Pure Nash Equilibrium in a Capacitated Selfish Resource Allocation Game

A resource allocation game with identical preferences is considered where each player, as a node of an undirected un-weighted network, tries to minimize his or her cost by caching an appropriate resource. Using a generalized ordinal potential function, a polynomial time algorithm is devised in order to obtain a pure-strategy Nash equilibrium (NE) when the number of resources is limited or the network has a high edge density with respect to the number of resources. Moreover, an algorithm to approximate any NE of the game over general networks is provided, and the results are extended to games with arbitrary cache sizes. Finally, a connection between graph coloring and the NE points has been established.