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 denition of WPBE. Further renements: 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 renements 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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