Evolutionary Dynamics of Resource Allocation in the Colonel Blotto Game

We provide an evolutionary game-theoretical formulation for a model of resource allocation—the Colonel Blotto game. In this game, two players with different total resources must entirely distribute them among a set of items. Each item is won by the player that assigned higher resources to it, and the payoff of each player is the total number of won items. Our evolutionary formulation makes it possible to obtain optimal strategies as the equilibrium states of a dynamical process. At the same time, it naturally requires considering a population of players—whose strategies evolve by imitation and random fluctuations—thus better approaching a realistic situation with many economic agents. Results show, in particular, how agents with low total resources manage to maximize their winnings in spite of their intrinsically disadvantageous condition.