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:

This paper describes the model that simulates enrollment management. 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.

The enrollment management model is the first model that the simulation engine runs after it sets initial defaults and after the player sets initial policies and parameters that specify the type of institution he or she desires to "lead" for the current game session. The model analyzes data and generates output for three phases of the enrollment process: application submissions, admission offers, and matriculation decisions. The results then inform the next model in the engine sequence, academic operations. The enrollment management model is run once before each new round or "academic year" as the game progresses in order to generate an appropriate mix of new students for the player-created institution.

Using both empirical data stored in Higher Education’s permanent database and preference functions informed from real life, the enrollment management model first determines the number of prospective student applications for the universe of all existing institutions and breaks down the results by institutional market segment, student market segment and subsegment, and student level. Then, it compares the parameters and policies of the player-created institution to institutional norms across market segments and calculates the number of applications for the player-generated institution based on market segment similarities. Next the model simulates the institutional decision-making process that determines which students will be offered admission. Admission decisions are generated for both the universe of institutions and for the player-created institution based on parameters and policies previously established by the player. Finally, the model simulates the behavior of accepted prospective students in deciding where to matriculate and calculates appropriate yields for the universe and for the player’s institution.

The model consists of two elements: one for the player-generated institution’s applications, admissions, and matriculations (local demand), and one that computes the same quantities for all institutions (primary demand). The local demand model will be included in the game’s simulation engine, whereas the primary demand model will be run before the game is released and used to populate the simulation engine database.

Since prospective students can apply to any number of different institutions in real life and receive more than one admissions offer, the model simulates a marketplace of multiple institutions, not just the player- created institution. The institutional market has been segmented by the University of Pennsylvania’s Institute for Research on Higher Education (IRHE) at the as part of their work on market taxonomy for the National Center for Postsecondary Improvement.

As a first step, IRHE developed the following segmentation criteria:

• Admit and yield rates, reflecting the aggregate demand for an institution’s undergraduate education.
• Percentage of freshmen who graduate with a BA/BS in five years, reflecting the degree to which the educational experience provided by the institution is seen primarily as a period of continuous, full-time enrollment.
• Percentage of undergraduate enrollment that is part-time, reflecting to which the institution accommodates students who have substantial commitments outside their pursuit of postsecondary education.
• Ratio of number of BA/BS degrees awarded to total undergraduate enrollment, reflecting the degree to which the institution serves the one-course-at-a-time or "spot" market for postsecondary education.

The next step was to was to develop a decision rule, based on the four variables, to assign each of the 1,200 sample institutions to market segments. Seven institutional segments were identified, as follows:

These Segments will be used to establish the game’s competitive environment.

The first three segments represent the name brand part of the market. These selective institutions conform to the idea of a traditional four- or five-year baccalaureate career—often with a liberal arts emphasis and often leading up to graduate or professional studies. Schools in the top two segments provide their students with a kind of medallion, representing some combination of quality and scarcity value, which is especially useful for entry into graduate school. The small set of highly selective, very competitive institutions in Segment 1 confer a particularly valuable super medallion.

Segments 4 and 5 represent the core of the market, where some students seek name brand experiences while others pursue their education on a part-time or intermittent basis. Schools in Segment 4 tilt toward the left while those in Segment 5 tilt toward the right, but both types must serve the traditional and nontraditional market simultaneously.

The last two segments represent the convenience/user friendly part of the market. These institutions serve large numbers of part-time and intermittent students who may or may not be seeking a degree. The super-convenient schools in Segment 7 cater to these students with special intensity.

