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ECON 201
Corey Van De Waal

up tailsuptails oror up headsupheads either it e the same side up then player 1 T1 11 1H1 11 1time show opposite sides up then player place last 12HTand from he extensive form and the normal formhand Lecture 201game their in offs as follows2 Player 2111pennies penny player a Player 111from take matching 11TTthedollarHTafriendsHHIf when they open their hands the pennies 2 gets a dollar from player 1RecallthematchingpenniesgamefromlasttimeRecallTwofriendstakeapennyintheirhandandplaceiteitherTwogetsadollarfromplayer2getsLets represent this game in both tIf when they open their hands the pennies arThey have agreed to payMATCHING PENNIES11ofthere will exist probability a with H completely determined by ame is finitegplays 2 ghtly more complex Battle of the T prob1 strategies then all of the strategies in e the players probability distribution and the Player the mixed strategy Nash equilibrium for ife has no pure strategy Nash equilibrium ies gpayoffsers mixed strategy is payoffs do depend upon the probability spayoffsifPlayer2playsHwithaprobabilityof1s ers mix strateyPlayerla ppyggT1 11 1H1 11 1consider 12H probsconsiderPlayer1lets and plays T with a probability of 1 distribution and hence a playRemember that we said that this gama mixed strategy Nash equilibriumMIXED STRATEGY NASH EQUILIBRIAIf a player is going to mix on a set of pure Of course the other playersLets clarify how this works by solving FirstletFirstHowever if these the set must have the same payoffHencover these strategies is arbitrarythe matching pennies game and then the sliSexes gamethe other players
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