On the existence of pure and mixed strategy Nash equilibria in discontinuous games

Article Abstract:

A pure strategy Nash equilibrium existence result for a large class of discontinuous games is presented. The strategy relies on a condition called better-reply security. Under this condition, a game is better-reply secure if for every nonequilibrium strategy x and every vector limit u results from strategies approaching x, some player i has a strategy yielding a payoff strictly above u, even if others slightly deviate from x. The results showed that games that possess a pure strategy Nash equilibrium are those with compact, convex strategy spaces and payoffs that are quasiconcave.

Models, Games of strategy (Mathematics)

---

Dynamic capacity choice in a Bertrand-Edgeworth framework

Article Abstract:

A 'Two Period Cournot' (TPC) model, which is a modification of the original Cournot model, was employed as a standard of measurement to analyze the effects of substituting the Walrasian auctioneer with Bertrand-Edgeworth behavior. The TPC model was applied in a three-stage noncooperative game composed by two firms rivalling each other in a homogenous product market. Results show the TPC model to correspond with the two period Bertrand-Edgeworth when capacity costs are significantly great.

Duopolies

---

An extension of the KKMS Theorem

Article Abstract:

The Knaster-Kuratowski-Mazurkiewick Theorem, as well as Shapley's (1972) KKMS Theorem have great significance in general economic equilibrium theory and mathematics. The KKM Theorem has been shown by Bennett and Zame (1988) to exhibit competitive payoffs in the presence of purely convex preferences. It is noted that balanced collections are 'minimally' partnered when the intersection of individual balanced and partnered collections contain a finite number of points.

Set theory

Similar abstracts:

• Abstracts: Discreteness of equilibria in incomplete markets with a continuum of states. The set of equilibria of first-price auctions
• Abstracts: On the existence and the structure of the pseudo-equilibrium manifold. Some consequences of the unknottedness of the Walrus correspondence
• Abstracts: Monopolistic behaviors and general equilibrium: a generalization of Nikaido's work. On monopolistic equilibria with incomplete markets: the case of an exchange economy
• Abstracts: Trend function hypothesis testing in the presence of serial correlation. Constructing instruments for regressions with measurement error when no additional data are available, with an application to patents and R&D
• Abstracts: Trend function hypothesis testing in the presence of serial correlation. part 2 Simple robust testing of regression hypothesis

This website is not affiliated with document authors or copyright owners. This page is provided for informational purposes only. Unintentional errors are possible.