Prospective students will be sorted into the following student market segments (appropriate definitions need to be derived from the IRHE-supplied data):

• Blue Chip: students with top academic and extracurricular qualifications
• Scholar: students with top academic qualifications
• Extracurricular: students with top extracurricular qualifications
• Athlete: students with top athletic qualifications
• Balanced: students with respectable academic and extracurricular qualifications
• Average: students with unremarkable academic, extracurricular, and athletic qualifications
• Stretch: students for which college represents a "stretch" goal because of shortfalls in ability or preparation

Students will be further sorted by gender and minority status (using EEOC qualifiers) to create the following student market subsegments:

• nonminority males
• minority males
• nonminority females
• minority females

Student market segments and subsegments in the enrollment management model will be cross-categorized by student level as follows:

• undergraduate: traditional degree-seeking
• undergraduate: nontraditional degree-seeking
• graduate: masters and professional (abbreviated "masters")
• graduate: doctoral
• non-matriculated

Traditional undergraduates are full-time, 18- to 22-year-old students seeking bachelors degrees.

Nontraditional undergraduates are part-time, nonresidential, often older students seeking bachelors degrees.

Masters and professional graduate students are those seeking admission into MBA, JD, and terminal masters programs (excluding students who earn masters degrees en route to or in lieu of doctorates). Medical degrees are not included as a medical school is beyond the scope of Higher Education’s simulation.

Doctoral graduate students are those in doctoral programs leading to the PhD, DBA, etc.

Non-matriculated students are those who take courses on an individual basis and are not seeking a degree.

The primary demand model has been constructed and tested with hypothetical data. As stated above, this model will not be part of the game’s simulation engine but rather will provide the data needed to populate the enrollment management model’s primary demand applications database. We describe the model here for completeness, because the procedure should be considered as part of the game’s underlying theoretical structure, and in order to specify the tables to be passed to the game’s database. A detailed description can be found in "Higher Education Technical Note 2.1: Enrollment Management Models."

Suppose a prospective undergraduate student has decided to submit applications to a certain number of institutions. How many applications will go to schools that are easy to get into? How many to more selective schools?

The applications part of the enrollment management model simulates the way students go about answering these questions. The modeling task was to allocate applications across the institutional segments. The primary demand applications model simulates what we believe to be a reasonable representation of actual behavior by using a student preference function. For each student market segment and subsegment, the student preference function calculates an index number that rates preference for a given institutional segment. The index is derived from weights the given student segment assigns to variables representing institutional characteristics such as the cost of attendance (tuition, and room and board where applicable), financial aid policies, school prestige, educational quality, admissions staff performance, and advertising. Different student market segments will weight the various institutional characteristics differently and decisions by students in all segments will be subject to the requirement that the cumulative probability of getting admitted somewhere exceeds a minimum threshold

The model assumes that the number of applications per student is determined exogenously, i.e., outside the model. This number may differ for different student segments and subsegments, and may vary over time. The number of applications per student to a given institutional segment multiplied by the number of prospective students in each market segment and subsegment equals the total number of applications each institutional segment receives.

The primary demand model for student applications will populate Table 1, which will be included in the game’s database:

The table is read row by row. For example, the first row shows that, on average, white male applicants who qualify for blue chip status submit 3.3 applications to segment-1 institutions, 2.1 to segment-2 institutions, and so on, for an average of 7.3 applications per student overall. These data will provide the initial conditions for generating the profile of applications for the player-generated institution. The figures may be adjusted as the game progresses to simulate the effect of exogenous factors.

Table 2 illustrates a second table that will be passed in the game’s database. It provides the institutional characteristics used by the primary demand model to calculate the applications for each student segment, and by the game’s engine to compare the player-generated institution with the primary demand segments.

The variable definitions follow:

