Hi. In this set of lectures we are talking about mechanism design. When you think
about designing mechanisms in effect what we are doing, we are designing incentive
structures so that we get the sort of outcomes we want. Now to get those
outcomes often what we're trying to do is we're trying to induce people into taking
the right kinds of effort. So, for example, if I'm an employer, what I'd like
to do is I'd like to write a contract so that people actually put forth a lot of
effort in their work as opposed to slacking off. Alternatively, if I'm
auctioning something off, what I'd like people to do is reveal their information.
I like them to reveal how much they value something. So, another feature that we
want when we construct mechanisms is revelation of information. So, when I
think about mechanism design, two of the core problems are dealing with these
hidden actions and dealing with hidden information. So, how do we write
mechanisms or incentive structures that overcome those two problems? That's what
we're going to talk about in this lecture in a really abstract way. So let's start
out by talking about [inaudible] matching. And what do I mean? What I mean is this.
Is, you're an employer, and let's suppose you hire people who make pots. So they
throw pots. These people can put forth effort. They can put forth a lot of
effort, or they can just slack off, and not put forth much effort at all. What
we'd like them to do is put forth a lot of effort. But I can't tell. The only way I
can tell is if I sat there and monitored them all the time, which would be really,
really costly. So instead, what I'd like to is I'd like to write some sort of
contract, so that they always put forth the right amount of effort. Now, sometimes
these are called moral hazard problems. And the reason is this, is that, because
I'm not being watched if I'm the employee, I sort of have some moral hazard. I could,
I could cheat, I could slack off. And so the question is, how do people write
contracts to overcome these moral hazard problems? So let's write down a simple
model and see sorta how it works. So let's suppose I get some workers, and these
workers can take some effort, they can take an effort level zero or an effort
level one. And again, that's not gonna be observed. What is going to be observed is
the outcome, I'm gonna see whether the pot is good or whether the pot that they made
is bad, or that it's floppy. So I don't know whether it's gonna be good or it's
gonna be a bad outcome. But I do know this, I know that if they're diligent and
they put in an effort of one, the, the probability that the output is good is, is
one, it's for sure gonna be good. But I also have a slack off. There's some
probability P that it's still gonna work. That they're gonna get a functional clay
pot. What I'd like to do is I wanna induce this effort level of one, but how do I do
it? The reason it's hard to do is because it's costly to put forward that effort. So
worker is gonna pay this cost C. Of working hard, and they'd rather not.
They'd rather slack off. So what I wanna do is I wanna write a contract so they put
forth the right level of effort. Well, how do I do it? Well, it turns out its not
very complicated. What I wanna do is I want a contract that says, I'll pay you M,
I'll give you M dollars if it's good, and I'll pay you nothing if it's bad. Here's
the core idea. The idea's I want what's known as incentive compatibility.
Incentive compatibility means that it makes sense for the worker to put in the
effort. So I wanna [inaudible] money M, so that everybody's gonna put forward the
effort. So how do I figure that out? Well, it's a very simple model. What's their
payout if they put forward the effort? Well that's M because they are gonna get
the money M because the outcome is gonna be good for sure. But then it's gonna by
minus C because they are gonna pay the cost C. What's their payout if they don't
put forth the effort? Well, it's gonna be P times M. Because, with probability P,
they're actually still gonna get a good outcome. And so they're gonna get P times
M, which is the payout for getting a good outcome. So the incentive compatibility
constraint, which is that it makes more sense for them to work hard, means that
M-C has gotta be bigger than [inaudible]. And if I manipulate things around, I get
the following Inequality that I've got to pay them at least C over one minus P. So
this is the solution. If I want to induce people to work hard, the amount of money
that I've got to pay them for a good clay pot is gonna be the cost of effort divided
by one minus the probability that if they were lazy, they got a good outcome anyway,
Me, very straightforward. Remember when we do models, somebody's going to get stuff
for free? Well, here we're going to get something for free as well. These are
sometimes called comparative statics. So, [inaudible] you make in comparative
statics is here's my equilibrium level of payment. This is what I should pay people
to make a good clay pot. But what this tells me is how that varies. As I change
other variables. So, for example, what happens if the cost of effort goes up?
