Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness

Johannes G. Reiter,Martin A. Nowak,Christian Hilbe,Krishnendu Chatterjee,David G. Rand

doi:10.1038/s41467-017-02721-8

Abstract

Direct reciprocity is a mechanism for cooperation among humans. Many of our daily interactions are repeated. We interact repeatedly with our family, friends, colleagues, members of the local and even global community. In the theory of repeated games, it is a tacit assumption that the various games that a person plays simultaneously have no effect on each other. Here we introduce a general framework that allows us to analyze “crosstalk” between a player’s concurrent games. In the presence of crosstalk, the action a person experiences in one game can alter the person’s decision in another. We find that crosstalk impedes the maintenance of cooperation and requires stronger levels of forgiveness. The magnitude of the effect depends on the population structure. In more densely connected social groups, crosstalk has a stronger effect. A harsh retaliator, such as Tit-for-Tat, is unable to counteract crosstalk. The crosstalk framework provides a unified interpretation of direct and upstream reciprocity in the context of repeated games.

Highlights

Direct reciprocity is a mechanism for cooperation among humans
We do not need to specify the particular psychological process at work: the resulting behavioral dynamics are independent of whether crosstalk is the result of a conscious decision, or the consequence of a subconscious error
Comparing the effect of different population structures, we find that a Generous Tit-for-Tat10 (GTFT) population can maintain cooperation more if players are arranged on a circle instead of a complete graph (Fig. 3a, b, Supplementary Fig. 5)

Summary

Introduction

Direct reciprocity is a mechanism for cooperation among humans. Many of our daily interactions are repeated. Cooperation is normally opposed by natural selection unless mechanisms for the evolution of cooperation are in place[3] One such mechanism is direct reciprocity, which is based on repeated interactions between the same two players[4,5]. Most previous models of direct reciprocity (with a few notable exceptions27–30) have either assumed that (i) individuals only engage in one repeated game at a time or that (ii) an individual’s action in one game is independent of all its other interactions. We do not need to specify the particular psychological process at work: the resulting behavioral dynamics are independent of whether crosstalk is the result of a conscious decision (as in upstream reciprocity), or the consequence of a subconscious error (as when individuals confuse the past actions of their co-players).

Objectives

Methods

Results

Conclusion