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.
Inhaltsverzeichnis
1. Introduction. - 1. 1 Adjustment processes in economies. - 1. 2 Some examples of globally efficient processes. - 1. 3 Outline of the monograph and main results. - 2. Preliminaries. - 2. 1 Notation. - 2. 2 The stationary point problem. - 2. 3 Notions related to simplicial algorithms. - 2. 4 Concepts from differential topology. - 3. Existence of adjustment processes. - 3. 1 Two price adjustment processes for a pure exchange economy. - 3. 2 The proportional process 37 3. 3. Direct approach towards the sign process 4l 3. 4. Homotopy approach towards the sign process. - 4. An adjustment process for an international trade model. - 4. 1 The model. - 4. 2 An example. - 4. 3 The process. - 4. 4 Description of the price adjustments. - 4. 5 Numerical illustration. - 5. An adjustment process for an exchange economy with linear production technologies. - 5. 1 The model. - 5. 2 Existence of the path 82 5. 3. The adjustment process 86 5. 4. Examples. - 6. Finding Nash equilibria in noncooperative games. - 6. 1 Solving the bi-matrix game as a stationary point problem. - 6. 2 The procedure. - 6. 3 Game-theoretic interpretation. - 6. 4 How to find more equilibria. - 6. 5 Interpretation and generalization of the Lemke-Howson algorithm. - 6. 6 Computing Nash equilibria in noncooperative more-person games. - References.
