Cooperation between Emotional Players

Lina Andersson

doi:10.3390/g11040045

Abstract

This paper uses the framework of stochastic games to propose a model of emotions in repeated interactions. An emotional player can be in either a friendly, a neutral, or a hostile state of mind. The player transitions between the states of mind as a response to observed actions taken by the other player. The state of mind determines the player’s psychological payoff which together with a material payoff constitutes the player’s utility. In the friendly (hostile) state of mind the player has a positive (negative) concern for other players’ material payoffs. This paper shows how emotions can both facilitate and obstruct cooperation in a repeated prisoners’ dilemma game. In finitely repeated games a player who cares only for their own material payoffs can have an incentive to manipulate an emotional player into the friendly state of mind. In infinitely repeated games with two emotional players less patience is required to sustain cooperation. However, emotions can also obstruct cooperation if they make the players unwilling to punish each other, or if the players become hostile when punished.

Highlights

The multitude of repeated interactions in everyday life are often modeled as repeated games.a crucial assumption of a repeated game is that the stage game is identical for each period.This is a strong assumption even when the material consequences of the interaction remain the same.For one thing, emotions are likely both to be affected by the outcomes of earlier periods and to influence preferences
This paper has proposed a model of repeated interactions between players who react emotionally to the history of play, and who can become friendly if the other player cooperates, and hostile if the other player defects
A player in a friendly state of mind values the other player’s material payoff positively, and a player in a neutral state of mind only cares for own material payoffs

Summary

Introduction

The multitude of repeated interactions in everyday life are often modeled as repeated games. The model is applied to a repeated prisoners’ dilemma game form with fixed material payoffs, but where the players’ preferences over outcomes evolve with the history of play. Both the finite and the infinite interaction is studied. In the model proposed in this paper, the altruistic preferences are conditional on the players’ emotional state of mind, which is affected by the history of play. When the players’ preferences over own and other’s material payoffs depend on their current state of mind, the repeated interaction can be modeled as a stochastic game. A strategy profile is a subgame perfect equilibrium of the stochastic game if, for any ex post history h ∈ H , the continuation strategy profile σ |h is a Nash equilibrium of the continuation game

Analysis

The Finitely Repeated Interaction

The Infinitely Repeated Interaction

Grim Trigger

Mutual Minmax

Discussion