Evolution of Risk-Taking Behaviour and Status Preferences in Anti-coordination Games

This paper analyses how risk-taking behaviour and preferences over consumption rank can emerge when individuals have an incentive to coordinate their actions. Using an evolutionary game theory framework, it is shown that when ex-ante homogeneous individuals face a strategic interaction where they benefit from choosing distinct actions, i.e. an anti-coordination game, stable types must be willing to accept risky gambles over consumption to differentiate themselves. This is the case despite an assumed concavity of the objective function, which makes any gamble costly in expectation. Consumption differences act as a form of costly communication that allows for coordination. More specifically, it is shown that when individuals have access to any fair consumption lottery, there exists a neutrally stable equilibrium where individuals choose a risky lottery and condition their action in the anti-coordination game on relative consumption. Furthermore, the evolutionarily optimal risk-taking behaviour can be induced by preferences over consumption rank. This suggests status preferences might have evolved and are salient in settings where miscoordination is particularly detrimental.