Evolutionary Stability of Other-Regarding Preferences Under Complexity Costs

Abstract: The evolution of preferences that account for other agents' fitness, or other-regarding preferences, has been modeled with the "indirect approach" to evolutionary game theory. Under the indirect evolutionary approach, agents make decisions by optimizing a subjective utility function. Evolution may select for subjective preferences that differ from the fitness function, and in particular, subjective preferences for increasing or reducing other agents' fitness. However, indirect evolutionary models typically artificially restrict the space of strategies that agents might use (assuming that agents always play a Nash equilibrium under their subjective preferences), and dropping this restriction can undermine the finding that other-regarding preferences are selected for. Can the indirect evolutionary approach still be used to explain the apparent existence of other-regarding preferences, like altruism, in humans? We argue that it can, by accounting for the costs associated with the complexity of strategies, giving (to our knowledge) the first account of the relationship between strategy complexity and the evolution of preferences. Our model formalizes the intuition that agents face tradeoffs between the cognitive costs of strategies and how well they interpolate across contexts. For a single game, these complexity costs lead to selection for a simple fixed-action strategy, but across games, when there is a sufficiently large cost to a strategy's number of context-specific parameters, a strategy of maximizing subjective (other-regarding) utility is stable again. Overall, our analysis provides a more nuanced picture of when other-regarding preferences will evolve.