Well, if C goes up, then C over 1-P is going to go up, which means that M has to
go up. But that makes sense. If it's costlier to put forward high effort, then
I'm going to have to pay people more money In order for making a good pot, to induce
them to work hard. What about P, well this complicated; P is the probability that
someone who slacks off still gets a good pot. Well if P goes up, that means that,
so if P goes up that means one minus P. Goes down, but it means one over 1-p goes
up, so it means that m goes up. So what we get here is that if the probability
someone gets a good clay pot anyway. Increases, I also have to pay people more.
And the reason why is because there's, if you think about it, there's more incentive
to slack off. Because there's a higher probability I'm gonna get a good outcome
anyway. So what we get, these comparative statics are that M is increasing, both in
the cost of effort, and in the probability of getting a good outcome even if you're
not putting forward the effort. So we get these nice, sort of, comparative statics
results. Here's maybe the most interesting thing about his whole model. We now know
what the action is. So even though I call this a hidden action problem, if M is
bigger than C over O minus P, I know what the action is. I know the effort is one
because it makes sense for people to put forward high effort. So, I've taken a
situation where I had hidden an action, and now I know the action. However, it
costs me. How much did it cost me? M, how big is M, C over one minus P. Let's now go
to hidden information. What is hidden information? Well, let's suppose you?re an
insurance provider and you don't know whether someone is a safe driver or a
risky driver and what you like to do is not get risky drivers and only get safe
drivers or alternatively you would like to, have risky drivers pay more for their
insurances. Or let's suppose you?re an employer and there is two types of
workers, theirs people that who really have high ability theirs people who are
low ability. What you like to do is, you only like to hire the high ability
workers. So, let's, let's work through that scenario. Let's suppose there's two
types of workers. There's these high ability workers, and there's low ability
workers. And you don't know which is which. We can look at their resumes, but
it's hard to tell. But suppose you know the following is true. Suppose you know
that the cost for these people to work. For high ability workers, it's fairly low
cost to put forward an hour of effort. But for low ability workers, it's higher cost
to put forth an hour of effort. So what you can usually do is say, okay, you can
come to work for me and I'll pay you some amount m. So suppose there is a fixed wage
that you have to pay people, there is a minimum wage. But you say this, But before
you come work for me, what I want you do is work a couple hours in the kitchen for
me, and. You know work a couple hours on this project for me just to see how well
you do. Well let's thi nk about the incentives for these two types of workers.
Let's let k be the number of hours I want to make these people work. If you're a
high ability worker, the cost of working K hours is just K times little C. And you're
going to be willing to do that, you're going to be willing to put in these hours,
as long as K times little C is less than M, the amount of money you're getting
paid. But if you're a low ability worker, if you choose M so that it's less than K
times big C, you're not gonna do it Because your cost, K times big C, is going
to be higher than the benefit, which is M. So what you'd like to do, in a way, is say
the number of hours is equal to M over base C cuz it's maybe you know plus maybe
a little bit here. That way the low ability workers won't take the job but the
high ability workers will. So what you're doing is you're, even though the
information is hidden, you don't know whether someone's low ability or high
ability, this will separate them out. Let's do comparative statics on this, how
does the number of hours depend on M and on C; well as M gets bigger K is gonna get
bigger. But that makes sense. If the job pays more, you're gonna have to make
people work more hours. What about with respect to big C? Well if C goes up, K is
gonna fall. This makes sense as well because if the cost for these [inaudible]
workers goes up then you are not gonna have to make them work as many hours
[inaudible] say look I'm not gonna do it, it's not worth it. Now, these are
sometimes called costly signaling models. And the reason why is this, is that the
high ability workers had to signal, by working K hours, that they're really high
ability. Let's go back to this contract. I've set K so that the high ability
workers are willing to work K hours, but the low ability workers are not. So,
here's what's gonna happen. All the high ability workers are gonna work, none of
the low ability workers are gonna work. So, I've separated them out. So, what I
get is again, the information is no longer hidden. I know whose high a bility, those
who chose to take the job, and I know whose low ability, Those who chose not to
take the job. Alright, so the simple foray and the [inaudible] information gives us
sort of a starting point for thinking about institutions and incentives. So how
we can write down sources of actions, payoffs from those actions to induce right
levels of effort and also to separate out who's of one type, who?s of another type.
What we're going to do next is look at auctions and see how we want to, how we
can use different institutional structures and those create different incentives,
people to take different behaviors and how those different institutional structures
affect the outcome. In some cases they'll have big effects on the outcomes; in other
cases they'll have no effect. All right. Thank you.
