotions, departures, and retentions. Working from the data on course demand and faculty availability, the course supply and teaching load model generates each department’s course offerings and faculty teaching assignments. Then the faculty discretionary time model simulates how faculty allocate the time available over and above direct student contact hours. The discretionary time The results inform various departmental performance models dealing with the quality of teaching, progress on educational development projects, the amount and quality of research, and faculty and student morale.

Forum/Sloan has selected Enlight Software of Hong Kong as its development partner on the CyberCampus project. Enlight has extensive experience in the development of games based on micro-analytic simulation concepts. Microanalytic models simulate the behavior of individual entities rather than groups of entities. The behavior of the individual entities is aggregated to obtain group behavior.

Microanalytic models offer the advantages of realism, algorithmic simplicity, flexibility, and ease of programming and documentation. The downside lies in their use of memory and computer cycles. Enlight’s experience indicates that it will be practical to represent CyberCampus’s key elements in microanalytic terms, and their DigitLife^TM.

• Student Model

The student model simulates the flows of students within the player-created institution: the flows into and out of major fields, and to graduation or exit from the institution for other reasons. The model computes performance statistics, such as graduation rates and time to graduation by student level and gender-ethnic group, that will interest many players. It also performs the necessary technical function of providing student FTE data for input into the course demand model. Players influence these results indirectly, by setting policies that affect departmental performance, but they cannot directly control the simulated student behavior.

The model performs three main functions: it determines the field of interest of entering students, generates the history of students once they have entered, and calculates the number of student FTEs that will be taking courses during the year being simulated.

Enlight believes that as many as 1,500 to 2,000 "students" can be simulated individually. (The number of simulated entities also must allow for faculty as discussed in section 3.) A separate population will be required for each student level, and the multiplier that scales the simulated population to the whole population will vary from level to level. For example, doctoral and non-matriculated students may be simulated 1:1 (multiplier=1); masters and professional students simulated 2.5:1; and undergraduates simulated by as much as 10:1.

1. The student database

   Each record in the student database will include:

   • student level (5 levels)
   • gender-ethnic group (4 groups)
   • talent indices (e.g., 1-10 scale)
   • academic
   • extracurricular activities
   • athletics
   • year admitted to the program (student level)
   • number of courses to be taken during each trimester (Autumn, Winter, Summer); may be zero for some trimesters (e.g., Summer, for traditional undergraduates)
   • major field: one of the simulated departments or "undecided"
   • courses being taken this semester: by department and course depth category (3 categories for undergraduates; 1 for graduate students and non-matrics—see below); may be represented as pointers to the course table
   • number of courses taken so far: by department and course depth category
   • for undergraduates (traditional or non-traditional), whether the student has upper or lower division status (UD or LD: depends on whether the student has taken half the courses needed for the degree)
   • academic achievement (e.g., 1-10 scale)
   • satisfaction indices:
   • academic
   • extracurricular and student life
   • athletics

   Students will engage in the following kinds of activities:

   • Entry: new student records will be generated each year as the result of enrollment management actions. The enrollment management model will produce frequency templates for student level, gender-ethnic group, and the talent and initial satisfaction indices. The initial major field will be blank (to be filled in by the academic operations model), the numbers of courses taken will be zero, and initial academic achievement will equal the talent index.
   • Major field choice: students are allowed to choose or change their major any time, but the change won’t affect course-taking until the next trimester. The transition probabilities will depend on exogenous and departmental performance factors.
   • Course choice: students choose the courses to be taken each trimester according to an algorithm to be described later.
   • Academic achievement: evaluated at the end of each semester before courses are chosen for the following trimester. Course achievement ratings are calculated as functions of the department’s teaching effectiveness and the student’s talent (e.g., high-talent students can learn even when teaching quality is poor). If the achievement falls below a certain threshold the student may fail the course. Then the student’s overall achievement rating is adjusted based on the individual course achievements, after which the course-by-course achievement data can be purged.
   • Change in satisfaction indices: the three satisfaction indices are functions of various institutional performance factors (many are described in TD 2.6), time since entry, other students’ satisfaction, athletic wins and losses, and exogenous factors.
   • Graduation: a student will graduate when a sufficient number of passed courses have been accumulated and the distribution requirements for general education and the major field have been met. The act of graduation updates the student performance and alumni databases and then purges the record from the student database. Statistics on time from entry to graduation, the difference between the academic talent rating and the final academic achievement, and the final satisfaction ratings will be kept.
   • Dropout: the probability of dropout depends on achievement, satisfaction, time since entry, and exogenous factors. Dropout updates the student performance and alumni databases and then purges the record from the student database.
2. Field of interest of entering students

New records are passed to the student database by the enrollment management model. That model does not differentiate entering students by field of interest. In real life, however, some students are admitted into particular academic programs—doctoral and masters students are almost always admitted to specific programs, for example—and some entering undergraduate and non-matriculated students have well-developed preferences about field of interest whereas others remain undecided. Therefore, the academic operations model assigns each simulated entering students either to a field of interest or as "undecided."

The current model considers field of interest to be synonymous with departmental major. (The inclusion of interdisciplinary programs awaits future enhancements.) The undecided category is treated like a department. Students who are initially undecided will migrate to a departmental major sometime before graduation, though they may exit for other reasons before making the transition. Students also may change majors during the course of their study. We anticipate that the undecided category will be empty for masters and doctoral students, though this depends only on parameter settings.

Students’ initial fields of interest depend on initial field preference coefficients, numbers summing to one that describe the proportion of each entering cohort that will prefer one or another field. The model allows the field preference coefficients to vary by student level and gender-ethnic group. For example, entering female or minority undergraduates may exhibit different interest profiles than white male undergraduates. The model does not differentiate among student market segments, so students of all ability levels are considered to have the same field preference profiles.

