On Derivation and Evolutionary Classification of Social Dilemma Games

Tadeusz Płatkowski

doi:10.1007/s13235-015-0174-y

Abstract

We propose an axiomatic derivation and a classification of multiperson social dilemma games. For the two-person symmetric games, the axiomatization leads to three types of the social dilemmas only: the Prisoner’s Dilemma (PD) game, the Chicken (Snowdrift) game and the Stag Hunt game. The popular multiperson games, such as for example the N-person PD, the Public Goods, the Tragedy of the Commons, the Volunteer’s Dilemma and the Assurance game, are included in the proposed frame. For general social dilemma games with arbitrary payoffs, their simple classification is proposed, based on the number of stable equilibria of the corresponding replicator dynamics.

Highlights

Social dilemmas describe situations in which selfish decisions by autonomous individuals jointly result in group inefficient outcomes
The definition of Liebrand extended the set of social dilemmas from the Prisoner’s Dilemma (PD) game, studied e.g., in the social sciences and in the evolutionary game theory as a paradigm for the evolution of cooperation, to other two-player games: the Chicken (Snowdrift) game and the Stag Hunt (Assurance) game
In the first part of the present paper, we propose an axiomatization of the social dilemmas for multiperson games, which embraces the most popular games, such as the Nperson PD, Public Good and Tragedy of the Commons, and, e.g., the Assurance game, the Volunteer’s Dilemma and their variants with a threshold

Summary

Introduction

Social dilemmas describe situations in which selfish decisions by autonomous individuals jointly result in group inefficient outcomes. The definition of Liebrand extended the set of social dilemmas from the PD game, studied e.g., in the social sciences and in the evolutionary game theory as a paradigm for the evolution of cooperation, to other two-player games: the Chicken (Snowdrift) game and the Stag Hunt (Assurance) game. These different types of social dilemmas can be characterized by a different level of “social tension.”. The paper ends with a discussion and suggestions of some directions of research

Multiplayer Social Dilemmas

Volunteer’s Dilemma

Axiomatization of Multiplayer Social Dilemmas

Two-Player Social Dilemmas

Classification of Social Dilemma Games

Discussion