Foundations of Game Theory

Historical notes and references for the Foreword and Introduction.- 1 Noncooperative games.- 1 Noncooperative games and their components.- 2 Optimality principles in noncooperative games.- 3 Realizability of A-optimality principles.- 4 Realizability of A-principles in metastrategies.- 5 Realizability of equilibrium situations in mixed strategies.- 6 Natural topology in games.- Notes and references for Chapter 1.- 2 Finite noncooperative games.- 1 Finite noncooperative games.- 2 Dyadic games.- 3 Solution of general finite noncooperative games.- 4 On the structure of the set of equilibria in finite noncooperative games.- 5 The complexity of solution of finite noncooperative games.- 6 Reduction to three-person games.- Notes and references for Chapter 3.- 3 Two-person zero-sum games.- 1 Optimality in two-person zero-sum games.- 2 Basis of the maximin principle.- 3 Minimax theorems.- 4 Finitely additive strategies.- 5 Analytic games on the unit square.- 6 Separable games.- 7 Convex games.- 8 Games with a simple payoff function.- 9 Games of timing.- Notes and references for Chapter 3.- 4 Matrix games.- 1 Basic concepts and propositions.- 2 Solution of matrix games of small format.- 3 Matrix games and linear programming.- 4 Description of all equilibrium situations in matrix and bimatrix games.- 5 Solution of matrix games with matrix payoffs of a special form.- 6 Approximate methods for solving matrix games.- 7 Structure of the set of a matrix game.- Notes and references for Chapter 4.- References.- Collections.- List of Joint Authors.- Index of Notations.