Direct Reciprocity in Games of Choice

Abstract

How does cooperation evolve in a population of self-interested agents? One of the primary mechanisms is through direct reciprocity, which occurs when individuals choose to cooperate because they expect to be rewarded with cooperation in return. Prior work has mainly analyzed direct reciprocity through the lens of the iterated Prisoner's Dilemma (IPD). However, the iterated Prisoner's Dilemma is a simplification of real-world cooperation because participants always face the same payoff structure in every encounter. In the real world, participants exert some control over the reward structure of their interactions: that is the motivation behind gaining trust and investing in deeper relationships. In order to capture the ability of future interactions to become more (or less) rewarding, I extend the IPD into a new model, games of choice. A game of choice is a stochastic game wherein the players directly choose between two Prisoner's Dilemma (PD) stage games each round. In a game-of-choice, each player specifies his preferred PD stage game, and a pre-specified resolution rule decides which stage game is played. Cooperating provides a larger benefit to one's co-player in one stage game than in the other. In this thesis, I explore how different resolution rules and strategy spaces affect cooperation rates in games-of-choice, determine the stability condition under which reciprocal strategies become subgame-perfect equilibria (SPE), and interpret the mechanism promoting direct reciprocity. I find that games of choice tangibly promote cooperation: cooperative SPE can exist in a game-of-choice between two PD stage games even when cooperative SPE do not exist in an IPD of either stage game alone. I discover that a single mechanism underlies all cooperative SPE strategies in the two most effective resolution rules. This fundamental mechanism stipulates that the only route back to mutual cooperation in the more-rewarding stage game is through mutual cooperation in the less-rewarding stage game. Requiring time to be spent in the less-rewarding game stabilizes cooperation by imposing an increased opportunity cost on defection. As a result of this work, we gain insight into the way that concepts such as "investing in deeper relationships" may manifest themselves in strategies and change the cost/benefit calculus of self-interested agents.