The preference coefficients will evolve as the game progresses: partly due to exogenous factors and partly due to departmental performance. For example, student interest in Chemistry will be affected by national trends, perhaps changes in the performance of Chemistry departments in peer institutions, and certainly by the performance of the player-created institution’s Chemistry department. As discussed in Section 9, player-generated departmental performance may include the types of courses offered, graduation and exit rates, prestige, and reputation for teaching quality and faculty accessibility. Departmental prestige depends on faculty research prowess, and teaching reputation depends on faculty mix and the allocation of faculty discretionary time.

Each year’s updated preference coefficients depend on the previous year’s values, the exogenous factors, and the results of applying an s-shaped or similar response function to the previous year’s performance data. Applying the updated field preference coefficients to the numbers of incoming students produces the number of new entrants to each field of interest category, by student level and gender-ethnic group.

3. Transition patterns of existing students

The student transitions model simulates what happens to students once they have entered the player-created institution. Like the entering student preference model, it is applied to each combination of student level and gender-ethnic group. Its job is to calculate the proportions of existing students who graduate, exit for other reasons, and change fields during the year.

The student transition matrix lies at the model’s core. Figure 1 shows a sample matrix. The rows represent the fields of interest as they existed at the end of the previous year. The columns represent fields for the year currently being simulated, plus the possibilities of graduation and exit. (Graduation will occur if and when a student accumulates the credits needed for the degree.) The entries in each row describe the transition probabilities for students who began the year in the row-designated field. Random numbers will be drawn against these probabilities to determine the behavior of the individual sims.

Consider the first row, which represents undecided students, for example. During the year on average some 40% will remain undecided, 5% will declare a major in English, 7% a major in Chemistry, and 30% a major in another department. Because students must declare a major before graduation, they cannot graduate directly from the undecided state. Some The "grad" column equals 0, but 10% of the undecided students do exit for other reasons during the year. Looking down to the "English" row, we see that on average 39% remain with their declared major, 1% revert to undecided, 7% switch their major to Psychology, etc.—in addition, 40% will graduate and 6% will exit the institution for other reasons. The switching of majors will be inhibited as the number of required extra for graduation increases. For example, it will be easier to switch from science to humanities in the second or third year than the other way around.

Figure 1. Sample Transition Matrix

	this year
last year	undec.	Engl.	Psych.	Chem.	other	grad.	exit	total
undecided	0.40	0.05	0.07	0.08	0.30	0.00	0.10	1.00
English	0.01	0.39	0.07	0.03	0.04	0.40	0.06	1.00
Psych.	0.00	0.05	0.35	0.10	0.05	0.38	0.07	1.00
Chemistry	0.00	0.10	0.05	0.40	0.05	0.35	0.05	1.00
other	0.00	0.08	0.02	0.05	0.40	0.35	0.10	1.00

Note: row probabilities must add to one without the "grad" column.

Graduation rates and student lifetimes will be calculated directly from the individual students’ simulated behavior. The transition coefficients provide all the information needed to calculate the fraction of each entering cohort that will graduate in each field, the average time to graduation, the fraction that will exit without graduating, the average stay in the institution prior to exit, and the average lifetime in each state. They will differ markedly across student levels. They also may vary across gender-ethnic groups—for example, if minority graduation rates differ from those of majority students. The degree to which such variations are built into the model’s initial conditions can be adjusted depending upon the player’s choice of institutional type and game scenario.

Like the initial field preferences, the transition coefficients will evolve as the game progresses. The changes depend on exogenous factors like national trends in graduation rates and time to graduation, and departmental performance in the player-created institution. For example, if Psychology improves educational quality while quality in Chemistry declines, more students will transfer from Chemistry to Psychology. Psychology also will lose fewer students to other departments, fewer will drop out, and a larger fraction will graduate with a diminished average time to graduation. The procedures for adjusting the transition coefficients are analogous to those for the initial preferences, discussed above.

• Faculty Model

We now turn to the supply side of the academic operations model. The model first step determines the numbers of faculty who will teach courses, do research, and perform other departmental duties. The faculty model begins by simulating departmental hiring decisions. Then it simulates computes the transition of existing faculty through the ranks and in due course out of the institution.

1. The faculty database

The last step combines the hiring and transition results to produce figures for faculty FTEs by department during the year being simulated. The faculty model is structurally similar to the student model. Each faculty member in the departments being simulated will be represented as an individual. This avoid the necessity of scaling for these departments, and thus the sampling problem mentioned in footnote 2. Faculty size per department may average 25 or 30 for a medium-sized university of the kind we plan to simulate. An all-other "department," whose faculty will not be simulated individually, will be provided for institutions with more than ten or eleven departments . The all-other multiplier will be in the range of 1 to 5 or 6, depending on the size of the institution.

Each record in the faculty database will include:

• department
• rank level (5 categories: asst prof, assoc prof, full prof, long-term adjunct, short-term adjunct)
• age
• gender-ethnic group (4 groups)
• talent indices (e.g., 1-10 scale)
• teaching
• scholarship
• research
• salary
• normal teaching contact hours per trimester
• teaching contact hours assigned for this trimester
• allocation of discretionary time this semester (5 categories)
• sponsored research projects currently active or proposed; the database—which should allow for, say, 5 proposals/projects per faculty member—will contain:
• total dollars
• time in months the project will be active
• project status (active; will accepted and become active; will be rejected)
• date the project will end, become active, or be rejected

• total monthly expenditures on sponsored research projects
• off-duty trimester (Autumn, Winter, Summer)
• third trimester teaching (number of courses)
• performance ratings
• teaching
• scholarship
• research
• satisfaction index

Faculty will engage in the following kinds of actions:

