Demand Allocation Games: Integrating Discrete and Continuous Strategy Spaces

In this paper, we introduce a class of games which we term demand allocation games that combines the characteristics of finite games such as congestion games and continuous games such as cournot oligopolies. In a strategy profile each player may choose both an action out of a finite set and a non-negative demand out of a convex and compact interval. The utility of each player is assumed to depend solely on the action, the chosen demand, and the aggregated demand on the action chosen. We show that this general class of games possess a pure nash equilibrium whenever the players’ utility functions satisfy the assumptions negative externality, decreasing marginal returns and homogeneity. If one of the assumptions is violated, then a pure nash equilibrium may fail to exist. We demonstrate the applicability of our results by giving several concrete examples of games that fit into our model.