Sunday, April 13, 2008

real time games

my dear zohaib asks for some real-life examples of game theory in ethics.

In many instances where game theory intersects real life, we just play the game according to the (local) Nash equilibrium. The phrase "All's fair in love and war" says that one is free to pursue the strategy that will bring the greatest immediate individual benefit. We construct specifically ethical systems when for one reason or another, we have to go "outside" the game to achieve what we intuitively feel is the best overall outcome.

For example, I can go into a restaurant, eat a meal, and then be presented with the bill. This is an example of a related game, the asymmetric closed bag exchange. Regardless of whether or not I'm actually served a good meal, I am always "better off" not paying (I get to eat the meal and keep my money). Paying before I eat (like at McDonalds) just changes the asymmetry; whether or not I pay, it's always "better" for the restaurant to not feed me (defect) once I've paid (cooperated).

The Pareto optimum (and usually the global maximum), though, is for the restaurant to serve me a good meal and for me to pay.

In a small community, we can play tit-for-tat. If I don't pay on Monday (he cooperates, I defect), the restaurant won't serve me again until I pay without eating (he "defects", I cooperate). However, a rational person with foresight will simply see the outcome of the repeated iterations. We call this foresight the ethical evaluation that you should pay for your meal.

In a larger community, where there are more non-communicating restaurants than I can eat meals, tit-for-tat doesn't work; I can play as many one-shot games as I like without fear of reprisal. So we make laws which follow from our idealized tit-for-tat strategy (i.e. good laws follow from good ethics).

But we can observe that the law is relatively easy to circumvent: There isn't a police officer standing at the door to every restaurant. Instead, we cultivate in ourselves ethical habits. In this case, the the thinking is one level more abstract: If too many people in general were to eat without paying, no one (myself included) could eat at restaurants, so we police ourselves.

There are other examples. I can work hard (cooperate) or slack off and just look busy (defect); my company can give me a raise next year (cooperate) or stiff me (defect). As an exercise, use game theory to relate the Communist slogan, "From each according to his ability, to each according to his need," with the cynical Soviet observation, "we pretend to work, and they pretend to pay us."

A lot of human behavior can be modeled just by reducing it to pure game theory and locally rational choice. But as the Prisoner's Dilemma shows, some situations are not so easy to reduce, even in theory. It is precisely those Prisoner's Dilemma and similar games which cause us to go outside the game and create ethics and laws.

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