• Entry: new faculty records will be generated each year as the result of hiring actions. The hiring model will produce templates for rank, gender-ethnic group, initial age and salary, and the talent and initial satisfaction indices. Initial research proposals, sponsored projects, and third trimester teaching will be zero; off-duty trimester will be "Summer," and initial performance ratings will equal the talent indices.
• Teaching contact hours: determined each semester by the teaching load model (see "Faculty Teaching Load and Discretionary Time," below).
• Discretionary time allocation: determined each semester by the teaching load model (see below).
• Research proposals and projects: faculty submit proposals to outside sponsors; successful proposals generate sponsored research expenditures (see "Research Proposals and Projects," below); the volume of research proposals will be governed by the factors described in Section 8.
• Change in the three talent indices: teaching, scholarship, and research talent will increase or decrease with the person’s experience (or lack of it) and performance, the performance of colleagues, and perhaps as functions of other factors.
• Teaching, scholarship, and research performance: the three performance indices depend on teaching loads and discretionary time allocations, class sizes, and sponsored research expenditures.
• Change in satisfaction indices: the three satisfaction indices are functions of salary, teaching load and discretionary time allocations, time in rank if less than full professor, various institutional performance factors, other professors’ satisfaction, and exogenous factors.
• Promotion (applicable to assistant and associate prof only)
• Discharge: assistant professors who are not promoted within seven years and auxiliary faculty whose teaching performance falls below a threshold will be discharged. Associate and full professors (who have tenure if it exists) may be discharged if their department is eliminated, but only upon payment of a substantial severance package. Associate and full professors whose performance is very bad may be discharged if and only if the player has previously taken steps to abolish tenure.
• Voluntary departure: faculty may accept offers from another institutions.
• Retirement or death: the probabilities depend on age and exogenous factors; retirement probabilities also may depend on early retirement programs.

The probabilities for promotion and exit depend on the variables described in Section 4.2.

The faculty model operates at the level of the department and gender-ethnic group. This allows data to be generated for white males, white females, minority males, and minority females—data which will support a significant inquiry into affirmative action issues. Faculty also are classified according to rank, age, and their primary talent for teaching, scholarship, and,and interest lies in teaching or research. research prowess. The player will be able to explore strategies dealing with hiring, tenure rates, and early retirement, and to attempt to build research capacity if he or she desires. Examples of output statistics include FTE numbers by age and rank, indices reflecting the faculty’s research and teaching prowess, the fraction of assistant professors who receive tenure, the number of senior full professors who retire, and the numbers of less senior people who leave the institution for other reasons. Each of these statistics can be broken down by department and gender-ethnic group if desired.

2. Faculty hiring

The number of positions, if any, that a given department will be allowed to fill during a given hiring season is determined by the resource allocation model. The program provides for hiring in the spring, after resource allocation has been decided, so that the new faculty will be on board for the next academic year. The faculty hiring model accepts player-generated input describing departmental hiring policies. Then it uses the hiring policies to determine the kinds of people to be hired.

The player (or the default initial conditions) assigns values to two sets of faculty hiring policy variables. These variables represent one of the two main levers available for influencing departmental behavior—though, as noted above, they operate only if opportunities exist for faculty hiring. Their relevance to faculty planning issues should be readily apparent.

The first hiring policy variables describe target values for the following quantities as they would exist after the new person or persons have been brought on board:

• minimum fraction of faculty who are female
• minimum fraction of faculty who are minority
• maximum fraction of faculty who are tenured
• maximum fraction of faculty who are long-term adjunct
• maximum fraction of faculty who are short-term adjunct

Suppose a department has nine faculty and is about to hire a tenth, that it presently has two minorities, and that its minority target is 30%. If the recruit is minority, the post-hire percentage will be on target at 30%. If the recruit is not minority the percentage will be 20%—below the target by ten percentage points.

The remaining hiring priority variables describe the relative importance of each of the above targets, plus the importance of teaching ability, research ability, and in-hire salary. For example, a department might weight the minority target twice as heavily as the tenured fraction target, and cost as being less important than teaching or research ability.

The faculty hiring model, which operates only if the department has been authorized to hire, allocates the available new positions according to. a linear programming procedure. The program’s objective involves the squared deviations from the aforementioned targets, the average teaching ability and research ability of the new faculty, and the salary commitment that will be required to attract them. The deviations count only if the target threshold is violated—for example, if the minority fraction after inhire remains below its target. The model seeks to minimize the deviations from the targets, to maximize teaching and research quality, and to minimize inhire compensation. There are twelve decision variables: specifically, the number of new hires in each faculty category.

The linear program includes seven constraints. First come five constraints that define the aforementioned deviations. A sixth constraint limits the total number of inhires—the sum of the decision variables—to the authorized figure. The last constraint makes it impossible to hire more than one person in a given category. It provides a technical simplification and ensures a degree of diversity when a department can hire more than one person. Depending on the policy settings, new hires can come in at the junior or senior level, as teachers or researchers, or in either adjunct category.

Tenure-line faculty members are characterized by three kinds of talent: teaching, scholarship, and research. The market for research faculty with strong research talent is more competitive than that for teaching faculty with teaching talent. (Scholarship talent falls between, but probably closer to the teaching end of the spectrum.) This means researchers generally cost more and are more difficult to retain, especially if the institution currently lacks prestige and research infrastructure or if teaching loads are high. The player will learn about this indirectly if he or she attempts to upgrade a department’s research capacity.

The prowess T- and R- indices for new faculty are determined as functions of initial salary. , then blended into the average for existing faculty on a proportional basis. Suppose, for example, a department of 9 people who’s average T-index equals 5 hires a new person at quality 7. Then the new
T-index is (9x5 + 7)/10 = 5.2. The faculty supply model will allow for correlations among the three talent indices. Faculty in each of the ten tenure-line categories are assumed to have characteristic quality indices for teaching and for research. Adjunct faculty possess indices for teaching only, but all tenure-line faculty possess both T-indices and R-indices. Teaching-oriented faculty will generally be better at teaching than at research and conversely, and the dedicated teacher’s research skills will generally lag those of the researcherHowever, it For example, faculty with strong research talent may have stronger teaching talent than those with less research talent, and the correlations may be more pronounced for scholarship and teaching. We shall see that what the faculty members do with their talent is another matter, howeverresearchers’ teaching ability will equal or even exceed that of teaching-oriented colleagues.

