Political Science Instructors Should be Teaching Infinite Games Earlier
Unending Repeated Games Are Surely More Common than Portrayed
I recently wrote about the error of treating social sciences like physical sciences. The crux of the issue is that we understate how much society is a complex adaptive system (CAS) instead of a deterministic “Newtonian problem.” In a similar vein, there is another problem that plagues the social sciences, particularly political science. The field overemphasizes basic finite games, leaving little room for adaptation and self-organization. This isn’t just an issue of having more accurate predictive models. Games with the wrong setup can lead to wildly wrong conclusions. Introducing students to infinitely repeated games earlier is better suited for real-world applications, where discount factors, learning, and uncertain game endpoints are more important.
The dominance of single-shot models is best illustrated by the fact that virtually every student’s first exposure to game theory is the prisoner’s dilemma (PD). Of course, the PD is very important and the game has added to our understanding of issues as diverse as cartelization, arms races, oligopoly pricing and even carbon emissions and dating. It is a helpful model to understand instances where individual rationality doesn’t lead to group rationality. But it and other games should be taught in a different order.
The PD is portrayed as a singular event where each prisoner makes their decision in isolation simultaneously and then the game ends. In game theory, this model type is called a “one-shot” game. In introductions to game theory, students are more exposed to these types of games, such as soccer penalty kick game, matching pennies and stag-hare assurance game. This works for a literal introduction, but it’s problematic to extrapolate policy conclusions based on the story without a further foundation.
Skipping the foundation is a disservice because it primes thinking about one-and-done games. Only thinking in terms of one-offs is akin to a student in a statistics class thinking that there are no dependent events, only independent events. Yet, in elementary statistics, the difference between independent and dependent events is rightfully among the first concepts taught.
Political actors do not exist in a vacuum. They engage in extended strategic interactions. Single-shot games assume that players maximize immediate payoffs without considering future costs. Consider the PD in international diplomacy. A one-shot game predicts mutual defection. However, just taking a cursory look at the world, we know that state actors engage in at least some reciprocal cooperation, as anticipated future interactions incentivize reputation-sensitive strategies. Similarly, in legislative bargaining, long-term coalition-building depends on credibility and reputation.
Bad faith negotiations carry reputational risks and costs. And that’s the problem: These games rarely apply in political contexts, where strategic relationships unfold over time. A lying, dishonest legislator is likely to find it difficult to form alliances. But we’re misleading students into thinking that short-term maximization is the dominant strategy.
Students are briefed on the basic games and then taught repeating games, typically finitely repeated games, to illustrate the tit-for-tat and grim trigger strategies and backward induction. It is often not adequately communicated that finite and infinitely repeated games typically evolve differently.
In practice, it is likely better to think more in terms of infinitely repeated games than finitely repeated games. A player’s evaluation of the future is one of the most central aspects of cooperation or defection. Politicians facing an impending election might have a high discount rate, prioritizing short-term gains over long-term policy stability. Conversely, a Supreme Court justice, insulated from immediate electoral concerns, might have a lower discount rate, favoring decisions that yield deferred benefits.
Single-shot games ignore these variations entirely, whereas infinite games allow students to see how different discount rates produce distinct strategic outcomes. This is way more relevant than extraneous backward induction exercises in finitely repeated games.
What is more, an underlying assumption of finitely repeated games is that players possess some sort of knowledge about the game’s terminal point. In finitely repeated games, backward induction suggests that rational players will defect in the final round, unraveling cooperation in earlier rounds. Obviously, in the real world, this rarely occurs because individuals are often uncertain about when their last interaction will be. Political actors don’t really ever have perfect foresight, so it is understated that even when games are technically finite, uncertainty about the endpoint can cause players to have effectively infinite time horizons.
Instructors should teach the basics with repeated games to show how cooperation evolves to better prepare students. Discounting should be incorporated early to show the effect of time horizons, and these games should be applied to real-world case studies rather than overly abstracted versions of models. Single-shot games like PD, limited-stage games, etc, are useful simplifications, but they should not dominate early instruction. Political science pedagogy should prioritize moving up infinite games.
