Econ 522 Economics of LawTuesday, we discussed efficiencyToday:But first, a quick digression…Slide 4A brief introduction to game theoryA classic example: the Prisoner’s DilemmaIn two-player games with finite actions, one way to present game is payoff matrixDominant StrategiesNash 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 16Why do we need property law at all?Why do we need property law?So how do we fix the problem?Slide 21So the idea here…Overview of Property LawAnswers to many of these seem obviousOne early, “classic” property law casePierson v. PostSame tradeoff we saw earlier:Slide 27The Coase TheoremAn example of the Coase TheoremCoaseExample from Coase – a rancher and a farmerSlide 33Other examples from CoaseQuoting from Coase (p. 13):Slide 36Tuesday: transaction costsEcon 522Economics of LawDan QuintFall 2009Lecture 32efficiency: “when there is no way to make some people in the economy better off, without making others worse off by more”saw some examples of forces that lead to inefficiencyexternalities; barriers to trade; monopoly/private information; taxesconsidered limitations of efficiencydoesn’t address equity/distribution; assumes value = willingness to pay (everything is monetizable); only considers outcomes, not processsaw two arguments why the law should be designed to be efficientPosner: ex-ante consentCooter/Ulen: if we’re worried about distribution/equity, better to design the law to be efficient, use tax system to redistribute wealthTuesday, we discussed efficiency3introduce some basic game theorybegin property lawToday:4I don’t have many “absolute beliefs” about economicsSome people doI hope that doesn’t make things too confusingRelatedly, if I don’t see economics as a set of rules to memorize, how do I know what I know?I need to see a model, or an example, that demonstrates itBut first, a quick digression…5Some basicgame theory6Today, 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 theory7(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 Dilemma8In 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 19In the Prisoner’s Dilemma, one player’s best action is the same, regardless of what his opponent doesThis is called a dominant strategyRegardless of what he thinks 2 will do, 1 will choose to play RatDominant Strategies-1, -1 -10, 00, -10 -5, -5Mum RatMumRatPlayer 2’s ActionPlayer 1’s Action10In most games, players won’t have a single move that’s always bestWe 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 Equilibrium11Is (Mum, Mum) an equilibrium?No, if player 2 is playing Mumplayer 1 gains by deviatingIf any player can improvehis payoff by changing hisaction, given his opponents’actions, then it is not a NashequilibriumA 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 Action12Given a possible action by my opponent, my best response is whatever 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 equilibriumIn the Prisoner’s Dilemma game, (Rat, Rat), or “Both players play Rat”, is the only Nash equilibriumIn two-player games, we find Nash equilibria by highlighting best responses-1, -1 -10, 00, -10 -5, -5Mum RatMumRatPlayer 2’s ActionPlayer 1’s Action13Another 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 Action14Growth 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 Action15Scissors, 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, 016Now on to…That’s a very quick introduction to static games17Property Law18In a sense, same question as,why do we prefer organized society of any sort to anarchy?Suppose there are two neighboring farmersEach can either farm his own land, or steal crops from his
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