The initial salary for each faculty category is determined during resource allocation, or the player may override the guidelines for a specific hiring round. The higher the salary relative to peer-institution competitive salaries, the better the inhire quality. (Competitive salaries will vary over time due to exogenous factors.) The model incorporates salary premiums for minority and female candidates—that is, it may cost a little more to attract a minority or female of a given quality. And as noted above, research faculty generally will cost more than teaching-oriented faculty of the same overall quality.

Hiring research-oriented faculty is essential for building a significant research program, though this can be a risky strategy. Researchers may spend less discretionary time than their teaching-oriented colleagues on education-related tasks, and this can have negative consequences for educational quality. On the other hand, talented research-oriented faculty who spend substantial time on course preparation, course development, and student contact may well produce high-quality education. An institution that opts not to pursue big-time research will find it easier to attract and retain faculty, other things being equal. A player who wants to shift from a teaching to a research strategy, or conversely, will be limited by his or her ability to change the faculty mix—which in turn depends on the capacity to fund new hires and/or elicit turnover of existing faculty.

3. Faculty transitions

Faculty move through the ranks and age groups according to the same logic that governs the student flows. At the center of the process lies a transitions matrix like the one shown in Figure 1. This time, however, the rows and columns represent faculty categories, with the columns being augmented by "exit" and "retirement" rather than "graduation" and "exit." The transition probabilities will govern the random processes that drive the individual faculty entities.

The faculty transitions matrix has a more diagonal look than the student matrix. Faculty can move from assistant to associate professor, from associate to full (age≤45), and so on, but they can’t jump from assistant to full professor or from full (≤45) to full (≥65). (The age variable is increment by one each year that the faculty member remains with the institution.) Nor can they jump from tenure-line to adjunct status: while it is true that individuals occasionally change tracks, Higher Education would treat any such move as an exit followed by a new hire. We assume that all departures from the full (≥65) group represent retirements or deaths, and that departures from all other categories represent exits for other reasons. Faculty can move from the research group to the teaching group, or in rarer cases from the teaching group to the research group, at the same or next highest rank. All these possibilities are quantified by the elements of the faculty transition matrix.

The transition coefficients will evolve during play as functions of player policies and departmental performance. Different coefficients respond to different influence factors.

• The probability of exit depends on faculty morale and the ratio of the category’s average salary to the corresponding competitive salary level.
• The probability of promotion depends on the difficulty of achieving tenure or being promoted from associate to full professor, as determined by player policy.
• The probability of retirement depends on the player-generated early retirement program, if any. Program parameters consist of the institution-wide multiple of annual salary that will be granted for early retirement (one to two times salary is not uncommon), and the degree of retirement pressure applied by the particular department.
• The probability of shifting between the teaching and research interest groups depends on the relative emphasis on teaching versus research that is extant in the department.

Changes are phased in by exponential smoothing. Then the rows of the matrix are rescaled so they sum to one, just as in the student model. Again as in the student model, the individual entity simulations provide updated transition matrix provides all the information needed to report statistics like average time in category and at the institution, exit and retirement rates, promotion rates, etc.. All such statistics can be broken down by department and gender-ethnic group if desired.

4. Student FTEs

What remains is to apply the transition coefficients to the prior year’s student FTE numbers in each field of interest category and then add in the new student FTEs previously computed for each field. This produces the actual numbers of graduates and exits, and the current-year numbers for each field of interest category. All the above are computed for each combination of student levels and gender-ethnic group. A final computation aggregates FTE enrollments over gender-ethnic categories to produce the figures for total enrollment by level and field (including the "undecided" category) that are needed by the course demand model.

• Course Supply-Demand Model

Students’ decisions about their majors and programs generate course demand. (Students’ decisions are conditioned by faculty-determined program requirements.) Faculty decisions about how much and what to teach generate course supply. The next few sections of this paper describe CyberCampus’s procedure for matching course supply and demand.

The course supply-demand model translates FTE enrollments by student level and field of interest into course enrollments by department, course type, and academic term. It produces statistics on enrollment faculty workload patterns and that will be of interest to advanced players. The model produces data on course demand by department, academic terms, and course type. It can also produce statistics that describe:

• where students take courses: for each student level and field of interest, the fraction of enrollments going to each department and course type;
• where departmental enrollments come from: for each department, the fraction of enrollments by students coming from each level and field of interest.

The model takes several behavioral elements into account. FTE students at different levels take different varying numbers of courses annually, and they may distribute them differently across academic terms. Students majoring in a given field of interest will take courses in many different departments, not just in their major. Faculty will have varying preferences for course types—for example, lectures, seminars, undergraduate or graduate courses. As in the case of the student model, players influence the course profile indirectly by their policies but they cannot directly control faculty or student behavior.

1. The course database

The CyberCampus course database will describe groups of courses with common characteristics. (We will not set up individual course sims as this would add processing time and greatly complicate the algorithms.) Each record in the database will include:

• department: the department offering the course
• depth category (D1, D2, D3; plus GR): based on the number of departmental courses typically taken before taking this course; this can be used to produce a measure of curricular structure.
• focus category (lower division [LD], mixed [M], upper division [UD], GR): when in a student’s program the course is usually taken.
• Only seven cells of the depth-focus matrix are populated:

	D1	D2	D3	GR
LD	√
M	√	√
UD	√	√	√
GR				√

• Taken together, the depth and focus variables define curricular structure. . Research has identified breadth and depth as key variables for understanding curricular structure and thus students’ curricular choices.
• teaching method: (1) seminars, (2) classes without breakout or lab sections, (3) classes with breakouts or labs, (4) the breakout or lab sections themselves. (The breakout sections will be called "labs" in science departments.) Breakouts or labs will be considered as a separate teaching method, linked to the primary method in the sense that student numbers assigned to the primary method also will be assigned to the breakout sections. Methods 1-3 will be called "primary teaching methods," method 4 is a "secondary teaching method."
• number of students taking the course by conventional means (i.e., on campus)
• number of students taking the course by distance means (e.g., by television or Internet)
• number of class sections for on-campus students
• normal class size for on-campus sections

