Unit 11- Lesson 40- Non-credible Threats and Subgame Perfection PDF

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Spring 2016
Prof. Kathleen Brown...

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Lesson 40: Non-credible Threats and Subgame Perfection Why didn’t we find NE number 2 and 3 via rollback? Compare definitions RE: Set of strategies, one for each player, in which each player chooses her best action at each node, give the choices of other players. A NE is a set of strategies (one for each player) such that no player can improve her pay-off by deviating from her equilibrium strategy, given that the other players are playing their equilibrium strategies. Answer: Both NE2 and NE3 require CL to make a choice that would be against her interests (Choose PC) at some node off the equilibrium path In particular, note that in NE2 Sup chooses less preferred principal because of the threat that if she didn’t (off the equilibrium path) CL will choose PC But this is not a ‘credible threat’! Specifically, the threat is that CL choose ‘PC’ at decision node 3. But if we got to this node, CL has no incentive to follow through on threat Can be part of NE because if Sup reacts to non-credible threat, CL never need to exercise it. Their bluff is never called. Non credible threats require suboptimal choices in some subgame (game that starts at node other than the initial node of game tree.) Because we don’t get to every subgame, these non credible threats can be part of NE (CL don’t have regrets because don’t have to make good on the threat.) Most people are suspicious of the NE that are supported by non credible threats. Wouldn’t Sup realize that CL is only bluffing? When this is an issue, we think the appropriate solution is the sublime perfect equilibrium SPE: NE in strategies are NE in every subgame (whether or not subgame is on equilibrium path) RE finds the SPE. SPE is a refinement of NE....