Explique y proponga a través de un caso (preferiblemente real) algunas recomendaciones y aspectos a tener en cuenta para prevenir el daño en los

Once during college, an annoying person asked me for game theory help. I offered to help even though it interrupted my own work. It was hard to turn down someone who lived in the same dorm.

I offered to help but wanted something in exchange. The person was a teaching assistant for a non- credit class my friends were taking. He was not being fair to my friends and essentially using his power to fulfill a personal grudge. I asked that he be nicer to my friends and act more professionally. He was furious at my suggestion since he felt it undermined his authority.

So I said I would not help him. I reminded him that I had work to do, so if he could not compensate me for my time, I would resume my studies.

He angrily responded that he did not need my help after all. He actually knew how to do the problem, he indicated, but he just wanted my perspective. And, he continued, the professor was holding office hours the next day, so he would ask someone smarter.

He then walked away, sort of.

As I resumed my studies, he conspicuously sat down at a neighboring table and faked that he was doing work. Every few minutes he peeked over his book to see if I would budge.

But I did not.

After thirty minutes, someone who saw the whole thing came up to me and said, “Presh, I can't believe you aren't helping him with game theory. I mean, I know you don't like him, but come on. He needs your help.”

To which I replied, “I am helping him. If he knew anything about game theory, he would know that I'm not going to tutor him unless he concedes to my request.”

On hearing this, the annoying person left the room and never asked me for help again.

I guess he did not really need my help after all.

I chose my actions because I had total negotiating power—a concept from the ultimatum game.

I Am The Decider!

Imagine you are participating in a college experiment. The researcher hands you $10. You are instructed to propose a split of the money to another person. For instance, you might propose that you keep $7 and the other person gets $3.

If the other person accepts the division, the money is split according to the proposal. If the other person rejects the division, neither person gets anything.

How might you go about deciding a split?

The first thing you can do is diagram the game dynamics.

You are player 1 and will offer money to player 2, an amount between $0.01 and $10. After hearing the offer, player 2 can either accept so the split goes through, or reject and leave both parties with nothing.

The way to read the diagram is from top to bottom: the player depicted in the topmost move goes first, and then the next player goes. However, to solve the game, you want to read the diagram in exactly the opposite way: from bottom to top. Since you start at the end, this technique for solving a game is called backwards induction.

What offers will player 2 accept?

If he rejects an offer, he goes home with nothing. If he cares about getting money, this would suggest that player 2's strategy is to accept any offer that player 1 makes. Even if the offer is for one cent, that is better monetarily than going home with nothing.

In the land of infinite rationality, player 1 understands this, and takes advantage of his bargaining power. Knowing any offer will be accepted, player 1 will offer the smallest amount to player 2—one cent—and basically take the entire pot for himself.

This solution—player 1 gets everything and player 2 gets nothing—is why the game is called the “ultimatum game.” Player 1 has complete negotiating power and knows any ultimatum will be accepted.

But Doesn't Player 2 Have The Power To Punish?

The situation stinks for player 2. It just does not seem fair that player 1 gets everything. I mean, player 2 does have the ability to punish player 1 by rejecting offers. Can that lessen player 1's power?

Imagine player 2 tries to gain power. Before the game starts, player 2 might try to taunt to player 1, “Hey, if you offer me less than a 50-50 split, I will reject it. I don't care if I go home with nothing; I'll

just be happy to know that I hurt you.”

In the theoretical world, player 1 understands this is a non-credible threat. If player 1 does offer a smaller amount, then player 2 faces a one-time decision of some money or no money. In this world, it only matters that one cent is better than nothing. There is no joy in inflicting pain on the other player. And because the game is not repeated, there is no reason player 2 should even care about punishing player 1.

As a technical aside, each offer that player 1 makes actually is a “subgame” where player 2 has to make a decision. Since player 1 always offers one cent and player 2 always accepts, we never observe what would happen if player 1 offers two cents or more.