• Institutional Prestige (prestige): depends on academic and support service inputs, research performance, and education quality. One might imagine something like the U.S. News and World Report index when thinking about this variable.
• Educational value added (eduVA): the actual delivered quality of education without regard to institutional prestige. Depends on the amount and distribution of faculty effort as well as the levels and quality of inputs.
• Student life (stuLife): the quality of student life outside the classroom. Depends on student residence, recreational, and academic facility quality, sums invested in student services, and similar variables.
• Athletic reputation (athRep): the school’s reputation for intercollegiate athletic prowess. Depends on the quality of athletes admitted, athletic facilities, and the sums expended on intercollegiate athletics.
• Institutional size (size): the relative size of the school (small is considered better); currently modeled as an inverse function of the sum of avePlaces over all student levels.
• Total cost of attendance (grossCost): for traditional undergraduates, the total outlays for tuition, room & board, and incidentals required for an undergraduate; for all other students the cost of tuition and incidentals.
• Percent of students receiving institutional financial aid (__FinAidPct): the fraction of students receiving need-based, merit-based, or athletics financial aid. Depends on the school’s financial aid policies and the attributes of the students who matriculate. (Financial aid is described further in connection with the admissions offers model.) The model will provide separate figures for traditional undergraduates, nontraditional undergraduates, and masters students. All doctoral students are assumed to receive aid.
• Average institutional aid award for students receiving aid (___FinAidAwd): the average aid award expressed as a fraction of the total cost of attendance; follows the same structure as finAidPct.

For example, Segment-1 institutions are assumed to score 10 on a 0.1-1 scale with respect to prestige, 0.9 with respect to educational value added, and so on. (The size index indicates that Segment-1 institutions tend to be larger than those in, say, Segment 2.) Segment-1 institutions have a gross cost of $25,000. They provide need-based aid to 60% of their traditional undergraduates with an average award of $8,000, merit-based aid to 10% with an average award of $4,000, and athletic scholarships to 6% with an average award of $25,000 (equal to gross cost).

Table 3 illustrates the third dataset passed from the primary demand applications model. It contains importance weights, as seen by students, for the institutional characteristics. The main body of the table provides the weights for traditional undergraduates (student level 1). The last three column refer to masters, nontraditional undergraduates, and non-matriculated students, respectively. Because these students care only about educational value added and cost, the tradeoff between the two can be described with a single figure. The weight is given for cost; that for value added is preset to one. Doctoral students are assumed to care only about institutional prestige, not cost (all are on full financial aid)—hence no importance weight is needed.

The primary demand model next simulates the institutional decision-making process involved in offering admission. How do colleges and universities decide which of the applications they receive will be accepted? The algorithm is used in the simulation engine’s local demand model as well as in the primary demand model. Because this procedure is central to the game’s enrollment management function, it will be described in the section on the player-created institution.

The model also can differentiate between setting a "need-blind" admission policy that guarantees aid for all admitted students who qualify and a budget-constrained policy that limits financial aid expenditures to a fixed sum and adjusts admissions offers accordingly.

The primary demand admissions model calculates the number of admissions offers extended from institutions in each institutional segment to applicants in each student market segment and subsegment. The admission rate for each institution-student type combination can be determined by calculating the ratio of admission offers to application submissions. The model also calculates the prospective financial aid requirement based on each institutional segment’s financial aid policies, admissions profile, and prospective yield.

The primary demand admissions model will produce a replication of Table 4 for each student level. This table will be used only in the preparation of performance indicators. It is read column by column. For example, Segment 1 institutions accept 50% of the blue chip white males and 52% of the white females that apply. These data are used as an input to the primary demand matriculations model, and they should be included in the database for reporting purposes. (As in the case of the applications model, the

figures may be subject to adjustment by the game’s engine to simulate the effects of exogenous factors.)

Like the applications model, the admissions offers model passes an additional table (illustrated in Table 5) to the game’s database. This one is used by the simulation engine in doing its own admission calculations. The data may be modified by exogenous factors during play of the game. There is one such table for each student level.

The variable definitions are:

• academic rating (acadRating): the student’s academic potential, as measured by (say) the SAT or ACT and high school grades.
• extracurricular rating (extCurRating): the student’s high school extracurricular record, except for the record relevant to intercollegiate athletics.
• athletic potential (athRating): the student’s potential for becoming a star athlete in a sport relevant to a school’s athletic reputation.
• average income (income): the student’s parental or personal income as applicable for calculating financial aid based on need.

The figures represent averages over all the applicants in the student segment and subsegment.

