gametheory7 - a dominated strategy when nature moves right...

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The game ¡ 2 has two WPBE outcomes. Equilibrium 1: player 1 plays R (if nature moves left), player 1 plays r (if nature moves right). player 2 plays left. Beliefs at the only multiple node information set are detemined by Bayes' rule: ¹ ( x 1 )=1,and ¹ ( x 2 )=0 :
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Equilibrium 2: player 1 plays L (if nature moves left), player 1 plays r (if nature moves right). player 2 plays right. Beliefs at the only multiple node information set are not detemined by Bayes' rule, because the probabil- ity of reaching the information set is zero, given the strategies. Some beliefs supporting the equilibrium are: ¹ ( x 1 )=0 ,and ¹ ( x 2 )=1 : To see that strategies are sequentially rational, given the beliefs, notice that player 2 is correct to choose right, since a payo® of 0 is better than a payo® of ¡ 1. Player 1 is correct to choose R, because 2 is better than ¡
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Notes: 1. Many beliefs are consistent and support the out- come of equilibrium 2. 2. It is not sensible to think that player 1 will choose
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Unformatted text preview: a dominated strategy when nature moves right, but this is still consistent with the de¯nition of WPBE. Further re¯nements: Attempts to strengthen WPBE have been made, such as PBE and sequential equilibrium. However, it is of-ten hard to check whether we have a (PBE or) sequen-tial equilibrium, and these re¯nements do not always rule out the \bad" equilibria. The problem is that beliefs about information sets that are \o® the equilibrium path" cannot be pinned down by Bayes' rule, but the beliefs are crucial in determin-ing what is on and o® the equilibrium path. Forward Induction Suppose that before playing the following version of the battle of the sexes, player 1 has an opportunity to publicly burn a dollar . player 2 left right player 1 top 3 ; 1 ; bottom ; 1 ; 3 Will player 1 burn the dollar if he does not intend to play top?...
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gametheory7 - a dominated strategy when nature moves right...

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