## Introduction to Game TheoryThe mathematical theory of games has as its purpose the analysis of a wide range of competitive situations. These include most of the recreations which people usually call "games" such as chess, poker, bridge, backgam mon, baseball, and so forth, but also contests between companies, military forces, and nations. For the purposes of developing the theory, all these competitive situations are called games. The analysis of games has two goals. First, there is the descriptive goal of understanding why the parties ("players") in competitive situations behave as they do. The second is the more practical goal of being able to advise the players of the game as to the best way to play. The first goal is especially relevant when the game is on a large scale, has many players, and has complicated rules. The economy and international politics are good examples. In the ideal, the pursuit of the second goal would allow us to describe to each player a strategy which guarantees that he or she does as well as possible. As we shall see, this goal is too ambitious. In many games, the phrase "as well as possible" is hard to define. In other games, it can be defined and there is a clear-cut "solution" (that is, best way of playing). |

### Dentro del libro

Resultados 1-5 de 8

Página 2

Backgammon is an

We have just said that the players receive a numerical payoff at the end of the

game. In real conflict situations, the payoff is often something nonquantitative like

...

Backgammon is an

**example**of this because a die is rolled at points in the game.We have just said that the players receive a numerical payoff at the end of the

game. In real conflict situations, the payoff is often something nonquantitative like

...

Página 3

An

of graphs (both directed and not directed) is a large and interesting subject. See [

BM76] for more information. We will use uppercase letters like G or H or T to ...

An

**example**is given in Figure 1.2. It has five vertices and five edges. The theoryof graphs (both directed and not directed) is a large and interesting subject. See [

BM76] for more information. We will use uppercase letters like G or H or T to ...

Página 4

e Usually, but not always, we draw trees in such a way that the root is at the top.

An

has eleven vertices and ten edges. Now let T be a tree. We make a few

definitions.

e Usually, but not always, we draw trees in such a way that the root is at the top.

An

**example**is given in Figure 1.3; all the vertices have been labeled. This treehas eleven vertices and ten edges. Now let T be a tree. We make a few

definitions.

Página 14

For

for

has reached a vertex u belonging to P, then u is in S and only one of its children ...

For

**example**, one of them contains the vertices: root, a, e, d, k, and l. ... Suppose,for

**example**, that player P is playing according to a choice subtree S. If the gamehas reached a vertex u belonging to P, then u is in S and only one of its children ...

Página 17

Alcanzaste el límite de visualización de este libro.

Alcanzaste el límite de visualización de este libro.

### Comentarios de la gente - Escribir un comentario

No encontramos ningún comentario en los lugares habituales.

### Contenido

1 | |

TwoPerson ZeroSum Games 35 | 34 |

Linear Programming | 65 |

Solving Matrix Games 99 | 98 |

NonZeroSum Games | 115 |

NPerson Cooperative Games | 149 |

GamePlaying Programs | 185 |

Appendix Solutions | 201 |

Two cuttings | 202 |

Equilibrium pair | 219 |

Bibliography | 223 |

### Otras ediciones - Ver todas

### Términos y frases comunes

alpha-beta pruning arbitration pair Axiom basic solution bi-matrix chance moves characteristic function form choice function choose coefficient column player compute constant-sum constraints cooperative core defined definition denoted directed graph dominated rows dual basic form edges entry equation equilibrium N-tuple equilibrium pairs example Exercise expected payoff feasible tableau feasible vector game in characteristic game shown game tree grand coalition imputation inequality inessential joint strategy labeled m x n matrix game maximin values maximum minimax theorem moves left nonbasic variable noncooperative nonnegative normal form objective function optimal mixed strategies optimal strategy Pareto optimal path payoff matrix payoff pair payoff region pivot player and column player plays plays according primal problem Prisoner's Dilemma probability proof Prove pure strategies root row player saddle point Shapley value shown in Figure simplex algorithm Solve stable set strategically equivalent supergame Suppose symmetric terminal vertex Ti(S ur(M ve(M verify vertices vr(M zero zero-sum