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We study a class of games which model the competition among agents to access some service provided by distributed service units and which exhibit 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.
We develop a computationally efficient technique to solve a fairly general distributed service provision problem with selfish users and imperfect information. In particular, in a context in which the service capacity of the existing infrastructure ca
Simple binary-state coordination models are widely used to study collective socio-economic phenomena such as the spread of innovations or the adoption of products on social networks. The common trait of these systems is the occurrence of large-scale
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