The seven depth-focus categories and four teaching method categories produce 28 course cells per department. Each cell will be flagged to indicate whether the courses can be used to satisfy the general education requirement and whether they are available on campus, by distance means, or both. If "both," some students will sit in class and others will watch synchronously via television. Strictly distance courses probably would be taught asynchronously, although the model won’t deal with this question. There is no "normal class size" for distance methods. Number of sections is determined by algorithm (described later) for on-campus courses; it equals 1 for courses taught strictly by distance means.

A teaching effectiveness function will be provided: effectiveness will depend on the department, focus category, teaching method, ratio of actual class size to the norm for that teaching method (for on-campus students only), and whether the student is taking the course by distance means.

A contact hours figure also will be provided for each department and teaching method. This represents the number of faculty hours per week required for class meetings or direct support of asynchronous teaching.

2. Curricular requirements and preferences

Departments impose course requirements on students majoring in their subject. Traditional and non-traditional undergraduates also must meet a general education requirement. There are no requirements for non-matriculated students.

The course requirements and preferences database contains the following information:

• student level
• major department (for undergraduates, the list includes general education)
• number of courses required for the degree (for major fields, the total number of courses for the degree including general education courses and electives; for general education, the total number of courses that satisfy the general education requirement)
• course requirements matrix: minimum number of courses to be taken in each depth category for each of (say) 5 departments, including the major department, in order to qualify for a degree
• induced course requirements matrix: takes account of the preparatory courses needed to take courses in the higher-level depth categories; if x_ij equals the course requirement for depth category i and department j and y_ij equals the induced course requirement, then
  y_i+1,j = Min[x_ij, 2y_ij] where y_ij = x_ij for i=3.
• elective course matrix: minimum number of free elective courses per year or trimester (for undergraduates, the value will depend on whether the student has upper or lower division status)
• student preference index for choosing electives: by department and focus category (for undergraduates, the values will depend on whether the student has upper or lower division status)
• faculty preference indices for the three primary teaching methods (classes with breakouts, classes without breakouts, seminars): by depth-focus cell

The requirements and preferences will be loaded as part of the game’s initial conditions. Changes may occur endogenously, perhaps influenced by the player. (How the influence occurs will be worked out during final design.)

3. Course choice procedure

Each trimester, simulated students fill out their programs based on their preferences and degree requirements, conditioned by faculty preferences which are assumed to affect teaching methods and course availabilities. Additional enrollments are banned when a class of courses becomes oversubscribed and no faculty are available to expand the number of sections offered. The student chooses another course in such circumstances, but the substitution may diminish his or her satisfaction and the new course may not represent satisfactory progress toward the degree.

Students may fill out their programs for the next trimester at any time during the previous trimester, and messages about enrollment bottlenecks will be generated as the bottlenecks become apparent. Quick action by the player to "encourage" faculty to open more sections (at a cost in faculty morale), or to fund additional sections taught by part-timers, may in some cases relieve the bottlenecks and open the way for later student registrants—however, students already denied entry to a course will remain denied.

The procedure executes the following steps for each trimester.

1. Loop for simulated students enrolled during the trimester.

Students should be processed in approximately random order within levels. The default for the order in which levels are processes is: doctoral; masters/professional; traditional undergraduates; non-traditional undergraduates; non-matriculated. The player might be given the opportunity to change the order. Note that students will not necessarily be enrolled for all trimesters; for example, absent player intervention most traditional undergraduates will not be enrolled during the summer.

2. Determine the student’s achievement in the courses taken during the previous trimester

For each course cell, achievement depends on the student’s academic talent and prior achievement, the teaching method and average class size ("enrollment per section") for the cell, and the teaching load and distribution of discretionary time for faculty teaching cell’s courses. If achievement is low enough, the student runs the risk of failing the course (a random event whose probably grows as achievement drops below a threshold); failure causes the course to be removed from the student’s cumulative courses taken table. The student’s overall achievement score (the only score stored permanently in the student record) is the sum of the individual course scores, adjusted downward if the student has failed courses.

3. Loop for the courses to be taken this trimester

Skip to the next student if the number of courses to be taken is zero (i.e., if the student is not enrolled this trimester)..

4. If this is not an elective course and required courses remain to be taken, do Step 4; else do step 5.
5. Select the next required course

Compare the cumulative number of courses taken with the requirements table for the student’s major, and for general education; choose the department with the largest number of courses yet to be taken. Then choose the maximum depth category that is possible given the number of courses already taken in that department. Finally, randomly select the focus category based on the chosen depth category and the student’s preferences. Then do Step 7. (The next section describes the procedure in more detail.)

6. Select the next elective course

For elective courses and for other course slots remaining after requirements have been fulfilled, randomly select a department based on student preferences. Then randomly select a depth-focus category based on student preferences and the number of courses already taken in that department. (The next section describes the procedure in more detail.)

7. Select the teaching method for the course and update the supply-demand balance for the resulting course cell; make adjustments as necessary and possible.

Select the teaching method. Attempt to increment the number of sections and enrollment for the selected department, depth-focus category, and teaching method category ("selected course cell"). If the attempt fails because enrollment per section is too large and no faculty are available to staff an additional section, close the selected course cell and substitute a different course cell. (The "Supply-Demand Balance" section describes the procedure in detail.)

Appropriate statistics for student achievement, course enrollment, course closures, and faculty teaching loads will be calculated upon completion of the student loop.

