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Опубликовано на портале: 24-01-2007John Hillas Econometrica. 1990. Vol. 58. No. 6. P. 1365-1390.
A new definition of strategic stability is shown to satisfy all of the requirements given by Elon Kohlberg and Jean-Francois Mertens (1986). The definition follows the general form of the original definition of Kohlberg and Mertens, but, rather than working with perturbations of the payoffs or strategy space, works directly with perturbations to the best reply correspondence. With the appropriate topology on this space of perturbations, the resulting definition does satisfy all of the requirements given by Kohlberg and Mertens. It is shown that one does not have much freedom in the topology one uses.
Опубликовано на портале: 28-04-2005John Donald Roberts, Paul R. Milgrom Econometrica. 1990. Vol. 58. No. 6. P. 1255-1277.
We study a class of non-cooperative games that includes many standard oligopoly games,macro economic coordination games, network and production externality games, and others. Forthese games, the sets of rationalizable strategies, pure Nash equilibrium strategies, and correlated equilibrium strategies are non-empty and have identical upper and lower bounds. Also,a large class of dynamic learning processes - including both best-response dynamics and Bayesian learning - lead eventually to behavior that lies between these same bounds. General comparative static and welfare theorems are provided. We study the class of (non-cooperative) supermodular games introduced by Topkis (1979) and further studied by Vives (1988). These are games in which each player's strategy set is partially ordered, the marginal returns to increasing one's strategy rise with increases in the competitors' strategies and, if a player's strategies are multidimensional, the marginal returns to any one component of the player's strategy increase with increases in the other components. The simplest examples of such games arise in oligopoly theory. These include the Cournot duopoly game with a wide range of demand specifications and arbitrary continuous cost functions, Bertrand oligopoly games, R&D racing games, and oligopoly games with endogenous choice of production technologies. Additional applications drawn from industrial organization include the Hendricks-Kovenock (1988) drilling game (in which oil firms decide whether to drill exploratory wells when the information obtained is a public good), network externality games, and certain oligopoly games that arise in connection with the Milgrom-Roberts (1988) model of manufacturing. Other examples include games used to model