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Strong Nash equilibrium in games with common and complementary local utilities
Affiliation:1. Department of Mathematics, Changsha University of Science and Technology, Changsha 410004, China;2. Department of Mathematics, Hunan City University, Yiyang 413000, China
Abstract:A rather general class of strategic games is described where the coalitional improvements are acyclic and hence strong Nash equilibria exist: The players derive their utilities from the use of certain facilities; all players using a facility extract the same amount of local utility therefrom, which amount depends both on the set of users and on their actions, and is decreasing in the set of users; the ultimate utility of each player is the minimum of the local utilities at all relevant facilities. Two important subclasses are “games with structured utilities,” basic properties of which were discovered in 1970s and 1980s, and “bottleneck congestion games,” which attracted researchers’ attention quite recently. The former games are representative in the sense that every game from the whole class is isomorphic to one of them. The necessity of the minimum aggregation for the existence of strong Nash equilibria, actually, just Pareto optimal Nash equilibria, in all games of this type is established.
Keywords:Strong Nash equilibrium  Weakest-link aggregation  Coalitional improvement path  Congestion game  Game with structured utilities
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