Capacitated Caching Games

Capacitated Caching (CC) Games are motivated by P2P and web caching applications, and involve nodes on a network making strategic choices regarding the content to replicate in their caches. Caching games were introduced by Chun et al (PODC 2004), who analyzed the uncapacitated case leaving the capacitated version as an open direction. In this work, we study pure Nash equilibria of both fractional (FCC) and integral (ICC) versions of CC games. Using erasure codes we present a compelling realization of FCC games in content distribution. We show that every FCC game instance possesses an equilibrium. We also show, however, that finding an equilibrium in an FCC game is PPAD-complete. For ICC games we delineate the boundary between intractability and effective computability in terms of the network structure, object preferences, and the total number of objects. A central result of this paper is the existence (and poly-time computability) of equilibria for hierarchical networks. Using a potential function argument, we also show the existence of equilibria for general undirected networks when object preferences are binary. For general ICC games, however, equilibria may not exist. In fact, we show that it is NP-hard to determine whether equilibria exist, even when either the network is undirected and there are only three objects in the system, or the network is arbitrary and there are only two objects in the system. Finally, we show that the existence of equilibria in strongly connected networks with two objects and binary object preferences can be determined in polynomial time, via a reduction to the even-cycle problem. A significant feature of our work is the development of the above results in a general framework of natural preference orders, orders that are entirely arbitrary except for two benign constraints - "Nearer is better" and "Irrelevance of alternatives".