Competing for Resources: on the Emergence of Property Rights

A game theory approach to the evolution of animal conflicts has shown that choosing an initial asymmetric feature, such as first come first served, to settle a contest is evolutionarily stable, as it avoids the costs of animal fights. In this context, we investigate the optimal strategies of a population of non-aggressive agents competing for multiple resources. Resources provide different payoffs and can only be exploited by one agent at a time. If an agent tries a resource that turns out to be occupied, it then looks for another resource, which has a cost. We show theoretically and numerically that this system admits two types of Nash equilibria. In an under-crowded system, resources are equally shared between agents; our reinforcement learning simulations find multiple optimal solutions, where agents each exploit different sets of resources but all earn the same average payoff. The average strategy of these agents matches with the theoretical mean-field solution. Over-crowded systems are instead conducive to the emergence of inequality; some agents can earn more than the others by establishing themselves as property owners of a medium-payoff resource. In the reinforcement learning simulations, such lucky agents emerge naturally from their random learning experience.