Player Capability and Locally Sub-Optimal Behavior in Strategic Games

Abstract

Game theory has a profound influence across many different disciplines, including economics, social science, logic, and computer science. Research in game theory has surfaced many interesting phenomena on how strategic players interact in various game settings. In this thesis, I consider two topics in game theory. The research in both topics surfaces and characterizes interesting phenomena of how strategic players interact in game theoretic settings.

The first topic is the emergence of locally suboptimal behavior in finitely repeated games. Locally suboptimal behavior refers to players playing suboptimally in some rounds of the repeated game (i.e., not maximizing their payoffs in those rounds) while maximizing their total payoffs in the whole repeated game. The emergence of locally suboptimal behavior reflects some fundamental psychological and social phenomena, such as delayed gratification, threats, and incentivized cooperation. The central research question in this part is when can locally suboptimal behavior arise from rational play in finitely repeated games. To this end, we prove the first sufficient and necessary condition that provides a complete mathematical characterization of when locally suboptimal behavior can arise for 2-player finitely repeated games. We also present an algorithm for the computational problem of, given an arbitrary game, deciding if locally suboptimal behavior can arise in the corresponding finitely repeated games. This addresses the practical side of the research question.

The second topic is the impact of player capability on game outcome. Varying player capabilities can significantly affect the outcomes of strategic games. Developing a comprehensive understanding of how different player capabilities affect the dynamics and overall outcomes of strategic games is therefore an important long-term research goal in the field. We propose a general framework for quantifying varying player capability and studying how different player capabilities affect game outcomes. We introduce a new game model based on network congestion games and study how player capabilities affect social welfare at Nash equilibria in this context. The results in this part surface an interesting phenomenon that in some situations, increasing player capabilities may deliver a worse overall outcome of the game. We characterize when such phenomena happen for the games we study.

We further extend the new game model introduced above with incomplete information on player capability and multi-round play. We establish (algorithmic) game theoretic properties in these extensions, regarding the existence of different types of equilibrium solutions and the complexity of finding equilibrium solutions. These extensions model aspects of interactions between strategic agents that lead to phenomena such as concealment and deception.