Interdependent Relationships in Game Theory: A Generalized Model

TL;DR

This paper introduces a comprehensive game theory model that incorporates relationships and beliefs among players, unifying cooperative, non-cooperative, and intermediate game types, with applications to classic game scenarios.

Contribution

It presents a novel generalized model of games based on relationships and beliefs, extending traditional game theory to include a wider range of interactions.

Findings

The model unifies cooperative and non-cooperative games.

Analysis of prisoners' dilemma and ultimatum game demonstrates the model's applicability.

Relationships influence players' strategies beyond material payoffs.

Abstract

A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships and supposed relationships between players. A relationship is a numerical value that denotes how one player cares for the payoffs of another player, while a supposed relationship is another numerical value that denotes a player's belief about the relationship between two players. The players choose their strategies by taking into consideration not only the material payoffs but also relationships and their change. Two games, a prisoners' dilemma and a repeated ultimatum game, are analyzed as examples of application of this model.