Lecture Notes: Nov. 4

Econ. 103, Fall 2002, Prof. Nancy Folbre

 Final points from Chapter 9:

Review profit maximizing point for a firm engaging in imperfect competition.

Go over deadweight loss that results (under these conditions, a firm produces less than they would under conditions of perfect competition).

Remember the "hurdle" method of price discrimination.

Chapter 10

This is about the REAL world.

Strategic games--situations in which the impact of what you do depends on what other people do.

Key technical skills: learn how to interpret payoff matrices and decision trees.

Most important concept: the prisoner's dilemma, a situation in which everyone pursues their own self-interest but is worse off than if they had agreed to cooperate.

War is a strategic game, as is monopolistic competition.

Games can be defined by their players, their possible strategies, and payoff matrix.

Examples of payoff matrices:

dominant strategy--yields a payoff no matter what you choose

dominated strategy--any other strategy available to a player who has a dominant strategy

Nash equilibrium--any combination of strategies in which each player's strategy is his best choice, given the other player's strategies....

give some examples of these:

10.1 Payoff matrix for an advertising game:

What should United do?

First, ask what United should do if TWA raises ad spending (cover the rightmost column):

United should raise ad spending

Second, ask what United should do if TWA does not raise ad spending (cover the leftmost column):

United should raise ad spending

Since they should do the same thing no matter what TWA does, United has a DOMINANT strategy--raise ad spending

TWA also has DOMINANT STRATEGY (THE SAME ONE)

IF THEY BOTH PLAY THEIR DOMINANT STRATEGY, THEY WILL BE IN NASH EQUILIBRIUM: NO ONE HAS ANY INCENTIVE TO DEVIATE FROM THEIR CURRENT STRATEGY.

Exercise 10.1:

What's the equilibrium solution?

TWA raises, and UNITED doesn't

Excerpt from The Invisible Heart: Economics and Family Values

The Nice Person's Dilemma

Economists have a parable that emphasizes the difficulties of cooperation. It is called the Prisoner's Dilemma. Two men who have committed a crime are swiftly apprehended by the police. They are taken to separate interrogation rooms. The prosecutor doesn't have enough evidence to convict without a confession. If both suspects deny any involvement in the crime, they could get off free. Each man knows that his best strategy is denial, if he can be sure that the other will do the same. Each has promised, ahead of time, never to rat on his pal.

But is there honor among thieves? The risk is obvious. Once nailed by the police, the suspect in the other room may opt for an opportunistic strategy, telling everything he knows in return for a short, suspended sentence. An individual who remains loyal while his partner defects suffers the greatest penalty. The cops know this and do everything they can to sow seeds of doubt. The prisoners lose faith in one another and confess at the same time. Both go to jail without any credit for helping convict the other. From the cops' point of view, it's the best possible outcome. From the prisoners' point of view it's the worst possible outcome. The opportunistic strategy, which entails breaking a promise, ends up making both prisoners worse off.

Prisoner's Dilemma:

The economist Amartya Sen has long argued that the Prisoner's Dilemma is really misnamed, because it applies to many situations that have nothing to do with crime, situations in which everyone would benefit from cooperation, but is afraid that someone else will defect or cheat. An arms agreement is an obvious example, or an effort to protect a common resource, such as a fish population. These agreements work only if everyone cooperates. For students, the best example is a study group. They can have more fun and get more done by collaborating, but they feel ripped off when some people show up just to copy down what the others have figured out.

We could call it the Nice Person's Dilemma. A person does something to help another person. If the other reciprocates, both will end up better off; if not, the nice person loses. Nice gals and guys finish last. It has long been observed that such dilemmas are easier to resolve among people who know each other well than among strangers. Many communities come up with pretty effective ways of governing access to common resources. Identification with a community is important because it encourages members to care about others in the group, emphasizing their common interests and restricting their contact with outsiders.

A kind of virtuous circle comes into play. Efforts to increase the probability of cooperation reward the payoff to cooperation. As Jane Mansbridge puts it in her classic essay "On the Relation of Altruism and Self-Interest:"

Arrangements that generate some self-interest return to unselfish behavior create an "ecological niche" that helps sustain that unselfish behavior. Arrangements that make unselfishness less costly in narrowly self-interested terms increase the degree to which individuals feel they can afford to indulge their feelings of empathy and their moral commitments, as well as their readiness to foster empathy and moral commitments in their children.

The big question is how such "ecological niches" for unselfishness are established and defended.

