Wednesday, August 01, 2007

The Ever Popular Topic: Game Theory

While economists call it game theory, psychologists call it the theory of social situations. I suppose next to the evils of totalitarian agriculture, one of the most frequent topics I post about here on my blog, is game theory. I am not very good at math in a traditional sense, but am fascinated by games, strategies and decision making processes. I suppose in many ways that relates to my feelings of farming being a poor strategy for making a living, my love of reality tv, and constructing paintings. Of course game theory also relates to my enjoyment of Shakespeare and Plato, both of whom use game strategy in their plots and characters. How does game theory relate to each of us? Politicians, urban planners and employers have all been exposed to some level of game theory: familiarity of game theory among employees and voters might have positive transformative influence on how regular citizens make their decisions. Familiarity of game theory might also help us understand how personal decisions affect our lives longterm as well. Here are some notes I found online...

In two of Plato's texts, the Laches and the Symposium, Socrates recalls an episode from the Battle of Delium that involved the following situation. Consider a soldier at the front, waiting with his comrades to repulse an enemy attack. It may occur to him that if the defense is likely to be successful, then it isn't very probable that his own personal contribution will be essential. But if he stays, he runs the risk of being killed or wounded—apparently for no point. On the other hand, if the enemy is going to win the battle, then his chances of death or injury are higher still, and now quite clearly to no point, since the line will be overwhelmed anyway. Based on this reasoning, it would appear that the soldier is better off running away regardless of who is going to win the battle. Of course, if all of the soldiers reason this way—as they all apparently should, since they're all in identical situations—then this will certainly bring about the outcome in which the battle is lost. Of course, this point, since it has occurred to us as analysts, can occur to the soldiers too. Does this give them a reason for staying at their posts? Just the contrary: the greater the soldiers' fear that the battle will be lost, the greater their incentive to get themselves out of harm's way. And the greater the soldiers' belief that the battle will be won, without the need of any particular individual's contributions, the less reason they have to stay and fight. If each soldier anticipates this sort of reasoning on the part of the others, all will quickly reason themselves into a panic, and their horrified commander will have a rout on his hands before the enemy has even fired a shot.

Decision theory can be viewed as a theory of one person games, or a game of a single player against nature. The focus is on preferences and the formation of beliefs. The most widely used form of decision theory argues that preferences among risky alternatives can be described by the maximization the expected value of a numerical utility function, where utility may depend on a number of things, but in situations of interest to economists often depends on money income. Probability theory is heavily used in order to represent the uncertainty of outcomes, and Bayes Law is frequently used to model the way in which new information is used to revise beliefs. Decision theory is often used in the form of decision analysis, which shows how best to acquire information before making a decision.

General equilibrium theory can be viewed as a specialized branch of game theory that deals with trade and production, and typically with a relatively large number of individual consumers and producers. It is widely used in the macroeconomic analysis of broad based economic policies such as monetary or tax policy, in finance to analyze stock markets, to study interest and exchange rates and other prices. In recent years, political economy has emerged as a combination of general equilibrium theory and game theory in which the private sector of the economy is modeled by general equilibrium theory, while voting behavior and the incentive of governments is analyzed using game theory. Issues studied include tax policy, trade policy, and the role of international trade agreements such as the European Union.

Mechanism design theory differs from game theory in that game theory takes the rules of the game as given, while mechanism design theory asks about the consequences of different types of rules. Naturally this relies heavily on game theory. Questions addressed by mechanism design theory include the design of compensation and wage agreements that effectively spread risk while maintaining incentives, and the design of auctions to maximize revenue, or achieve other goals.

Optimal Tax Theory is choosing your supper. Where and how you have dinner is more likely a result of a politician and their economist than what you feel like eating, or what may be best nutritionally and spiritually for your family. The incidence of sales taxes on commodities also leads to distortion if say food prepared in restaurants are taxed but supermarket bought food prepared at home are not taxed at purchase. If the taxpayer needs to buy food at fast food restaurants because he/she is not wealthy enough to purchase extra leisure time (by working less) he/she pays the tax although a more prosperous person who say enjoys playing at being a home chef is less lightly taxed. This differential taxation of commodities may cause inefficiency (by discouraging work in the market in favor of work in the household). Individual freedom is considered the definitive benefit of marketplace economy.

Are you playing the game or are you being played?

A few Game Theory posts on this blog
Plato's Cave
Mark Burnett
Interview with Martin Gardner
What is game theory?
Stanford Game Theory Pages


felix said...

Game theory is one of many empty places in my little store of knowledge. But the example Plato gives of the Battle of Delium and soldiers reasoning away participation made me think of Henry IV, Pt. I, V,i:

A word. What is that word Honour? Ayre: A
trim reckoning. Who hath it? He that dy'de a Wednes-day.

If all soldiers were Falstaffs, war would cease immediately.

Candy Minx said...

Well if there ever was a story to give pause, it's Henry IV all right, Felix. Keep that chin up fella!

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