Cooperation when wealth is a measure of reputation

Abstract

A wealth-based cooperation is studied in a regular lattice network with periodic boundary. A population with exponentially distributed initial wealth plays a Prisoner’s Dilemma game with their Neumann neighbors. We describe the cooperation norm as follows: The players do not have knowledge on their neighbors’ actions. Thus, a player defects against its neighbors with a probability proportional to the difference of its wealth and the wealth of its wealthiest neighbor. It is found that the average cooperator density is stable even when the temptation to defect is increased. However, when a fraction of the population play against the norm, the average cooperator density increases nonlinearly with the density of players playing against the norm. This suggests a system where poor cooperators are exploited by their wealthy defecting neighbors.