The Value of Caring About the Future: A Study on the Folk Theorems

Abstract

In the world today, one has to cooperate in some capacity almost every day. However, cooperating is not always the most valuable thing to do for the individual and can be costly, so how can we sustain cooperation? Mathematically, one can model the interactions between people with repeated games, where cooperation is a possible strategy. In this thesis we try to answer if repeating a game helps in sustaining cooperation, which will lead us to the folk theorems. We start with the main folk theorem that tells us that one can construct Nash equilibrium strategies for any feasible payoff when the discount factor is large enough. We will also take a look at Friedman’s folk theorem, and after that the Fudenberg and Maskin theorem, which aim to prove the folk theorem for strategies that are subgame-perfect equilibria. This means we have a somewhat nuanced answer to our research question as all feasible and individually rational payoffs can be sustained via an equilibrium, also the less desirable. After this, we will discuss the results of Kandori where we let go of the idea that a repeated game is played with the same set of players every round and introduce random matched opponents. With this random matching one might think we lose the concept of reputation, but this is not the case, as we will see that deviating may lead to the ”contagion” of the game. Before we start with the folk theorems, this thesis will also introduce game theory itself where we will work our way up to repeated games and the one-shot deviation principle, after which we start with the folk theorems.