General structure of a class of resource allocation games

In this paper, we study a class of games that are generalizations of the minority game, and model, more generally, systems in which agents compete for a scarce resource. In particular, we study a set of games in which the demand and supply of the resource are specified independently. This allows us to study the ways in which such systems behave as the resource becomes increasingly scarce or increasingly abundant relative to demand. We find an intricate and rich structure to these games with a number of very intriguing features. Among these is the existence of a robust phase change with a coexistence region as the demand/supply ratio is varied, and the games move from scarce to abundant resources. This coexistence region exists when the amount of information used by the agents to make their choices greater than a certain level, which is related to the point at which there is a phase transition in the standard minority game. We also discuss practical and theoretical implications of our work.