《法律经济学》课程PPT教学课件（法律的经济分析）经济学与法律的对话（大卫·弗里德曼）L&E 2 16 Value of Life

Game Theory The Problem of Strategic Behavior What I do depends on what he does and .. ·Vice versa

Game Theory • The Problem of Strategic Behavior • What I do depends on what he does and … • Vice versa

What Von Neumann Was Trying to Do A general solution to strategic behavior how each player should play And will play,being rational And assuming the other players are .A solution that would cover ·Economics ·Politics ·foreign policy ·poker,.. But what he actually did was

What Von Neumann Was Trying to Do • A general solution to strategic behavior • how each player should play • And will play, being rational • And assuming the other players are • A solution that would cover • Economics • Politics • foreign policy • poker, … •But what he actually did was

Two Player Fixed Sum Game Fixed Sum:What helps me hurts you Strategy:A full description of what I will do in any situation Including "flip a coin,if heads do A,if tails do B" Consider "scissors paper stone"where being predictable loses Solution concept:A pair of strategies such that each is best against the other Does not include the benefit of stealing candy from babies Von Neumann demonstrated how to find the solution for any such game Provided,of course,that you have unlimited computing power to do it with

Two Player Fixed Sum Game • Fixed Sum: What helps me hurts you • Strategy: A full description of what I will do in any situation • Including “flip a coin, if heads do A, if tails do B” • Consider ”scissors paper stone” where being predictable loses • Solution concept: A pair of strategies • such that each is best against the other • Does not include the benefit of stealing candy from babies • Von Neumann demonstrated how to find the solution for any such game • Provided, of course, that you have unlimited computing power to do it with

Scissors Paper Stone 。The solution: Roll a die out of sight of your opponent .1-2 scissors,3-4 paper,5-6 stone Whatever your strategy,I win 1/3rd,lose 1/3rd,tie 1/3rd ·Average payout zero If you follow the same strategy,whatever I do gets the same average payout So a Von Neumann solution And it does not matter if you know my strategy As long as you can't see the die And similarly if I know yours Which is true in general of a VN solution

Scissors Paper Stone • The solution: • Roll a die out of sight of your opponent • 1-2 scissors, 3-4 paper, 5-6 stone • Whatever your strategy, I win 1/3rd, lose 1/3rd, tie 1/3rd • Average payout zero • If you follow the same strategy, whatever I do gets the same average payout • So a Von Neumann solution • And it does not matter if you know my strategy • As long as you can’t see the die • And similarly if I know yours • Which is true in general of a VN solution

Many Player Not Fixed Sum VN Solution concept:A set of outcomes (who gets what) Such that any outcome not in the set is dominated by one in the set Where one outcome is dominated by another if The people who prefer it(get more in it) Are sufficient,working together,to get it There may be many different solutions Each containing many outcomes So a "solution"in a very weak sense

Many Player Not Fixed Sum • VN Solution concept: A set of outcomes (who gets what) • Such that any outcome not in the set is dominated by one in the set • Where one outcome is dominated by another if • The people who prefer it (get more in it) • Are sufficient, working together, to get it • There may be many different solutions • Each containing many outcomes • So a “solution” in a very weak sense

Three Player Majority Vote:Allocating S1 ·Solution:(.5,.5,0),(0,.5,.5)(.5,0,.5) Consider any other allocation of the dollar There is always one of these that two people prefer So every other allocation is dominated by one of these Solution:(.1,x,.9-x)for all values of 0>x>.9 Also a solution,but one that includes An infinite number of allocations Try to find an allocation that isn't dominated by one member of either the first or the second set of allocations

Three Player Majority Vote: Allocating $1 • Solution: (.5,.5,0), (0,.5,.5) (.5,0,.5) • Consider any other allocation of the dollar • There is always one of these that two people prefer • So every other allocation is dominated by one of these • Solution: (.1, x, .9-x) for all values of 0>x>.9 • Also a solution, but one that includes • An infinite number of allocations • Try to find an allocation that isn’t dominated by one member of either the first or the second set of allocations

Bilateral Monopoly .Selling an apple ·Putting a child to bed •A Doomsday Machine

Bilateral Monopoly •Selling an apple •Putting a child to bed •A Doomsday Machine

The Human Doomsday Machine Defer to me or I beat you up .A fight hurts both of us,but... You don't want to be hurt,so I don't have to beat you up Hawk/Dove game Equilibrium number of hawks Why crimes of passion can be deterred

The Human Doomsday Machine •Defer to me or I beat you up • A fight hurts both of us, but … • You don’t want to be hurt, so I don’t have to beat you up •Hawk/Dove game • Equilibrium number of hawks • Why crimes of passion can be deterred

Economics of Vice and Virtue Economics of vice:The bully strategy ·Economics of virtue Why are there people who won't steal Even if they are sure nobody is looking? What if your utility function was written on your forehead? The cost to me of hiring someone who will steal from me Is greater than the benefit to him of stealing from me So I will pay the honest man more than enough more so that honesty pays Your utility function is written on your forehead ·Vith a fuzzy pencil ·So honesty pays Unless you are a very talented con man

Economics of Vice and Virtue • Economics of vice: The bully strategy • Economics of virtue • Why are there people who won’t steal • Even if they are sure nobody is looking? • What if your utility function was written on your forehead? • The cost to me of hiring someone who will steal from me • Is greater than the benefit to him of stealing from me • So I will pay the honest man more than enough more so that honesty pays • Your utility function is written on your forehead • With a fuzzy pencil • So honesty pays • Unless you are a very talented con man

Implication of the economics The bully strategy only works for involuntary interactions If you announce at the employment interview that you beat people up if they don't do what you want ·You don't get the job The virtue strategy only works for voluntary interactions So a society where more interaction is voluntary will have less vice and more virtue. ·Nicer people

Implication of the economics • The bully strategy only works for involuntary interactions • If you announce at the employment interview that you beat people up if they don’t do what you want • You don’t get the job • The virtue strategy only works for voluntary interactions • So a society where more interaction is voluntary will have less vice and more virtue. • Nicer people