Under the Microscope: Game theory is a mathematical analysis of any situation involving conflict of interest with the intent of indicating optimal choices leading to desired outcomes, writes Dr William Reville.
John von Neumann established the theoretical framework of game theory in the 1920s and 1930s and highlighted the utility of game theory by linking it to economic activity.
Classical economics believed that people should be left to their own devices, free to make selfish choices and that these choices would produce an efficient economy. The rise of game theory has significantly modified this assumption. Game theory and methods derived from it assume that people make rational (a brave assumption) selfish decisions that game theory can predict. In 1994, Kaushik Basu, professor of economics at Cornell University, devised a game called Traveller's Dilemma (TD) that has been used in many studies since. TD undermines the idea that free-flowing selfishness is good for the economy and the game theory assumption that people will behave rationally and selfishly. Basu outlines the implications of TD in Scientific American, June 2007.
Basu describes TD as follows. Lucy and Pete return from holidays to find that the airline has damaged identical antique vases each had bought. The airline agrees to compensate and asks Lucy and Pete to each value their vases, but without conferring together. Each is asked to write down a dollar value for the vase, picking an integer between two and 100.
If both write the same number, each will receive that amount. If the numbers differ the airline will assume the lower figure is the correct one. The airline will then pay the person who wrote the lower number that amount, plus a bonus of $2 for honesty, and the person who wrote the higher number will be paid the lower value minus a penalty of $2 for cheating. For example, if Lucy wrote $40 and Pete wrote $80, Lucy would receive $42 and Pete $38. What value would you write down?
Most people pick a high value near $100, both those who haven't thought through the logic of the game and those who fully understand that in picking the high value they are deviating from the "rational" choice. But, players win a greater reward by not abiding by the logic of TD. The decision not to be rational when playing TD is therefore somehow rational. Many studies of TD have been made since 1994 providing valuable insights into human decision-making.
The logic of TD dictates that $2 is the best option. Basu explains as follows. Your first thought might be to write $100 which would win you the maximum money if the other player is equally greedy. However, if you wrote $99 you would get a little more - $101 if the other player wrote $100. Then you think, surely the other player will also think this and write down $99. So you decide, write $98 and you will get $100 if your opponent writes $99. Continuing this line of reasoning will spiral both players down to the smallest possible value $2 - this is the logic of the game - backward induction.
Many tests of TD show that players choose much larger amounts than $2. A University of Virginia study enrolled students to play the TD game. They were paid $6 to play it and could keep any money they earned in the game. The range of choices was 80 to 200 cent and the value of the penalty/reward was varied for different tests of the game, from as low as 5 cent to as high as 80 cent. Regardless of the size of the penalty/reward, playing the game according to backward induction should always lead to the choice of 80. However, the results were an average choice of 180 when the reward was 5 cent and an average choice of 120 when the reward was 80 cent.
Researchers attempt to explain why most people do not choose $2 in TD as game theory predicts. Perhaps many people can't do the necessary deductive reasoning and therefore make irrational choices. This is not entirely satisfactory as the result is the same, with some games played by theorists.
Perhaps altruism is hardwired into our psyches along with selfishness. Many may not feel like letting down the other player simply by trying to earn an additional dollar. Some people may simply ignore game theory logic and select a large amount, assuming their opponents will do the same. The interesting point is that this rejection of formal rationality has a meta-rationality attached to it. The rules of behaviour generated by rationally rejecting rational behaviour are difficult to divine. It will be a subject for further researches.
I'm not convinced that much game theory analysis is very helpful in the real world, so I will end with this joke.
A man out walking in the countryside meets a shepherd tending a large flock of sheep. He says: "I'll bet €100 against one of your sheep that I can tell the exact number in the flock." "Okay," says the shepherd. "973," says the man. The astonished shepherd says "Okay, take an animal," and the man picks one up.
"Give me a chance to get even," says the shepherd. "Double or nothing that I can guess your exact occupation?" "Sure," the man replies. "You are an economist," says the shepherd. "That's right," says the man in amazement. "How did you know?"
"Well," says the shepherd, "put down the dog and I will tell you."
• William Reville is associate professor of biochemistry and public awareness of science officer at UCC - http://understandingscience.ucc.ie