Biologists explore similar concerns when they consider the ways in which groups or teams, rather than individuals, may compete. In some circumstances, the group or team with the highest level of cooperation is likely to win.

Both biologists and economists tend to assume that solidarity and care are completely natural within families. As the previous chapter emphasized, however, there was nothing natural about rules and laws that forced women to specialize in family care. Now that women have gained rights similar to those of men, they are entering a world in which they have more freedom to consider the penalties imposed on unselfish behavior.

Consider the Good Parent's Dilemma. Two people decide to rear a child, but one of them makes more sacrifices than the other. Usually it's the mother who agrees to take time away from her career to stay home with the baby, and to move wherever the father's career dictates, so he can earn money to support the family. "Later on," she might say, "It will be my turn. We'll put my career first, and you can be the Good Parent." Sometimes, this implicit agreement works just fine. Sometimes it doesn't, because it involves one of those aspects of the marriage contract that is not enforceable by law. The only thing the Good Parent can do if the other parent refuses to take their turn is to end the relationship, which can have unpleasant consequences for both parents and children.

This risk of default on an implicit agreement is not limited to couple dynamics. It also faces parents in their relationships with their children, which also involve an implicit contract: we take care of you, and when you're grown-up you will take care of us--if and when we really need your help. Most children respect this implicit contract, though teenagers have been heard to mutter "I didn't ask to be born into this family." They're right, of course. Precisely because they feel they have not been given an individual choice, some adult children default on responsibilities to parents. If and when that happens, there's not much parents can do about it unless they have enough wealth to threaten disinheritance.

Individual decisions are made in a social context. What we want and how we will behave is strongly affected by our perceptions of what other people want and how they are likely to behave. Moral values and social norms probably evolved because they encourage cooperative behavior that is productive in the long run. Norms of fairness and reciprocity are surprisingly robust.

Economists have developed an experiment that illustrates their impact. You can play it with your friends more easily than most card games. Take two people aside and give one of them ten one dollar bills. The person with the cash is required to make a take-it-or-leave-it offer to share part of this money with the other person. If the other person accepts the offer, they both can keep the amounts agreed upon. If the other person refuses the offer, however, the money must be returned. For instance, if I start out with the cash, I might offer you three dollars. If you accept, you get three and I get seven. If you refuse, neither of us gets anything.

It's called an Ultimatum Game. Where a windfall is concerned--money that wasn't earned or deserved in any way--most people think that a fifty/fifty split is fair. Furthermore, a significant percentage will turn down a less-than-equal offer, even though this leaves them worse off than they would have been had they accepted. In the example above, many will turn down the three dollars offered, on the grounds that it is unfair. They want a fair share, or they want nothing at all, as if they intend to punish those who offer less.

When I have conducted this experiment in my own classes, students have been skeptical, insisting that there would be less concern for fairness if larger--and actual-- amounts of money were involved. As one cynic put it, "You should change the $10 to $10,000,000 and watch the fairness freaks crumble." But Ultimatum Games have been conducted in many different places, and under many different conditions, with very large sums of money. The results are remarkably consistent.

Most of the economists who conduct such experiments are interested in the way people think strategically. I am more interested in how the players feel. Does concern for other people's welfare affect their perception of their own payoff? Think back to the Nice Person's Dilemma. If you love the person you are helping, then you are less likely to be inhibited by fear that you will be ripped off.

But love, affection, and connection are aspects of the cooperation game that experimental economists have largely neglected. Consider the maxim traditionally known as the Golden Rule: Do unto others as you would have them do unto you. This is not exactly a rule of reciprocity. It's a rule of empathy. It asks you to think about what it would feel like to be in the other person's situation. It is related to another prescription for altruism: "Love thy neighbor as thyself." In this context, it matters whether or not you actually know who your neighbors are. It also matters how much choice you have in determining who they will be. Some neighbors, after all, may be more lovable than others.

Some multiple choice exercises:

If both players of a game choose the best strategy available given the other player's strategies, the game is a(n).

A) dominant strategy

B) dominated strategy

C) Nash equilibrium

D) ultimatum equilibrium

E) Rambler equilibrium

 

The correct answer is C.

The prisoner's dilemma refers to games where:

A) neither player has a dominant strategy

B) one player has dominant strategy and the other does not

C) both players have a dominant strategy

D) both players have a dominant strategy which results in the largest possible payoff

E) both players have a dominant strategy which results in a lower payoff than their dominated strategies

The correct answer is E.