We take a game-theoretic approach to analyzing the uncapacitated caching problem among networked selfish servers. We model the selfish caching problem as a non-cooperative game with n players (servers/nodes) whose strategies are sets of objects to cache. In the game, each server chooses a pure strategy that minimizes its cost. Our focus is to investigate the resulting configuration, which is the Nash equilibrium of the game. It should be emphasized that we consider only pure strategy Nash equilibria in this paper.
The cost model is an important part of the game. Let Ai be the set of feasible strategies for server i,and let Si ∈ Ai be the strategy chosen by server i. Given a strategy profile S =( S1,S2,...,Sn), the cost incurred by server i is defined as: