Resource Allocation Games with Multiple Resource Classes

Abstract

We define and study a resource-allocation game, arising in Media on Demand (MoD) systems where users correspond to self-interested players who choose a MoD server. A server provides both storage and broadcasting needs. Accordingly, the user’s cost function encompasses both positive and negative congestion effects.

A system in our model consists of m identical servers and n users. Each user is associated with a type (class) and should be serviced by a single server. Each user generates one unit of load on the server it is assigned to. The load on the server constitutes one component of the user’s cost. In addition, the service requires an access to an additional resource whose activation-cost is equally shared by all the users of the same class that are assigned to the same server. In MoD systems, the bandwidth required for transmitting a certain media-file corresponds to one unit of load. The storage cost of a media-file on a server is shared by the users requiring its transmission that are serviced by the server.

We provide results with respect to equilibrium existence, computation, convergence and quality. We show that a pure Nash Equilibrium (NE) always exists and best-response dynamics converge in polynomial time. The equilibrium inefficiency is analyzed with respect to the objective of minimizing the maximal cost. We prove that the Price of Anarchy is bounded by m and by the size of the smallest class and that these bounds are tight and almost tight, respectively. For the Price of Stability we show an upper bound of 2, and a lower bound of $2- \frac{1}{m}$. The upper bound is proved by introducing an efficient 2-approximation algorithm for calculating a NE. For two servers we show a tight bound of $\frac{3}{2}$.

A brief-announcement introducing this work was presented in the 8th International Symposium on Algorithmic Game Theory (SAGT), 2015.