4. Individual course selection

This section applies to Steps 5 and 6 of the student course choice procedure. All choices are limited to courses not declared "closed" according to Supply-Demand Balance Step 5-b.

Required courses.

1. Choose the department (j) for which y_3j is largest. If all the values are equal (e.g., if all are zero), choose the maximum for y_2j; if all values are zero do it for y_1j; if all those values are zero, skip to the elective course procedure. If two departments are tied at any point, choose between then randomly.
2. With n = the number of courses previously taken in the department, choose the depth category (D) as follows:
   n≤2->D1; n≤4->D2; else D3.
3. Randomly select the focus category according to student preference, working from the following frame: D1->{LD, mixed, UD};
   D2->{mixed, UD}; D3->{UD}.

Elective courses.

1. Randomly select the department based on the student’s preference indices, multiplied by a function that adjusts for the number of courses already taken in the department (n). (The multiplier may increase or decrease with n so simulate the effect of experience—which in turn may depend on teaching effectiveness.)
2. Randomly select the focus category based on the student’s preference indices.
3. Choose the depth category according to: F=L-> D1;
   F=mixed & n≤2->D1 else D2; F=UD & n≤2->D1 else n≤4->D2 else D3.
5. Supply-demand balance

This section applies to Step 7 of the student course choice procedure. Once a student has chosen a department and depth-focus category (D-DF cell):

1. Randomly select a primary teaching method (TM), based on the departmental faculty’s teaching method preferences for the depth-focus cell, from the set of non-closed choices (see Step 5-b). If the primary TM is "with breakouts," also create a secondary TM for the breakout section(s).
2. If no course exists in the D-DF-TM cell (i.e., sections=0):
   1. Select a faculty member for whom
      (normal teaching contact hours) – (contact hours already assigned) >=
      (contact hours required to teach a section of this course).

   2. If the primary TM has breakout or lab sections, select an instructor for the first secondary section. The priority is someone from the graduate student teaching assistant pool (to be added to the resource allocation submodel for institutions that have doctoral students). If the pool is empty, select a regular faculty member with sufficient available contact hours.
   3. If no faculty member with sufficient available contact hours exists, then proceed to Step 5.
3. If a course already exists for the D-DF-TM cell and
   EPS <= LIMIT1*(normal class size) - 1, increment enrollment by 1 and exit.

   (EPS = enrollment per section. LIMIT1=1.25 implies a 25% enrollment overload before another section is created; see the Faculty Teaching Load section.)

4. If a course already exists for the D-DF-TM cell and
   EPS > LIMIT1*(normal class size) - 1,
   execute the substeps of (2) and exit if they succeed.

   (That is, add a section if teacher capacity is available. This will reduce enrollment per section.)

5. If Step 2 or Step 4 fails because no faculty member is available:
   1. If EPS <= LIMIT2*(normal class size) - 1, increment enrollment and proceed.

      (LIMIT2=1.33 implies that a 33% overload will be allowed before a course is closed; see the Faculty Teaching Load section.)

   2. Set a flag that declares the course closed, then do Step 6.
6. Getting here means that the choice of D-DF-TM cell has failed and that a new choice must be made. First increment the table(s) for failed course choices. Then make a new choice as follows:
   1. Go back to Step 1 and select a new TM.

   2. If the above fails because no TM is open for the D-DF cell, repeat the individual course choice procedure described in paragraph 6. Do the Step 3 first, then step 2 if 3 fails, etc.. If this is a required course and all steps fail, then convert the course to an elective. If no course for which the student qualifies is available, reduce the student’s course load: this represents an extreme situation which is not likely to occur.

The final modeling step aggregates course demand and supply for each department from students in each level and field of interest combination. Then it is a simple matter to aggregate over fields to produce total course demand for each department by students at each level. Figures for teaching load by faculty age/rank and prowess characteristics also can be provided.

6. Faculty Teaching Loads
1. Summer teaching

The course supply-demand model requires data on the availability of faculty for teaching during the summer. This consists of two elements: The first step is to determine what fraction of departmental enrollments will be taught in the summer trimester, and what fraction of these will be taught by regular faculty as part of their normal duties. The first figure comes from the course demand model, which breaks enrollments down by trimester. the fraction of summer enrollments to be taught by regular faculty within their normal duties, and the number of courses taught by faculty for extra pay during the summer. These are player-generated policies. Regular summer teaching is assumed to be offset with off-duty time during the fall or spring trimester. Therefore, this portion of summer enrollments can be lumped with the fall and spring enrollments for purposes of the course supply algorithm.

Higher Education treats enrollments not handled within normal duties as being "bought" on a per-course basis—either through extra pay for regular faculty or by bringing in outsiders. The extra-pay model is very simple: students realize their course-type preferences, class size equals the norm for the course type, and a department-specific unit cost is applied to the resulting course requirements.

2. Regular teaching

Each trimester, the faculty member’s normal teaching contact hours ("normal teaching load") is set equal the normal teaching load for his/her rank/age category, adjusted by the individual’s active sponsored research project dollars and a player-determined priority for academic year faculty salary offsets (see "Research Proposals and Projects," below).

Massy and Zemsky’s model of course supply focuses on the way departmental faculty make tradeoffs among class sizes, teaching loads, and their corresponding norms. Faculty are viewed as having well-developed views about reasonable class sizes for each course type and about what constitutes a normal and acceptable teaching load absent research buyouts or other special considerations. These views evolve over time as the result of experience and exogenous factors. The tendency for teaching load norms to decline over time, in response to pressures and special circumstances favoring research, has been enshrined with the name, "the academic ratchet."

