Econ 522 Economics of LawReminderLast week, we…Slide 3A brief introduction to game theoryA classic example: the Prisoner’s DilemmaIn two-player games with finite actions, one way to present game is payoff matrixNash EquilibriumA strategy profile is a Nash Equilibrium if no player can gain by deviatingIn two-player games, we find Nash equilibria by highlighting best responsesSome games will have more than one equilibriumSometimes, there will be a “good” and a “bad” equilibriumSome games don’t have any equilibrium where players only play one actionThat’s a very quick introduction to static gamesSlide 14Why do we need property law in the first place?Slide 17So how do we fix the problem?Slide 19So the idea here…But once we have property rights, yours will sometimes conflict with mineOverview of Property LawAnswers to many of these seem obviousHow do we design property law to achieve efficient outcomes?Slide 24How should property rights be allocated to achieve efficiency?The Coase TheoremExample of Coase: you have a car worth $3,000 to you, $4,000 to meAnother example: you want to have a party in the house next door to mineThe conditions for this to holdCoase’s example: a rancher and a farmerRancher’s versus farmer’s rightsOpen range versus closed rangeCoase: either law will lead to efficiencyNote that there’s no sense of “blame” hereRancher and farmer: numerical exampleOther examples from CoaseQuoting from Coase (p. 13):Slide 39What does Coase mean by “a cost for both parties”?So, summing up…Slide 41One early, “classic” property law caseSlide 44Same tradeoff we saw earlier:Doesn’t Coase make Pierson v Post irrelevant?Transaction costsQuoting Coase…We can see the Coase Theorem as either a positive or negative resultMany externalities can be thought of as missing property rightsThat’s it for todayEcon 522Economics of LawDan QuintSpring 2014Lecture 42HW1 due noon Thursday via Learn@UWIf you want to read ahead for Wednesday:Harold Demsetz, “Toward a Theory of Property Rights”Reminder3Defined efficiencyMaximizing total surplus achieved by everyone in society……with value measured by willingness-to-payAsked whether efficiency is a good normative goal for a legal systemPosner: yes, because ex ante (before we knew which part we would play), we’d all agree to efficient rulesCooter and Ulen: yes, because even if society has other goals in mind, such as redistribution, it’s better to make the law efficient and achieve redistribution through taxesOpen discussion questionWhat are other plausible normative goals for a legal system?When would you expect them to conflict with efficiency?Last week, we…44Some basicgame theory55Today, we focus on static gamesAlso known as simultaneous-move gamesA static game is completely described by three things:Who the players areWhat actions are available to each playerWhat payoff each player will get, as a function ofhis own action, andthe actions of the other playersAny complete description of these three things fully characterizes a static gameA brief introduction to game theory66(Story)Players: player 1 and player 2Two actions available to each player: rat on the other, or keep mumPayoffs:u1(mum, mum) = -1u1(rat, mum) = 0u1(mum, rat) = -10u1(rat,rat) = -5Same for player 2A classic example: the Prisoner’s Dilemma77In two-player games with finite actions, one way to present game is payoff matrix-1, -1 -10, 00, -10 -5, -5Mum RatMumRatPlayer 2’s ActionPlayer 1’s ActionPlayer 1’s Payoff Player 2’s PayoffAlways Player 188We solve a game by looking for a Nash equilibriumNash equilibrium is a strategy profile (an action for each player) such that:No player can improve his payoff by switching to a different action……given what his opponent/opponents are doingNash Equilibrium99If any player can improvehis payoff by changing hisaction, given his opponents’actions, then it is not a NashequilibriumIs (Mum, Mum) an equilibrium?No, if player 2 is playing Mumplayer 1 gains by deviatingA strategy profile is a Nash Equilibrium if no player can gain by deviating-1, -1 -10, 00, -10 -5, -5Mum RatMumRatPlayer 2’s ActionPlayer 1’s Action1010My best response to a particular play by the other player is whichever action(s) give me the highest payoffTo find Nash Equilibria…Circle payoff from player 1’sbest response to each action by his opponentCircle payoff from player 2’sbest response to each actionAny box with both payoffscircled is an equilibriumBecause each player is playinga best-response to his opponent’s action……so neither one can improve by changing his strategyIn two-player games, we find Nash equilibria by highlighting best responses-1, -1 -10, 00, -10 -5, -5Mum RatMumRatPlayer 2’s ActionPlayer 1’s Action1111Another classic: Battle of the Sexes(Story)Circle player 1’sbest responsesCircle player 2’sbest responsesWe find two equilibria: (ballgame, ballgame) and (opera, opera)Game theory usually doesn’t have that much to say about which equilibrium will get played when there are more than oneSome games will have more than one equilibrium6, 3 0, 00, 0 3, 6Baseball Game OperaBaseballGameOperaPlayer 2’s ActionPlayer 1’s Action1212Growth model(Story)Circle player 1’sbest responsesCircle player 2’sbest responsesTwo equilibria: (invest, invest)and (consume, consume)Some papers explain differences in growth across countries by saying some are in “good” equilibrium and some are in “bad” oneSometimes, there will be a “good” and a “bad” equilibrium2, 2 0, 11, 0 1, 1Invest ConsumeInvestConsumePlayer 2’s ActionPlayer 1’s Action1313Scissors, Paper, Rock for $1Look for Nash Equilibria by circling best responsesNo square with both payoffs circledNo equilibrium where each player plays a single actionIn this class, we’ll focus on games with a pure-strategyNash equilibriumSome games don’t have any equilibrium where players only play one action0, 0 1, -1-1, 1 0, 0Scissors PaperScissorsPaperPlayer 2’s ActionPlayer 1’s Action-1, 11, -1Rock1, -1 -1, 1Rock0, 01414Now on to…That’s a very quick introduction to static games1515Property Law1616We already saw one reasonTragedy of Commons – overuse of land is held in commonFor another example,
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