Chapter 11: Nash Equilibrium
Jürgen Eichberger Nash equilibrium1 is arguably the most important equilibrium concept in economics. Debreu (1952) shows that even the traditional notion of a demand and supply equilibrium is a special case of a Nash equilibrium if one introduces a player who adjusts prices. Most important, however, is the application of this equilibrium concept in the context of strategic interactions, as one can find them in oligopoly theory, industrial organization models, in models with externalities or public goods, or in modern industrial-organization-based international economics. We will focus here on the case of strategic interaction between two players. All concepts introduced here can and have been extended to many-player situations. There are innumerable text books on Game Theory, as the theory of strategic interactions is usually called; for a very informal introduction one can recommend Binmore (2007), for an excellent more advanced treatment we recommend Osborne and Rubinstein (1994). Strategic interaction between two players, say Player A and Player B, can be described by the strategy sets of these players, SA and SB, and their payoff functions pA(sA, sB) and pB(sA, sB), which indicate the individual evaluation of the outcome arising from the strategic interaction by the two strategies sA and sB. A pair of strategies (sA, sB), a so-called strategy combination, describes an interactive situation where Player A chooses strategy sA from the set of strategies SA and Player B chooses sB from the strategies in SB. If each player has only a small and finite number of...
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