Higher Education embodies the tradeoff idea. The model starts with data about normal class sizes and teaching load. For example, the normal class for history department undergraduate lecture courses might be 100 students. (Such courses often are limited only by the size of the available auditorium.) In contrast, the norm for undergraduate seminars and other courses might be 12 and 25, respectively. The teaching load norms will vary by faculty category. Adjuncts will teach more than tenure-line faculty, for example, and assistant professors may be expected to carry different loads than full professors. Research-oriented faculty also may enjoy advantageous teaching load norms in some departments, in order to spur research output and aid retention. The norms, which come originally from the game’s initial conditions, will evolve over time in response to player-generated policies and factors identified in the academic ratchet theory. Therefore, the course supply model’s first step is to update the norms.

The model also requires input about the relative importance of class size and teaching load in the faculty’s tradeoff calculus. The Massy-Zemsky research has documented that the tradeoff parameters are asymmetric, at least for class size. Overly large class sizes carry much larger penalties than those that are too small, whereas the teaching load penalties are almost linear. The penalties will depend on a combination of intrinsic and extrinsic incentives as discussed in Section 7.2.

The rank/age normal teaching load (NTL_i) and the faculty’s view about normal class size (NCS) will be adjusted each trimester as follows:

NTL_i,t = lS_i (NTL_i,t–1) + (1- l)NTL_i,t–1

and similarly for NCS. This is an exponentially weighted moving average, of the kind described in the Appendix except that the sum of the prior year’s NTLs is used instead of an externally-determined target value.

The Supply-Demand Balance procedure uses two constants, LIMIT1 and LIMIT2, to determine course availability and faculty staffing. WFM will define a single-equation function for determining LIMIT2, based on the Massy-Zemsky theory of faculty time tradeoffs. LIMIT1 = f (LIMIT2–1)+1, where f is a parameter between 0 and 1.

7. Faculty Discretionary Time

Most faculty enjoy substantial amounts of discretionary time—that is, hours in the workweek that are not scheduled for in-class student contact. How they use these hours goes a long way toward determining the mix of departmental outputs and the various dimensions of departmental performance. Higher Education models the allocation of tenure-line faculty discretionary time for each simulated faculty entity , department by department, in sufficient detail to capture the most important of these effects.

1. Discretionary time categories

The model recognizes six discretionary time categories. It allocates time so as to minimize the deviations from certain norms, which are described in conjunction with the category definitions.

• Course preparation: time spent preparing for courses the person is teaching during the current academic term. The norm is proportional to the number and type of sections being taught.
• Out-of-class student contact: time spent with students outside of class; includes office hours and drop-in visits by students in current courses, sessions with advisees, and any other information or mentoring meetings. The norm combines a fixed number of hours for advising and mentoring with a term proportional to the number of students in current courses.
• Educational development: time spent in curricular and course development, including the development of non-traditional delivery methods. The norm is based on player-generated policy variables.
• Research: time spent on sponsored and departmental (unsponsored) research. The norm combines a fixed number of hours representing the scholarly effort expected of all faculty with a term proportional to sponsored research volume.
• [This category may be deleted to simplify the model.] Institutional and public service: time spent on institutional governance, public service, and similar activities. The norm will depend on player-generated policy variables.

In addition to the above, Higher Education defines excess work as the total time spent on departmental activities over an exogenously-determined "normal work week." The normal work week may vary by department and faculty category. Total time spent on departmental activities is the sum of the discretionary time commitments plus the time required for in-class student contact.

2. Incentives

Faculty respond to incentives and prioritize their time commitments accordingly. Incentives include penalties for failing to meet time norms and rewards for exceeding them. The model also assesses a penalty for excess work hours. The rewards and penalties may vary by department and faculty category.

The model allows for two kinds of incentives: intrinsic and extrinsic. It will combine the two to produce blended figures for use by the course supply and discretionary time allocation algorithms.

Intrinsic incentives come packaged with faculty categories. Teaching-oriented faculty will have different incentives than research-oriented ones, for example, and assistant professors may differ from full professors. Within each category, it may prove desirable to allow the intrinsic incentive mix to vary with the teaching and research quality indices.

Extrinsic incentives stem from player-generated policies. The interface design will provide opportunities for players to describe policies that favor course preparation, student contact, educational development, research, or institutional service. Examples include statements about the criteria for gaining tenure and salary increases, serious use of teaching ratings, and the volume of sponsored research awards expected from faculty in different categories. Some policies will be promulgated at the departmental level and some at the institutional level.

3. Discretionary time allocations

The time allocation algorithm uses quadratic programming to minimize the weighted sum of squared deviations from the aforementioned discretionary time targets. There are six decision variables: hours allocated to each discretionary time category plus excess work hours. The model treats positive and negative deviations asymmetrically. The blended incentive coefficients are used as weights. The constraints consist of identities that define total hours and the deviations from the norms.

The model allocates discretionary time separately for each faculty sim. As usual, the results can be phased in by means of exponential smoothing. The resulting figures can be used to produce reports that may prove especially interesting for advanced players. Aggregating over faculty categories produces the total number of hours applied to each discretionary task by all faculty in the department, which is a key input for the departmental performance models.

8. Sponsored Research

Some institutions depend on externally-sponsored research to fund prestige-generating activities and contribute to fixed costs. Faculty submit proposals for work they would like to perform and learn sometime later whether the proposals are successful. The market for sponsored research funding is highly competitive, and usually only a small fraction of submitted proposals result in awards.

Simulated faculty members submit proposals for sponsored research projects, and some but by no means all proposals get funded. The faculty database will allow, say, 5 proposals/projects to be active at any one time for a given faculty member.

Proposals may be submitted at any time. The probability of submitting a proposal and the size and duration of the proposed project depend on the player’s research volume expectation, the faculty member’s research prowessquality index, and the amount of discretionary time he/she devotes d to research for the faculty category, plus the total number and value of extant proposals and projects.

Whether the proposal will be accepted and the date when the faculty member will be notified as to success ("decision date") will be generated as part of the proposal-creation procedure. Gestation time on proposals will be approximately six months, but may be adjusted randomly and/or for programming convenience.