The primary demand model again simulates student behavior in its final phase. How do prospective students decide where to matriculate given multiple offers of admissions? The model’s matriculation decisions component uses the same student preference function as defined earlier to determine the matriculation distribution across student segments and subsegments. However, the weights assigned to the institutional characteristics by students in the various student segments are likely to have changed at this stage of student decision making as a result of evolving sensitivities (e.g., heightened price sensitivity in the face of impending matriculation). Therefore, a new set of index ratings will likely be used.

Before matching matriculations to institutional segments based on student preference, the model must first transform the aggregate number of offers generated by the model’s admissions component into the average number of offers extended by each institutional segment to a given student in each student market segment/subsegment. It uses probability theory to determine the degree to which different institutions offer admission to the same students—both institutions within a single institutional segment and those from different segments. The model then accounts for these overlaps so that only one matriculation per student is possible. The maximum number of matriculations per institutional segment thus equals the number of students in each student market segment/subsegment times the average number of unduplicated offers per student from a given institutional segment.

For each institutional and student segment, the model ensures that the number of matriculations is dependent upon and does not exceed the number of total applications submitted. Yield rates and financial aid commitments can then be calculated for each institution-student type combination.

The primary demand matriculations model will produce Table 6 for each student level. Table 6 will be included in the game’s database. It is read row by row. For example, blue chip white males accept 60% of the offers they receive from Segment 1 institutions. These data are used by the game’s simulation engine to produce yield figures for the player-generated institution. As in the case of the applications model, the data may be subject to adjustment by the game’s engine to simulate the effects of exogenous factors.

As it would in real life, the institution that a player evolves during a given game session must operate within the context of a competitive marketplace that distributes prospective students with a variety of characteristics into matriculated students at a variety of colleges and universities. The connections between this simulated external student market and the player-created institution—and how the latter’s numbers of applications, admissions offers, and matriculations are determined—are described here.

To determine the number of applications the player’s institution receives, and subsequently its numbers of matriculants, the model compares the player institution’s attributes to those of the institutional segments used in the primary demand model. In effect, the model simulates how the player’s institution looks to prospective students—through their eyes, using their student preference function. If, for example, the institution resembles a "medallion," it can expect to draw applications from the same student market segments and subsegments and generate similar yield rates. The player’s degrees of freedom lie not in making the prospective students’ decisions for them but in setting and modifying policies that will change how his or her institution is perceived by prospective students.

The local demand models for applications and matriculations determine the player-created institution’s relative similarity to each institutional segment by comparing cost of attendance, financial aid, prestige, and the other performance values incorporated in the student preference functions. Weighted coefficients, positive numbers that sum to one, represent the degrees of similarity and are entered into a function that calculates the player institution’s application and yield rates as a weighted average of the application and yield rates of the institutional segments. The student preference functions differ by student market segment and subsegment so application and yield rates for the player institution also can be calculated on a segment-by-segment basis.

The admissions model uses an institutional preference function to spread player-created institutions offers of admission across student market segments and subsegments. The preference function calculates an index number that rates preference for a given student market segment and subsegment. The index is derived from player-defined importance weights for the variables representing student characteristics: the academic, extracurricular, and athletic ratings. In addition, information on the distribution over student market segments of a family’s ability to pay the cost of education will inform the model’s financial aid element. For example, blue chip students may be expected to have a larger average ability to pay than students in some of the lower segments and this may influence an institution’s decision to offer admission. (IRHE-collected data will be helpful in quantifying these relationships.)

Applying the preference function to the student characteristics data produces a desirability rating for each student market segment and subsegment. (When the model is applied in the primary demand calculations, colleges and universities in the various institutional segments will weight the various student characteristics differently.) The model seeks to maximize the desirability rating, subject to limits reflected in the numbers of applications received, financial aid policies, and the requirement that admission be offered to enough students to fill the entering class. The number of admissions offered will always exceed the targeted number of places in the entering class to compensate for those admittees that matriculate elsewhere. (The exact number will be dependent on historic yield rates.)

