Here's another payoff matrix similar to one from last class.

Both United and TWA have a dominant strategy.
TWA raises, and UNITED doesn't

The equilibrium is the best for the two--note that the combined payoff is $12,000 which is greater than the combined payoff in any other cell.

Now, let's revisit the Prisoner's Dilemma but apply it more concretely to an economic situation.

In a PD game, both players have dominant strategies and there is one equilibrium solution. However, it is not the best outcome in terms of the players' combined welfare. That's the paradox of the game--people could do better if they could figure how to collaborate reliably rather than playing a strategic game....

Everyday examples of PDs are:

people standing up at a concert (no one can see any better than if everyone remained seated).

people talking loudly at a party (no one can hear any better than if everyone spoke quietly).

An interesting economic example:

When the federal government forbade tobacco companies to advertise on TV their profits went way up. Why? Because they no longer spent money on advertising--and yet this didn't hurt their sales because they were all equally affected by the ban. The money they spent on advertising before the ban was like the people all standing up at the concert, or talking loudly at the party...because all the companies were advertising equally fiercely, none was deriving any benefits from it in terms of market share.

Two Firms in a Prisoner's Dilemma

In this case, they would actually be better off if they didn't raise price...
but they both do for fear the other might....

Now, let's consider a payoff matrix in which there are no dominant strategies but there are nonetheless two equilibria.

Two Firms, No Dominant Strategies and Two Equilibria

Firm A does not have a dominant strategy. If firm B raises price it should not raise. But if Firm B doesn't not raise price it should raise.

But Firm A still knows what is best for it GIVEN what firm B does--it has two preferred cells, the lower left and the upper right.

To determine if these are Nash equilibria, we have to ask whether Firm B would prefer these cells too.

So now look at Firm B:

If Firm A raises price, Firm B should not raise price. If Firm A does not raise price, Firm B should raise price. So it prefers those two cells two.

We can't predict which of the two the firms will end up in, but we can predict it will be one of those two--because in those two cells each firm is doing the best it can given what the other firm is doing.

Now let's try an Ultimatum Game.

I have four quarters.
I give Person A the four quarters and instruct him to make a take it or leave it offer to Person B.
If Person B accepts the offer they can keep the money.
If Person B does not accept the offer they must give the money back.

Person A offers Person B one quarter.
She refuses it.
Why, we asked her.
"Because it's unfair," she explains.
There are catcalls.
"But you could have had twenty five cents and now you got nothing."

In fact, economic self-interest suggests that Person B should accept ANY non-zero offer, no matter how low, because he or she will then get SOMETHING, rather than nothing.

But experimental studies show that people are often willing to forego a benefit (and inflict a punishment on another person) to defend a norm of fairness.

A norm of fairness is particularly strong for "windfall" gains. Clearly, in this example, Person A did nothing to "deserve" a larger share than Person B.

By refusing the offer, Person B sent a signal that unfair behavior was not acceptable.

Interestingly, this signal gives an incentive to self-interested types that they need to take fairness into account--because if they make an unfair offer it might get refused, and they might suffer as a result....

It's a fascinating example of a social norm that helps enforce a kind of social cooperation that can benefit everyone, and prevent us from getting into Prisoner's Dilemmas.

Restaurant tipping--even in a place that you don't expect to return to, is another example of norm-driven behavior that seems to violate the presumption that people always act in narrowly self-interested ways.