Ex Post/Ex Ante: The Idea In Ordinary Life Should I go home by 880 or local streets? Should I have bought that lottery ticket? Should you have gone to law school? In Employment Do we pay salesmen by the hour? Or by a commission on each sale? In The Context of Law and incentives Do we punish bad outcomes, or Inputs that produce them?

Why Punish Attempts? Why are you arresting me? The bullet hit the tree. The man I was shooting at is fine The tree is fine To stack an ex ante punishment on an ex post punishment Why? Because we are not willing to impose an adequate ex post punishment

Advantages of Ex-Post Punishment Exploits actor’s private information I can monitor myself at no cost And can see and know things the external regulator cannot Rather like the advantage of an effluent fee over regulation Which is also an ex-post punishment Court can observe damage instead of guesstimating probability and damage Probably lower enforcement costs easier to spot crashes than speeders and a lot fewer of them

Disadvantages of Ex-Post Punishment Wrong. Punishment prevents by deterrence We want to prevent, not punish? Ex-post requires large punishment with low probability People are risk averse And may be judgement proof And non-monetary payments are inefficient But there is an organ shortage … (We will return to this)

Why There Should Not Be Pure Ex-Ante Systems A Small ex-post punishment does not have the problems of ex-post Does have the advantages So why not always supplement ex-ante with ex-post? Are there any counter-examples?

Ex Post + Insurance Could Provide a Market Mechanism to Generate Ex-Ante Rules To drive, I require adequate liability insurance The insurance company can set any rules it wants as a condition So makes the optimal tradeoff between risk aversion and moral hazard How do we enforce the rules? Convert traffic cops into private contractors enforcing the contract Uber for (private) speeding fines?

Should We Punish Voodoo Killers? More generally, should we punish impossible attempts? In some sense, all failed attempts were impossible So this brings us back to “should we punish attempts.”

The Moral Argument for Punishing Attempts Punish on the basis of moral guilt Being a bad shot is not a moral virtue Which brings us to the problem of moral luck Should you think worse of an ex-Nazi concentration camp guard than of someone who would have been one If he happened to be born in that time and place?

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

The Coward’s Solution: Evasion Perfect competition Monopoly Doesn’t work for oligopoly When my firm expands output Will my competitors drop their price to compete Or hold price, accept fewer sales?

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 Party Fixed Sum Game Fixed Sum: What helps me hurts you So no room for bargaining, threats or bluffs I don’t have to do it to hurt you, since doing it helps me Strategy: A full description of what I will do in any situation 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

From this standpoint, chess is trivial Given enough computing power All you have to do is to look at all possible games Assume each player makes the right last move The other player makes the right move before that, knowing what the last move will be And then work backwards Until you get to the first move. Select one for which at the end of the sequence white wins If there is no such, then black wins Or the solution is a stalemate The number of possible games is large

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 $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

A Doomsday Machine Dr. Strangelove The two we built If you are the last one out of the vault What is the last thing you do? Cut the wire

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 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

Prisoner’s Dilemma Mike Confess Say Nothing Joe 2 years, 2 years 3 months, 5 years 5 years, 3 months 6 months, 6 months Dominance as a solution concept if choice A is better for me than choice B Whatever the other player does Then A dominates B “Confess” dominates “Say Nothing” for both criminals So they get 2 years each instead of 6 months each

Repeated Prisoner’s Dilemma With a fixed number of plays Both Criminals know they will betray on the last round So … A good reason not to get into that game

Consider Plea Bargaining as a Real Prisoner’s Dilemma If most defendants cop a plea The D.A. can spend lots of resources on those who don’t Which raises the risk to those who don’t Which makes those who do willing to accept worse terms They might all be better off going to trial Since the D.A. doesn’t have the resources to convict them all

Implications Commitment strategies matter Bilateral monopoly with a wide range Makes it in each party’s interest to spend a lot on winning Think of it as an example of rent seeking So avoid legal rules that create that game Such as specific performance Or injunctions Crimes of passion are to some degree deterrable

Some More Approaches to Solving Games Nash Equilibrium Each player is acting optimally, given what every other player is doing This assumes we can freeze the other players while I adjust my strategy But what does “freeze” mean? Consider Oligopoly: A few firms in competition When I increase my output The other firms cannot keep both price and quantity fixed Because a larger quantity (due to my increase) implies a lower price If we assume they hold quantity fixed we get one equilibrium If we assume they hold price fixed, a different equilibrium So the outcome depends on how we define a strategy

Subgame Perfect Equilibrium A two player sequential game First I make a choice Then you make a choice Then I … And each sequence of choices ends with a payoff for each of us Go to the last choice, assume the chooser takes the branch that gives him the higher payoff. Cross off the other branch Repeat as you go back up the tree diagram But this assumes that each player will make the choice that maximizes his return then Instead of committing himself to the other choice, so as to influence the other player’s decision “If you do that I won’t do what gives me the best payoff but what gives you the worst” “So don’t.” Looks like my chess solution, but this time not a fixed sum game

The Tantrum Game

Kids Have Commitment Strategies Too

To Think About Why is Marriage Different? Why are patent law and copyright law so different? Why are some torts strict liability, some negligence? How, in principle, do you set the punishment for a crime? Why do we have both criminal law and tort law?