Ebook: Adjustment Processes for Exchange Economies and Noncooperative Games

This monograph is a treatise on adjustment processes. We consider price adjustment processes in exchange economies and strategy adjustment processes in noncooperative games. In the most simple version of an exchange economy, i.e. a pure exchange economy, there exist markets on which prices are determined by the demand and supply created by a finite number of consumers willing to exchange their initial endowments in order to maximize their utilities. An equilibrium situation is attained if, for some price vector, demand equals supply in all markets. Starting from a situation not being an equi­ librium an adjustment process reaches an equilibrium via adaptations of prices. The advantage of the adjustment processes we will present in this monograph is that they exist and converge under far weaker assumptions than existing processes. The second subject concerns the problem of finding Nash equilibria in noncooperative games. A Nash equilibrium is a situation from which no player can improve his position by unilaterally changing his strategy. We present a new algorithm for finding such equilibria. The sequence of stra­ tegy vectors generated by the algorithm can be interpreted as the path followed by a strategy adjustment process.

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The first part of this book deals with tatonnement processes in different general equilibrium models. The standard price exchange model, an international trade model and an economy with production are considered. Theadvantage of these processes, in contrast to the standard Walras process, is that their convergence is guaranteed under weak conditions. The second part of the book deals with game theory. More special, with the computation of Nash equilibria in noncooperative games. It is shown how to find a perfect equilibrium and illustrated that the described method is superior to the Lemke-Howson method and can be used for finding more equilibria.