Author | Vorob'ev, N. N. author |
---|---|
Title | Game Theory [electronic resource] : Lectures for Economists and Systems Scientists / by N. N. Vorob'ev |
Imprint | New York, NY : Springer New York, 1977 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6341-8 |
Descript | XII, 179 p. online resource |
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: 2ร2 games -- 1.18 A graphical solution of 2รn games -- 1.19 A graphical solution of mร2 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: 3ร3 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 production capacities 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