Book Reviews

Geir B. Asheim
<span title="2003-03-01">2003</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z74xxpszdjezhircz7fc4u4vae" style="color: black;">Journal of Economics</a> </i> &nbsp;
A decision-maker chooses rationally if his choice is weakly preferred to all of his alternatives. In a game, each decision-maker is a player, the alternatives consist of plans of action (or strategies), while the player's preferences over strategies depend on both the utility (or payoff) derived from different outcomes and his conjecture concerning opponent behavior. In an extensive form game, a player must also form beliefs about what his opponents will do in parts of the game that will not be
more &raquo; ... reached if the opponents play according to their rationally chosen strategies. Hence, in game-theoretic analysis of extensive form games, a player's beliefs about what an opponent will do must be specified in greater detail than the opponent's own strategy. This observation -which has been pointed out by, e.g., Rubinstein (1991)motivates a game-theoretic analysis of extensive form games in terms of what players believe their opponents will rationally do, rather than in terms of their own rational behavior. It is precisely such an analysis that Andrés Perea presents in his book. Perea, who is affiliated with the University of Maastricht, starts in chap. 2 by presenting a decision-theoretic framework for extensive form games as well as introducing the concept of a behavioral conjecture. A behavioral conjecture specifies beliefs about how a player will act at each of his information sets. The author emphasizes that a behavioral conjecture is "in the mind of the player's opponents" instead of being "in the player's own mind". Given that a player has behavioral conjectures about his opponents, one can determine what constitutes rational behavior at each of his information sets. The assumption that underlies the analysis of this book is that a player should assign positive probability only to opponent behavior that is rational given the behavioral conjectures held by the opponents. In chaps. 3-6 it is assumed that a player's behavioral conjectures about his opponents are stochastically independent, and that two players have the same behavioral conjecture about a common opponent. It is also implicitly assumed that each player is informed about the behavioral conjecture held
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