On the verification and computation of strong nash equilibrium

Computing equilibria of games is a central task in computer science. A large number of results are known for Nash equilibrium (NE). However, these can be adopted only when coalitions are not an issue. When instead agents can form coalitions, NE is inadequate and an appropriate solution concept is strong Nash equilibrium (SNE). Few computational results are known about SNE. In this paper, we first study the problem of verifying whether a strategy profile is an SNE, showing that the problem is in P. We then design a spatial branch--and--bound algorithm to find an SNE, and we experimentally evaluate the algorithm.

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