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2.4 Equilibrium Selection > 2.4.1 Equilibrium Selection in Concave Games - Pg. 59

2.4 Equilibrium Selection 59 games (Cooper, 1998). Another important scenario where such a problem arises, cor- responds to games where the choice of actions of different players is not independent, for instance, non-cooperative games with correlated constraints and generalized NE (Altman and Shwartz, 2000; Debreu, 1952). A central feature in these constrained games is that they often possess a large number of equilibria. The selection of an appropriate equilibrium is the natural concern. What can be done when one has to deal with a game having multiple equilibria? Are there some dominant equilibria? Are some equilibria fairer and more stable than others? Obviously, the selection rule is strongly related to the used fairness criteria. Equilibrium selection is a theory in itself (Harsanyi and Selten, 2003). The goal of the theory of equilibrium selection is to provide a convincing theory of rationality which selects a unique outcome in every game and this theory has to be common knowledge. While the theory developed by Harsanyi and Selten (2003) is recognized as an important contribution, it takes some positions which are still being discussed and with which some authors disagree (Hillas and Kohlberg, 2002). We will just men- tion one point about this theory and then focus on more pragmatic ways of solving the problem of equilibrium selection. Some equilibria can be utility/payoff dominant or risk dominant in the sense of Harsanyi and Selten (2003) and Damme (2002). An