Resource pricing games on graphs: existence of Nash equilibria

In this letter, we consider a non-cooperative resource pricing game on a graph where sellers (i.e., players) set the prices for their own resources to maximize the payoffs and buyers migrate to seek the least expensive resources. We present a model for the resource pricing game and prove the existence of Nash equilibria on regular and hierarchical graphs. The results obtained are applicable to the study of market economies, social networks and computer networks where individuals trade resources in a spatially extended environment.