Outline
Develop the theoretical framework linking finitely and infinitely repeated normal form games (such as the prisoners’ dilemma), and validate it on a real-world-inspired strategic scenario.
Motivation
The Prisoner’s Dilemma is one of the most well-known models in game theory [1], capturing situations where individual incentives conflict with collective benefit. Its repeated version has been widely used to model strategic interactions in areas such as international diplomacy, environmental agreements, business competition, and public health policy.
A key theoretical insight in the context of infinitely repeated games is provided by the folk theorem [2], which states that under suitable conditions, a wide range of payoff profiles, including those that sustain cooperation, can be supported as Nash equilibria. In contrast, the finitely repeated Prisoner’s Dilemma presents a striking challenge: backward induction implies that the unique Nash equilibrium prescribes defection at every stage, ruling out the possibility of sustained cooperation. The disconnect between these two settings is not yet fully understood [3], and finding ways to encourage or sustain cooperation in the finitely repeated game could have valuable implications for real-world scenarios.
Milestones
-
M1 (Weeks 1-2): Conduct a literature review on normal-form games, repeated games, and finite-state automata [4] as strategy representations;
-
M2 (Weeks 3-9): Extend existing results from linear-quadratic games to general normal-form games by formalizing the required mathematical structures and proving key theoretical properties;
-
M3 (Weeks 9-12): Apply the developed framework to a representative real-world-inspired scenario (e.g., environmental agreement compliance or competitive market regulation) to illustrate how cooperation can be sustained in finitely repeated settings;
-
M4 (Weeks 12-14): Evaluate the results, compare them with existing approaches, and finalize the thesis.
Requirements
We are looking for motivated students with a strong background in mathematics and some knowledge in game theory. If you are interested, please send an email containing your BS and MS transcripts to [email protected] .
References (selection)
[1] Kuhn, Steven. “Prisoner’s dilemma.” (1997).
[2] Fudenberg, Drew, and Eric Maskin. “The folk theorem in repeated games with discounting or with incomplete information.” Econometrica 54.3 (1986): 533-554.
[3] Benoit, Jean-Pierre, and Vijay Krishna. “Finitely repeated games.” (1984).
[4] Kalai, Ehud, and William Stanford. “Finite rationality and interpersonal complexity in repeated games.” Econometrica: Journal of the Econometric Society (1988): 397-410.