Introduction to Game TheorySpringer Science & Business Media, 2012 M12 6 - 252 páginas The 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 47
Página 2
... shown in Figure 1.1 . The little circles in the diagram are called vertices , and the directed line segments between them are called edges . A play of the game starts at the top vertex ( labeled " Thelma " ) and arrives , via one of the ...
... shown in Figure 1.1 . The little circles in the diagram are called vertices , and the directed line segments between them are called edges . A play of the game starts at the top vertex ( labeled " Thelma " ) and arrives , via one of the ...
Página 10
... shown in Figure 1.6 . ( Most of the payoff pairs have been left out . ) This tree for two - finger morra does not embody all the rules of the game . It appears from the tree that P2 could guarantee herself a positive payoff by making ...
... shown in Figure 1.6 . ( Most of the payoff pairs have been left out . ) This tree for two - finger morra does not embody all the rules of the game . It appears from the tree that P2 could guarantee herself a positive payoff by making ...
Página 11
... game of Matching Coins ( Figure 1.1 ) . The rules of this game state that Louise does not know which coin Thelma is holding ... Show that the second player has a sure win . ( 7 ) A slightly less simple version of nim is played as follows ...
... game of Matching Coins ( Figure 1.1 ) . The rules of this game state that Louise does not know which coin Thelma is holding ... Show that the second player has a sure win . ( 7 ) A slightly less simple version of nim is played as follows ...
Página 13
... game has reached vertex u ( owned by P ) : She would choose c ( u ) . Now ... game tree from the root to a terminal vertex is determined . Define ( C1 , C2 ... shown in Figure 1.5 , a choice function for player P1 which calls for him to ...
... game has reached vertex u ( owned by P ) : She would choose c ( u ) . Now ... game tree from the root to a terminal vertex is determined . Define ( C1 , C2 ... shown in Figure 1.5 , a choice function for player P1 which calls for him to ...
Página 15
Alcanzaste el límite de visualización de este libro.
Alcanzaste el límite de visualización de este libro.
Contenido
Linear Programming | 65 |
Solving Matrix Games 99 | 98 |
NonZeroSum Games | 115 |
NPerson Cooperative Games | 149 |
GamePlaying Programs | 185 |
Appendix Solutions | 201 |
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 choice subtree choose coefficient column player compute constant-sum constraints cooperative defined definition denoted directed graph dual basic form edges entry equation equilibrium N-tuple equilibrium pairs example Exercise expected payoff feasible tableau feasible vector game in characteristic game theory game tree grand coalition imputation inequality inessential joint strategy labeled mancala matrix game maximin values maximize maximum minimax theorem nonbasic variable noncooperative nonnegative normal form objective function optimal mixed strategies optimal strategy P₁ Pareto optimal path payoff matrix payoff pair payoff region pivot 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 subject to x1 supergame Suppose symmetric terminal vertex theorem vc(M verify vertices zero zero-sum