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 vacationing 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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Andrés Perea accomplished his Ph. D. in 1997 at Maastricht college, The Netherlands. From 1997 to 1998 he labored as a vacationing professor at Universitat Autonòma de Barcelona. furthermore, from 1998 to 2000, Andrés labored at Universidad Carlos III as a vacationing professor, and from 2000 on as an affiliate professor.
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Extra info for Rationality in Extensive Form Games
However, this means that either player 1 strictly prefers a over c, or strictly prefers b over c, which is a contradiction. Hence, J-L2 cannot be substituted by a local mixed conjecture A2 without altering player 1's preference relation over his strategies. Now, suppose that the local mixed conjecture Ai is given. Then, one can easily "recover" a mixed conjecture J-Li such that Ai is induced by J-Li· We refer to this J-Li as the mixed conjecture induced by Ai. Recall that Hi(Ai) is the collection of player i information sets not avoided by Ai and Hi(Si) is the collection of player i information sets not avoided by the strategy Si.
X In a game with perfect information, not every Nash equilibrium satisfies backward induction, however. 6. The behavioral conjecture profile ~ = (b, d) is a Nash equilibrium, but it does not satisfy backward induction. The fundamental difference between both concepts is that Nash equilibrium does not require players to believe that their opponents choose optimally at every subgame, whereas backward induction does. Note that in this example, d is a best response for player 2 against ~, but it is no longer a best response in the subgame that starts at player 2's decision node.
1 A behavioral conjecture about player i is a vector O'i = (O'ih)hEHi where O'ih E ~(A(h)) for every hE Hi. For every h E Hi and every action a E A(h), the probability O'ih(a) is to be interpreted as the players' common subjective probability assigned to the event that player i would choose action a at h. The crucial difference with a local mixed conjecture Ai is that the latter only specifies a local probability distribution for every information set hE Hi that is not avoided by Ai, whereas O'i specifies a local probability distribution also at those information sets that are actually avoided by 0' i.
Rationality in Extensive Form Games by Andrés Perea (auth.)