2. 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?

3. 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

4. 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

5. 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)

6. 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?

7. 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?

8. 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.”

9. 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?

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

11. 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?

12. 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

13. 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

14. 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

15. 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

16. 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

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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. The Tantrum Game

29. Kids Have Commitment Strategies Too

30. 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?