1 Matrix games. - 1. 1 Definition of a noncooperative game. - 1. 2 Admissible situations and the equilibrium situation. - 1. 3 Strategic equivalence of games. - 1. 4 Antagonistic games. - 1. 5 Saddle points. - 1. 6 Auxiliary propositions about extrema. - 1. 7 Minimax equalities and saddle points. - 1. 8 Matrix games. - 1. 9 Mixed strategies. - 1. 10 A mixed extension of a game. - 1. 11 Existence of minimaxes in mixed strategies. - 1. 12 Convex sets. - 1. 13 The lemma on two alternatives. - 1. 14 The minimax theorem. - 1. 15 The value of the game and optimal strategies. - 1. 16 Three properties of the value of a game. - 1. 17 An example: 2×2 games. - 1. 18 A graphical solution of 2×n games. - 1. 19 A graphical solution of m×2 games. - 1. 20 Sufficient criteria for the value of a game and optimal strategies. - 1. 21 Domination of strategies. - 1. 22 Diagonal games. - 1. 23 Sets of optimal strategies in a matrix game. - 1. 24 An example: 3×3 games. - 1. 25 Symmetric games. - 1. 26 Matrix games and linear programming. - 2 Infinite antagonistic games. - 2. 1 Introduction and motivation. - 2. 2 Situations of ?-equilibrium; ?-saddle points and ?-optimal strategies. - 2. 3 ?-optimal strategies and minimaxes. - 2. 4 Mixed strategies. - 2. 5 Properties of the value of a game and of optimal strategies. - 2. 6 The Helly metric. - 2. 7 Conditionally compact games. - 2. 8 The basic theorem for conditionally compact games. - 2. 9 Continuous games on the unit square. - 2. 10 Convex functions. - 2. 11 Convex games; pure optimal strategies for player II. - 2. 12 Convex games; optimal strategies for player I. - 2. 13 Strictly convex games. - 2. 14 Examples of convex games and their solutions. - 2. 15 Market competition. - 2. 16 Allocation of production capacities; minimization of the maximal intensity of a production scheme. - 2. 17 Allocation of productioncapacities under partial uncertainty. - 3 Noncooperative games. - 3. 1 Mixed extensions of noncooperative games. - 3. 2 Equilibrium situations. - 3. 3 Nash's theorem. - 3. 4 Properties of equilibrium situations. - 3. 5 Bi-matrix games. - 3. 6 Solutions of bi-matrix games. - 3. 7 Almost antagonistic games. - 3. 8 Prisoner's dilemma. - 3. 9 The battle of the sexes. - 3. 10 Noncooperative games with two pure strategies for each of the players. - 3. 11 False advertising. - 3. 12 Preservation of ecology. - 4 Cooperative games. - 4. 1 Characteristic functions. - 4. 2 Characteristic functions of noncooperative games. - 4. 3 Properties of characteristic functions for noncooperative games. - 4. 4 Imputations and cooperative games. - 4. 5 Essential and inessential games. - 4. 6 Strategic equivalence of cooperative games. - 4. 7 Zero games. - 4. 8 The 0-1 reduced form. - 4. 9 Classification of cooperative games with a small number of players. - 4. 10 Dominance of imputations. - 4. 11 The core of a game. - 4. 12 The core of a general three-person game. - 4. 13 von Neumann-Morgenstern solutions. - 4. 14 vN-M solutions for three person constant sum games. - 4. 15 vN-M solutions for general three-person cooperative games. - 4. 31 Shapley's vector; axiomatization. - 4. 32 Shapley's vector; existence and determination. - 4. 33 Examples of Shapley vectors. - Exercises. - Selected bibliography. Language: English