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# Class_4(2) - GameTheory Lecture 4 Outline From previous...

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Econ -171 Introduction to  Game Theory Lecture 4

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Outline From previous class: Learned about NE and MSNE . Saw how to calculate MSNE . Today: An example finding a MSNE . Interpretation of NE and MSNE . Comment on “strategic tensions”. Begin applications of NE . Tomorrow: Continue applications
Finding MSNE Find the MSNE of the following game which has no pure strategy NE .

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Finding MSNE Let p be the probability of P1 playing U and q be the probability of P2 playing L. Remember, in order for a mixed strategy to be a best response, the probabilities must make the EU from their strategies equal.
Finding MSNE Find q a) 1/4 b) 2/7 c) 3/4 d) 5/7 e) ?

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Finding MSNE Find p a) 1/4 b) 2/7 c) 3/4 d) 5/7 e) ?
Finding MSNE The probability of outcomes (U,L) (U,R) (D,L) (D,R) occurring, given each player mixes, are (6/28), (2/28), (15/28), (5/28). P1’s expected payoff from playing the game when both players mix is 2(6/28) + 1(2/28) + 1(15/28) + 4(5/28)

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Interpreting NE Iterated Dominance is a constructive tool to analyze games because it does not assume players know the strategy choices of others (only rationality). In NE , players have beliefs about what the other is doing and those beliefs are self-fulfilling, or consistent with each other- stricter solution concept. Where do beliefs about what other players do come from?
Sources of NE 1. Play Prescription : Some outside party proposes a ‘prescription’ of how to play the game. The prescription is stable, i.e. no player has an incentive to deviate if she thinks others are following the prescription thus a NE .

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Class_4(2) - GameTheory Lecture 4 Outline From previous...

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