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By Xavier Vives

The "oligopoly problem"--the query of the way costs are shaped while the marketplace includes just a couple of competitors--is one of many extra continual difficulties in the heritage of financial concept. during this e-book Xavier Vives applies a latest game-theoretic method of increase a concept of oligopoly pricing.Vives starts off by means of concerning vintage contributions to the field--including these of Cournot, Bertrand, Edgeworth, Chamberlin, and Robinson--to sleek video game conception. In his dialogue of simple game-theoretic instruments and equilibrium, he can pay specific consciousness to contemporary advancements within the thought of supermodular video games. the center component to the ebook, an in-depth therapy of vintage static versions, offers really good lifestyles effects, characterizations of equilibria, extensions to giant markets, and an research of comparative statics with a view towards utilized paintings. the ultimate chapters research dedication matters, access, info transmission, and collusion utilizing a number of instruments: two-stage video games, the modeling of pageant less than uneven details and mechanism layout conception, and the speculation of repeated and dynamic video games, together with Markov ideal equilibrium and differential video games.

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Extra resources for Oligopoly Pricing: Old Ideas and New Tools

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Indeed, consider the case of a twice-continuously differentiable function g. According to the previous remark supermodularity only puts restrictions on the cross partials of g; the other concepts impose restrictions also on the diagonal of the matrix of second derivatives. html [7/8/2007 9:35:13 PM] Document Page 26 Remark 9 The complementarity properties of a family of functions gn : X × T ® R are preserved under several elementary transformations like positive linear combinations, pointwise limits and maximization.

A first type of approach is based on nontopological methods and exploits monotonicity properties of optimization problems using lattice-theoretical results. This approach, which defines the class of supermodular games, will be expounded with some detail given its recent introduction in economic analysis. A second type of approach restricts attention to symmetric games and uses a onedimensional fixed point theorem. Still a third approach uses constructive methods applied to the 8 Cournot model with homogeneous product.

The basic existence theorem with mixed strategies is due to Gliksberg (1952). 9 Consider the game (Ai. pi i p N). If the (pure-) strategy sets are nonempty compact subsets of Euclidean space and payoffs are continuous there is a mixed-strategy Nash equilibrium. Remark 18 It is worth noticing that no quasiconcavity requirement on payoffs and no convexity requirement on strategy spaces are necessary due to the convexifying effect of mixed strategies on best responses. The payoffs and strategy spaces of the mixed extension have the appropriate convexity properties.

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