The science of game theory can be applied across a variety of domains and circumstances. Until fairly recently, game theory has been relegated to the auditoriums of elite universities, used during tabletop simulations for international affairs, and occasionally applied within global business strategy planning. Now the science and application of game theory is becoming more readily available.

### Background

According to Wikipedia, game theory is "the study of mathematical models of strategic interaction among rational decision-makers". Meaning, how are people likely to behave when they pursue incentives. It is "the science of logical decision making in humans, animals, and computers".

### Practical Application

An example of game theory put into practice is in the determination of roommate assignments for a freshman dormitory. Let's say there are 20 individuals, whom will be paired up and assigned to a room. Each roommate begins the process by answering some simple questions regarding their preferences:

- field of study?
- student-athlete?
- full load or part-time?
- up early or up late?
- orderly or messy?

An event is then hosted to allow everyone to meet each other. At the conclusion, each person ranks the 19 people from most favorite to least. All of the individuals' responses would then be collated. Done manually, this is an arduous task.. likely a "best effort" either involving a lengthy and tedious process, or resulting fairly arbitrary matches. Neither is necessary if game theory can be applied.

### Matching Process

By applying a matching algorithm using the qualitative and quantitative information provided by the 20 individuals, it is fully feasible to determine the optimal assignment of roommates. Each qualitative attribute is assigned a weight and a score; for example, field of study and student-athlete are worth 10 points each, and the other criteria are worth 5 points each. The ranking of each person is incorporated, to determine pairings such that there is "stability" in the assignments. That means that as the school year begins, no two individuals would determine that they are in fact a better match. They are effectively the "best possible" pairing. What would seem nearly impossible to calculate, is done easily.

Although the dorm roommates example is simplistic, there are many more complex scenarios that can be handled with two-sided (or even multi-sided) matching algorithms. With the availability of advanced computing and low-cost highly-scalable processing, the use of game theory in the "real world" will certainly grow by leaps and bounds.

Game theory draws from mathematics, operations research, and economics. The topic has been popularized by recent works including A Beautiful Mind, describing the life and work of John Nash in his development of the Nash Equilibrium and winning of the Nobel Prize.

### Reference Material

Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis is a seminal work in the field of game theory. Authors Alvin E. Roth and Marilda A. Oliveira Sotomayor delve into practical examples of how these powerful concepts can be applied to marriage, school systems, and medical internships.

When creating a game theoretic model, remember that it's important to consider whether the parties have complete (perfect) information. It's also important to understand the incentives to action. As outcomes are evaluated, it is possible to determine the stability of the proposed matches.

### Next steps

Volley Solutions believes in the power of game theory and two-sided matching to power the growth of organizations.

What use cases does your organization have for game theory?

How sophisticated is your organization's culture regarding decision optimization?

Whether simple or complex, our technology platform can help you decide better. Let's talk.

*Topics: matching, game theory*