The player can consider race and gender targets as a part of his or her admissions policies. One may, for example, seek to maintain a certain percentage of minority representation in the incoming undergraduate class. Such percentages will not be treated as quotas but as targets that may or may not alter the results of the institutional preference function calculations as they are factored in.

The model allows for three kinds of institution-supplied financial aid:

• Need-based aid: depends on student (and parental) income in relation to cost. There is no need-based aid for other than traditional undergraduates.
• Merit-based aid: depends on one or more of the student attributes defined in connection with institution’s preference function. Merit aid can be given to traditional undergraduates, nontraditional undergraduates, and masters students. No aid of any kind is given to non-matriculated students (student level 5).
• Universal aid: given to all doctoral students.

Student loans and grant aid supplied by other entities are not modeled explicitly, though they can be considered as taken into account via the ability-to-pay and price sensitivity parameters.

Financial aid policies provided by the player include:

• for need-based aid, the fraction of calculated need to be supplied;
• for merit aid, threshold levels for academic, extracurricular, and athletic ratings required to get aid; the fixed amount to be supplied to students that meet each threshold; and the incremental amount of aid for rating point in excess of the threshold;
• for universal aid, the amount over and above cost of attendance to be supplied.

The player decides whether to spend whatever is needed to meet the aid policies given the matriculating class, or whether to adopt "admit-deny" policies for any given student level, segment, and subsegment when the aid budget has been exhausted. ("Admit-deny" means the student is admitted but denied aid even if he/she qualifies under the policy. If the decision is to cut off admissions, the player must also allocate the financial aid budget across student levels and types of aid.

The financial aid structure can handle a wide variety of financial aid arrangements. For example, Stanford’s policy of meeting 100% of calculated need would be represented by an income threshold determined as a function of total attendance cost, a zero fixed increment, and a 100% variable increment. All merit components except for athletics would be zero. Full-ride athletic scholarships would be represented by an appropriate threshold value on the athlete attribute, a fixed increment equal to the full-ride award, and a zero variable component. The components are independent and additive, so the player-created institution can offer a combination of aid components—which might apply to different students within a given segment-subgroup cell or be awarded cumulatively to the same students.

Table 7 illustrates the player-generated policies. For example, we assume this player prefers academic to extracurricular performance in the ratio of 10:7 and academic to athletic performance in the ratio 10:5. Minority students’ academic ratings will be boosted by 10% and their extracurricular ratings will be boosted by 5% before applying the weights. Females’ athletic ratings will be boosted by 15% (the college is trying to build up female sports). Financial aid policies call for 80% of need to be met (this applies to traditional undergraduates only), with no special treatment for minorities.

Merit aid is provided to traditional undergraduates whose academic rating exceeds 9, extracurricular rating exceeds 10.5, and athletic rating exceeds 11. One may recall from Table 1 that the average extracurricular rating for Blue Chip students equals 10. How, then, can any student’s rating exceed 10? The answer is that the model considers each student segment and

The enrollment management algorithms provide a rich array of potential player reports. These will be especially valuable if CyberCampus ever includes a specialized player model dealing with enrollment management.

The reports can depict not only the admissions numbers themselves but all antecedent calculations as well: for example, yield rates, admissions offers and admission rates, and numbers of applications. They can provide information for CyberCampus, for the new-student market as a whole, and for the various institutional segments within it. They can isolate student levels, segments, and subsegments in any combination.

Building CyberCampus’s intake numbers from a set of underlying behavioral algorithms were run off-line to produce primary demand data, and using the segment/subsegment structure described herein, provides important additional benefits. First, we assure that the micro data elements will move independently of one another: for example, that the various disaggregated reports relate to one another in ways that do not seem artificial. At the same time, the disaggregative data will be consistent with one another, and with the exogenous variables, because they have been derived from a common set of structural algorithms. Finally, because the structural algorithms operate independently with behaviorally meaningful inputs and outputs, they can be modified one at a time as our understanding of the student-market phenomena grows.