Statics and Dynamics of Selfish Interactions in Distributed Service Systems

Abstract

We study a class of games which models the competition among agents to access some service provided by distributed service units and which exhibits congestion and frustration phenomena when service units have limited capacity. We propose a technique, based on the cavity method of statistical physics, to characterize the full spectrum of Nash equilibria of the game. The analysis reveals a large variety of equilibria, with very different statistical properties. Natural selfish dynamics, such as best-response, usually tend to large-utility equilibria, even though those of smaller utility are exponentially more numerous. Interestingly, the latter actually can be reached by selecting the initial conditions of the best-response dynamics close to the saturation limit of the service unit capacities. We also study a more realistic stochastic variant of the game by means of a simple and effective approximation of the average over the random parameters, showing that the properties of the average-case Nash equilibria are qualitatively similar to the deterministic ones.

Futility of being selfish in optimized traffic

“…Second, we generalized the cavity method, originally developed for analyzing equilibrium properties, to analyze the route-changing dynamics. This distinguishes our results from other studies of Nash equilibria by the cavity method [21,22]. The generalized framework can be readily adapted to study other dynamical problems.…”

Serving by local consensus in the public service location game

“…In determining the locations of the public services through the local-consensus mechanism, for simplicity we ignored the issue of possible future congestion in accessing service, but this is itself an interesting factor to explore 7 . We didn’t discuss the actual implementation of the local-consensus mechanism.…”

“…A simplest decision-making strategy is best response to the current situation of the neighborhood 2 7 20 . If node i has one or more neighboring servers it just chooses to be a consumer ( c i = 0), otherwise it chooses to be a server ( c i = 1).…”

“…Our public service location problem actually is a network game [3,15] in which each agent makes decision under the strong self-interest of having access to the service and the weak incentive of lowering the number of servers. A simplest decision-making strategy is best response to the current situation of the neighborhood [2,7,16]. If an agent i has one or more neighboring servers it just chooses to be a consumer (c i = 0), otherwise it chooses to be a server (c i = 1).…”

“…Under such a free-market mechanism, if an agent can access service from a neighboring agent, it will have no motivation to be a service provider itself, and an agent will choose to be a service provider only if none of its network neighbors offers service. This best-response mechanism has been investigated in the recent literature 2 3 4 6 7 , and it was found that the resulting maximal independent-set solutions are far from being socially efficient.…”