An Evolutionary Simulation of Probabilistic Decision-Making, Financial Aid, and Market Structure in Post-Secondary Higher Education

An Evolutionary Simulation of Probabilistic Decision-Making, Financial Aid, and Market Structure in Post-Secondary Higher Education

Griffin Vernor Drutchas and Péter Érdi

Kalamazoo College Center for Complex Systems

A computational agent-based model is proposed to study the effect of probabilistic decision-making on market efficiency, market structure, and student access to financial aid in an American post-secondary education admissions system. For applying students and educational institutions alike, uncertainty exists in the admissions process. Each student—or more generally, each education consumer—must make an informed guess whether a school can and will provide preferred education service at an acceptable price, with or without subsidy. Likewise, each institution—or education service firm—accepts qualified students knowing there is some chance they will attend a competing school, or that their attendance will require sufficient economic aid. Due to the uncertainty about other agents’ behavior in an admissions system or any economic market, well-defined deductive reasoning does not apply—a fact that limits logic and rationality and that an inductive model of boundedly rational of agent behavior takes into account (Arthur, 1994). Consequently, a combination of a behavioral rule Classifier System (CS) and Genetic Algorithm (GA) rule generator (see Holland, 1992) are used to model boundedly rational behavior in the market for post-secondary higher education.

The proposed admissions system model is built on a literature lineage of self-organizing evolutionary matching models of a market economy beginning with Vriend (1995), but following most closely the heterogenous agent generalization and education market application of the “Q-model” described in Ortmann, Slobodyan, and Nordberg (2003), and Ortmann and Slobodyan (2006). The Q-model’s multi-stage admissions process is modified here to more closely resemble an education market’s matching structure in three key dimensions: (1) price is determined endogenously, (2) students can be accepted to multiple schools, and (3) their attendance behavior is based on learned rules relating personal income and academic quality to likelihood of financial aid. This new choice (3) implies a separate stage in the matching model that is post-acceptance but pre-enrollment (see DesJardins, Ahlburg, and McCall, 2006). Also, to complement the new student choice stage, dynamic behavioral rules are modified and added in the student application stage and the university application evaluation stage. To ensure stable model calibration and tractability the CS and GA structure of Ortmann and Slobodyan (2006) is retained.

The resulting model allows systematic exploration of emergent global behavior resulting from locally interacting, heterogenous, and boundedly rational agents in three exercises. The first establishes the basic dynamics and asymptotic behavior of the addition of income and post-acceptance choice to the base equilibrium Q-model. Second, market behavior is examined independently in the presence of three opportunistic behavioral mutants: one offers merit aid, another offers need-based aid, and a third offers both. Finally, aid is offered market-wide and then with additional exogenous aid. The model results indicate that competitive pricing and partial tuition waiving offer greater mobility toward the top of a quality segment, and to a lesser extent, a higher probability of moving into a higher quality segment at the cost of short-term profits.

References

Arthur, W. B. (1994): “Inductive Reasoning and Bounded Rationality,” American Economic Review (Papers and Proceedings), 84(2), 406-11.

DesJardins, S.L., D. A. Ahlburg, and B. P. McCall (2006): “An Integrated Model of Application, Admission, Enrollment, and Financial Aid,” Journal of Higher Education, 77(3), 381-429.

Holland, J. H. (1992): Adaptation in Natural and Artificial Systems. An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence (2nd ed.). Cambridge, MA: MIT Press.

Ortmann, A., S. Slobodyan, and S. S. Nordberg (2003): “(The Evolution of) Post-Secondary Higher Education: A Computational Model and Experiments,” CERGE-EI Working Paper 208.

Ortmann, A. and S. Slobodyan (2006): “(The Evolution of) Post-Secondary Higher Education: A Computational Model and Experiments,” CERGE-EI Working Paper 335, under review for Economics of Education Review.

Vriend, N. J. (1995): “Self-Organization of Markets: An Example of a Computational Approach,” Computational Economics, 8, 205-31.