Unit 03- Lesson 11- Knife Edge Cases PDF

Preview

Summary

Spring 2016
Prof. Kathleen Brown...

Description

Lesson 11: Knife Edge Cases 11A: Equal Pay-Offs = Player is ‘indifferent' 11B: Neither Choice wrong 11C: More than one equilibrium What can we conclude in cases where the actions lead to equal pay-offs? Player is indifferent between the two strategies = thinks they are equally good. Pay-offs exactly equal Most important thing is to know what we cannot conclude: We cannot (within the framework of game theory) rule out either choice. At node 3, neither choice would be wrong for the Challenger if V = C. Have to accept this ambiguity. Game theory not hugely helpful here. Vc = Cc is ‘knife edge’ because the smallest difference is enough to break the utility tie Graph represents all values C - - only one point ________________________________|_________________________ ____________ V C E.g. Vc = 2 and Cc = 1.999999999 is still enough Okay on tests and HW to ignore knife-edge cases where all choices give the same payoff Not okay to make false inferences. Don’t say more than you know. Wrong to claim that C would choose N because C is nice and I does better with N. Wrong to say that C would choose RF to spite I. If we think that C cares about I in these ways, it should show up in pay-offs. Technically speaking, there are two equilibria with V=C If C ≤ V, RE is Inc RF, Chal N if RF, FR if N (Inc Wins) If C ≥ V, RE is Inc N, Chal N if RF, N if N (Inc Wins) Not too helpful to know this. Only happens in one special case. In the second part of the course We are going to have to worry about multiple equilibria...