Capacitated Caching Games

Capacitated Caching (CC) Games are motivated by P2P and web caching applications, and involve nodeson a network making strategic choices regarding the content to replicate in their caches. Caching gameswere introduced by Chun et al [6], who analyzed the uncapacitated case leaving the capacitated version asan open direction.In this work, we study pure Nash equilibria of both fractional (FCC) and integral (ICC) versions ofCC 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 anequilibrium in an FCC game is PPAD-complete.For ICC games we delineate the boundary between intractability and effective computability in termsof the network structure, object preferences, and the total number of objects. A central result of this paperis the existence (and poly-time computability) of equilibria for hierarchical networks. Using a potentialfunction argument, we also show the existence of equilibria for general symmetric networks when objectpreferences are binary. For general ICC games, however, equilibria may not exist. In fact, we show that itis NP-hard to determine whether equilibria exist, even when either the network is symmetric and there areonly 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 binaryobject 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 ofnatural preference orders, orders that are entirely arbitrary except for two benign constraints “Nearer isbetter” and “Irrelevance of alternatives”. A novel aspect of our framework is that the results apply even tothe situation where different nodes have utility functions of completely different functional forms (e.g. onenode’s utility could depend on the sum of distances to the objects of interest whereas another’s could dependon the maximum distance).