In theory, player 2 could do whatever he wants—he could reject those higher offers. But as argued above, the only credible thing player 2 would do in any subgame is to accept the offer.

So we call the equilibrium where player 2 accepts any offer and player 1 gets everything the subgame perfect equilibrium. In this game, it is the unique subgame perfect equilibrium.

But That Is Simply Not What Happens In Real Life!

Yes, imagine you are playing this game with your crazy significant other, who is the role of player 2. From experience, you know that your significant other might even reject offers where you give less than 90% of the money.

You'd be wise to forget the subgame perfect equilibrium stuff and make sure to adjust your offer. Your significant other is crazy, after all.

Indeed, experimenters have repeatedly shown that the subgame perfect equilibrium does not happen because people reject offers perceived to be unfair.

But I believe these experiments do not mean game theory is wrong. In fact, they illustrate why game theory is a powerful tool.

It Is All About the Beliefs

A Nash equilibrium is based on your beliefs about other players, and how accurate those beliefs are. The subgame perfect equilibrium is the only Nash equilibrium where both players have infinite reasoning ability and they only care about money.

What people seem to miss is that the ultimatum game really has an infinite number of Nash equilibria.

Let's go back to the game with you and your crazy significant other. Your strategies are something like the following.

Significant Other: “Give me at least 90%, or I reject.”

If you really believe the threat, and it is accurate, the resulting division is a Nash equilibrium of the game. Your significant other is not playing rationally, but the result of you getting $1 and your significant other getting $9 is in fact a Nash equilibrium.

The threat to reject should be non-credible, except that your significant other cares more about money, including things like about power and fairness. There is power in being perceived as crazy.

When Does This Game Happen In Real Life?

The game happens all the time in homes. My brother and I would be arguing about something, like what video game to play. Eventually, my parents would tell us that we could either agree on a game or we would not get to play at all. My older brother would often speak first and pick a game that only he would like. And I was stuck with the game because it was still better than nothing.

A similar situation happens with labor strikes. The boss offers terms to workers. If the workers accept, then both workers and the company profit. If the workers reject and go on strike, both sides get nothing and lose money while waiting.

An example of this is the 2007-2008 strike of the writers in Hollywood (called the Writer's Guild of America strike). While the writers went on strike, both the writers and studios lost a lot of money. For instance, the canceled Golden Globes that year was estimated to be a $75-million to $100- million loss to the L.A. economy.

And just like in the ultimatum game, while the strike persisted, each side tried to gather negotiating power by tricking the other side about what it truly believes. Each side wanted to demonstrate to the other that it would reject solutions that were deemed unfair, even if that action appeared crazy.

As stated on the blog of James D. Miller, the producers were showing they were committed to a prolonged strike. One of their weapons was siding with Rupert Murdoch, a business magnate who is perceived as a hard line negotiator.

In response, the writers were drumming up their beliefs to high ideals such as a war on labor using a socialist argument. It was unlikely the writers were actually devoted to socialism, as they mostly are fine working within the rules of a capitalist economy. The socialist claims may have helped them appear intransigent, which would have helped their negotiating power.

Who ended up winning? According to a piece in The New York Times, it appears that both sides played a pretty hard line and each had to compromise. Writers ended up winning a higher percentage of digital sales for the long run, but they lost out on money in the short-run for traditional distribution. The ultimatum game can definitely get ugly sometimes.

Sources

Experimental result of ultimatum game: Oosterbeek, Hessel, Randolph Sloof, and Gijs Van De Kuilen. “Cultural differences in ultimatum game experiments: Evidence from a meta-analysis.” Experimental Economics 7.2 (2004): 171-188.

Carr, David. “Who Won the Writers Strike?” New York Times. 12 Feb 2008. Web. http://www.nytimes.com/2008/02/12/arts/television/12strike.html

The Writer's Strike and Game Theory. James D. Miller. 04 Jan 2008. Web. http://jamesdmiller.blogspot.com/2008/01/writers-strike-and-game-theory.html