By Andrés Perea (auth.)
Andrés Perea accomplished his Ph.D. in 1997 at Maastricht collage, The Netherlands. From 1997 to 1998 he labored as a traveling professor at Universitat Autonòma de Barcelona. additionally, from 1998 to 2000, Andrés labored at Universidad Carlos III as a traveling professor, and from 2000 on as an affiliate professor.
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Additional info for Rationality in Extensive Form Games
2 position. For such a game, it is easily seen that there is a unique behavioral conjecture profile that satisfies backward induction. Suppose namely that a satisfies backward induction for such a game. Consider a final decision node x E XO, controlled by some player i. Since every action at x leads to a different terminal node, and player i's utilities Ui(Z) are different for different terminal nodes, it follows that there is a unique optimal action a(x) at node x. Hence, it should hold that aix = a(x) for every x E XO.
An assessment ((7,13) may therefore be seen as a sufficiently complete description of the players' conjectures about the opponents' behavior at every instance of the game. It seems natural to require, however, that the conjectures about the opponents' past play contained in 13 be "consistent" with the conjectures about opponents' future play contained in (7. 2i). 6 to b. 6). This consistency condition is defined formally in the following section. 6 Best Responses to Conjectures Suppose that the players' conjectures about the opponents' behavior at every stage of the game is given by an assessment ((7, 13).
A behavioral conjecture O'i about player i thus specifies, at each of player i's information sets, the opponents' common conjecture about player i's play. However, it may also be necessary for a player j to revise his conjecture about the opponents' past play at some of his own information sets. 6. Assume that player 2 holds the behavioral conjecture 0'1 = c. If player 2's information set is reached, then player 2 knows that his initial conjecture about player l's behavior has been contradicted, and should thus revise this conjecture.
Rationality in Extensive Form Games by Andrés Perea (auth.)