## A response to “Is Game Theory Useless?”

To my classmate who chanced upon the article Is Game Theory Useless, thank you for the interesting read. If you are still interested in looking at the flaws or, perhaps the intricacies of game theory, I believe a great place to start is the field of Behavioral Economics, taught by a wonderful Professor Ted O’Donoghue here at Cornell University.

Firstly I fully agree that classical game theory is largely impractical when applied to figure out how many people will react to economic incentives. However, the post that you linked takes a fairly simplistic approach to analyzing game theory.

There are many factors in the rock paper scissors example that are left out of the list of factors considered in that particular game. For instance, a rock paper scissors game with nothing on the line would be considered by many people to be a rather trivial game, especially if there was no substantial reward on the line. Similarly, what does it actually cost for someone to lose a game of rock paper scissors? Between bored friends, clearly not much will be at stake! So what changes when you throw actual money on the line? Under classical game theory/utility maximization, we assume that the nash equilibrium will be 1/3chance to play any of the three options. However, this may not always be the case, with lower and trivial sums of money. Under trivial circumstances, people are more likely to play irrationally, and take bigger risks. When non-trivial rewards/losses are thrown into play, people are more likely to play less riskily.

Take for example coin flipping with a fair coin. If there is no reward on the line, many people would be content to play this game. However, would you play this game if there was a dollar on the line? If you called correctly you win a dollar, incorrectly you lose one. Many people would say yes. How about a million dollars? If you won a million dollars on a correct coin flip, but lost a million on an incorrect call, would you still play? Classical game theory still says, yes, everyone would play, since expected outcome is still 0. However, when asked, many people choose not to play this game.

Prospect theory in the field of behavioral economics attempts to address this issue by more accurately modeling preferences and decision making under risk, rather than classical utility functions. In prospect theory, one fundamental change is the addition of risk aversion, wherein a loss hurts more than the utility gained from a win.

If anyone is interested in looking at a model that is better than utility maximization at predicting outcomes in choice under risk, I would suggest giving Kahneman and Tversky’s “Prospect Theory: An Analysis of Decision under Risk”, a read.

Many other factors that affect the outcome of player choice also exist, but this is a great starting point.

For the class’s personal consideration:

How much would you be willing to pay for the right to play a casino game with an infinite payoff? The game is outlined as follows:

The pot starts at 1 dollar and is doubled every time a head appears. The first time a tail appears, the game ends and the player wins whatever is in the pot. Since the expected payoff of this game can be shown to be infinite, how much would you be willing to pay for the right to play such a game? Why?

This is known as the Saint Petersburg Paradox, and is commonly used as an example to highlight the problems found in probability theory and decision theory.

References:

Kahneman, Tversky “Prospect Theory: An analysis of Decision under Risk” http://www.princeton.edu/~kahneman/docs/Publications/prospect_theory.pdf

-JX