28. Mixed and Behavior Strategies in Infinite Extensive Games
1964; Princeton University Press; Linguagem: Inglês
10.1515/9781400882014-029
Autores Tópico(s)Artificial Intelligence in Games
ResumoA game has four moves: in the first move P 1 (player 1) chooses a real number x 1 ; in the second move, P 2 , knowing x 1 , chooses a real number y 1 ; in the third move, P 1 , knowing y 1 , but having forgotten x 1 , chooses a real number x 2 ; and in the last move, P 2 , knowing y 1 and x 2 , but not knowing x 1 , chooses a real number y 2 .(The payo¤ is then some function of the four variables x 1 , x 2 , y 1 , and y 2 .)A pure strategy for P 1 is now an ordered couple fa; f g, where a is a real number and f is a function of one real variable (it depends on y 1 ); and a pure strategy for P 2 is an ordered couple fg; hg, where g is a function of one real variable (it depends on x 1 ) and h is a function of two real variables (it depends on y 1 and x 2 ). . . .It is clear that the payo¤ function for a game of the type just described need not necessarily have a saddle point, and hence it is natural to suppose that the players will make use of mixed strategies. . . .''The di‰culties that McKinsey goes on to describe correspond precisely to those we discussed in connection with the first example.Our third example involves the notion of the supergame of a given game G.This is a game each play of which consists of a number of repeated plays of G; the payo¤ to the ''superplay'' usually is defined as some kind of average of the payo¤s to the individual plays.The super-
Referência(s)