Spatiotemporal dynamics of cooperation and spite behavior by conformist transmission

Joe Yuichiro Wakano

doi:10.3934/cpaa.2012.11.375

Article Contents

2012, Volume 11, Issue 1: 375-386. Doi: 10.3934/cpaa.2012.11.375

This issue Previous Article On the solvability conditions for the diffusion equation with convection terms Next Article Appearance of anomalous singularities in a semilinear parabolic equation

Spatiotemporal dynamics of cooperation and spite behavior by conformist transmission

Joe Yuichiro Wakano^1,

1.
Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 1-1-1 Higashi Mita, Tama-ku, Kawasaki, Kanagawa 214-8571

Received: December 2009

Revised: August 2010

Published: January 2012

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Abstract

In this paper, we propose a model describing the dynamics of human society. Then we show that classic theorems on traveling wave solutions in a reaction diffusion equation can be readily applied and we obtain some mathematical result. Our model considers a human society where people play a two-strategy multi-player game. The key concepts are 1) payoff-dependent update rule of strategy and 2) social learning with conformism. Because of conformism, the system can be bistable and our primary concern is whether one global majority appears or not when multiple societies that initially have different local majorities are spatially connected. Applying the result of this general framework to a public goods game example, we show that cooperation is less likely maintained by conformism and that the spread of irrational spite behavior can occur.

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Mathematics Subject Classification: Primary: 35Q91, 35Q92.

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