Computer Science – Computer Science and Game Theory
Scientific paper
2011-11-26
Computer Science
Computer Science and Game Theory
19 pages
Scientific paper
Rosenthal (1973) introduced the class of congestion games and proved that they always possess a Nash equilibrium in pure strategies. Fotakis et al (2005) introduce the notion of a greedy strategy tuple, where players sequentially and irrevocably choose a strategy that is a best response to the choice of strategies by former players. Whereas the former solution concept is driven by strong assumptions on the rationality of the players and the common knowledge thereof, the latter assumes very little rationality on the players' behalf. In this paper we obtain necessary and sufficient conditions for the equivalence of these two solution concepts. Such equivalence enhances the viability of these concepts as realistic outcomes of the environment. The conditions for such equivalence to emerge for monotone symmetric games is that the strategy set has a tree-form. Quite interestingly, these conditions are similar to those obtained by Holzman and Law-Yone (1997) for the equivalence of the set of strong equilibria and the set of Nash equilibria.
Kuniavsky Sergey
Smorodinsky Rann
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