The fate of each proposal will be determined randomly with probability equal to the proposal success rate. Proposal success rates depend on competitive market as well as internal information. Examples of competitive market information include average sponsored research volume per faculty FTE, the indirect cost rate, and the proposal success rates. These data will be generated for each institutional segment and stored in the game’s database. The research volume and proposal success rates can be department-specific, but they will not vary by faculty category because no breakdown by category will be available for the peer institutions. The market data may be made to vary over time in response to exogenous factors. Internal information includes the player-generated indirect cost rate, the faculty research quality index, the department’s prestige (which represents its past research record), and the level of institutional support for research infrastructure.

The model determines proposal success rates for each department and faculty category by applying Higher Education’s standard s-shaped response function to adjust the overall market success rate to reflect the aforementioned internal variables. Whether the response function output will be phased in through exponential smoothing remains to be seen. Eachseen. research proposal will succeed or fail as the result of a random process with probability equal to the proposal success rate. Research awards are produced by multiplying the resulting figures by the proposal volume for the department and faculty category, and summing over categories produces departmental awards. The departmental awards will be spent during the following year. They will enter expenditure reports and influence the discretionary time norms at that time.

Successful proposals will be converted to active projects on the decision date, at which time the date field will be converted to the project ending date (decision date plus duration). Unsuccessful proposals will be purged on the decision date. Active projects will be purged on their expiration date. The faculty member’s total monthly expenditures on sponsored research projects (dollar value of each active project divided by its duration, summed over active projects) should be updated whenever a change of project status occurs.

Two research expenditure priority parameters affect the utilization of monthly expenditures. Both can be represented as numerical scales which may be adjusted by the player.

• priority for academic year faculty salary offsets: larger values decrease the faculty member’s teaching load and increase the sum fed into the "AY Fac comp" column of the "sponsored research" row in Table 2 of TD 2.3.
• priority for doctoral research assistant stipends: larger values increase the sum available for doctoral student financial aid (to be described in a forthcoming revision of TD 2.1).

Logistic response functions will be defined for each of the aforementioned variables. Each function will depend on both priority parameters and on the faculty member’s total monthly expenditures.

9. Departmental Performance

There can be no single measure of departmental performance. Instead, Higher Education will offer multiple measures. Each of them can be viewed as summarizing the results of the preceding academic models in a different way. The measures generally will be weighted averages of the underlying variables, but certain interaction possibilities are noted. Because some measures share the same variable sets, albeit with different coefficients, the correlations among them will be high.

The simulation engine offers more potential performance indices than are likely to be accommodated in the game design, so the final list cannot be determined at this point. It also is too soon to finalize the driver variables. Nevertheless, we can be confident that the indices given below are likely to appear in some form. Many previously-defined variables also will qualify as performance indicators. Institution-level performance indices, some new and some aggregations of departmental indicators, will be determined in due course.

• Faculty publications: depends on faculty numbers and the associated research quality indices, sponsored research volume, discretionary time allocated to research, and research infrastructure.
• Departmental academic standingprestige: depends on faculty publications, average faculty researchquality (probably in both teaching and research), academic ability rating of departmental doctoraldocatoral admits, if any, and sponsored research volume.
• Technology utilization in teaching: depends on investments in technology and faculty time allocated to educational development. The technology utilization variable applies to both on-campus and distance courses. Heavy utilization implies advanced delivery methods appropriate to the course type.
• Educational quality (the delivered quality of education): depends on the course type mix and class sizes in relation to their norms, any course supply shortfalls, the curricular structure index, technology utilization factors, the faculty teaching and research quality indices, and faculty discretionary time devoted to course preparation, out-of-class student contact, and educational development.
• Faculty morale: depends on teaching loads, class sizes, and discretionary time allocations in relation to their norms, technology utilization in teaching, salary levels relative to the competition, turnover rates, academic ability rating for the department’s masters and doctoral students; and various player-generated policies that affect faculty. Heavy technology utilization may mitigate negative effects from excess class sizes and teaching loads.
• Student morale: depends on the delivered quality of education, any course supply shortfalls, technology utilization, and faculty discretionary time devoted to out-of-class contact.

The values of these and any additional indices will be available for reporting at the departmental level. Some will trigger events like newspaper articles and e-mails. Some will influence academic operations during the following year, as described earlier. Some may influence resource allocation and institution-level performance during the current year. Some will influence student applications and yields the following year. Finally, some will enter the player’s scorecard and trustee evaluations.

Appendix: Response Functions

General response functions

Purpose: to transform a list of input variables into a single output variable, as in graduationProbability =f[intDept performance, student academic rating]. These functions are used throughout the program to update parameters, determine the results of budget allocations, etc.

Approach: an s-shaped curve or the sum of two s-shaped curves (‘logistic functions’). The s-shaped curve is easy to compute and provides limits on the degree of variation of the output variable.

Method 0: basic logistic function used in both subsequent methods. The mathematical expression is:

(Eq A.1)

where v is the input variable and m the norm for the input (v and m are usually lists of variables).

Method 1: single logistic with ceiling and floor, used when the output variable is a simple "s," with maximum slope midway between the extremes.

respF[ceiling, floor, m, v]; floor = 0, ceiling = 1, and m = 0:



Method 2: dual logistic, used when the output variable does not necessarily have maximum slope midway between the extremes —e.g., where there is a range of relative insensitivity around the middle of the curve.

respF[ceiling, floor, base, m1, m2 , v]; floor = 0, ceiling = 1, and m = 0:



Exponential smoothing

Purpose: to introduce response lags so that a change in a policy or other variable take effect over a number of periods.

Method: uses a ‘distributed lag model,’ also known as ‘exponential smoothing.’ Let y_t be the variable to be smoothed, x_t the driver variable(s), and z [x_t] the long-run value of y after the effects of x_t have fully worked themselves into the system. Then:

(Eq A.2)

where the smoothing parameter, l , must be between 0 and 1. This will be denoted by:

(Eq A.3) ExpSm[z(x)]