Game theory has become an important tool in socio-economic experimental studies ranging from explaining how cooperation arises to stock market simulations (see The Minority Game (MG) ).
Three of the most intensively studied games are:
The above games have forced us to reflect on human nature itself regarding our rationality, and selfishness. Are we rational, does rational mean optimizing self-interest, and is Nash Equilibrium the necessary outcome of rationality?
The results of the above games are often counter-intuitive, and can be seen as an attack on the concept of Homo economicus—a rational individual relentlessly bent on maximizing a purely selfish reward.
In all cases, assuming the players are rational but selfish, the solution given by the Nash Equilibrium is not the action real people choose in experiments.
In the PD selfishness wins, but in IPD, "Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more altruistic strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behavior from mechanisms that are initially purely selfish, by natural selection."
TD was introduced by Kaushik Basu:
An airline loses the suitcases of two travelers. Both suitcases happen to be identical and contain identical pieces of antique. An airline manager tasked to settle the claims of both travelers explains that the airline is liable for a maximum of $100 per suitcase, and in order to avoid inflated claims he separates both travelers and asks them to write down a number no less than 2 and no larger than 100. He also tells them that if both write down the same number, he will treat this number as the true dollar value of both suitcases and reimburse both travelers that amount in dollars. However, if one writes down a smaller number than the other, this smaller number will be taken as the true dollar value, and both travelers will receive that amount plus a bonus/malus: a $2 extra amount for the traveler who wrote down the lower value and a $2 deduction for the person who wrote down the higher amount. The question is: what strategy should both travelers follow to decide which number to write down?
PD can be seen as a special case of TD with only 2 values.
The surprising result of analysis, is that the unique Nash Equilibrium is for both travelers to write down $2. If we only consider the choices $99 and $ 100, $99 is clearly better than $100, because if the other person chooses $100, we get $99+2=$101. The same argument can be applied to $98 and $99, and continuing by backwards induction, leads to the result that $2 is best. Of course this assumes that both players are selfish.
Bashu wrote about the economic implication: " The game and our intuitive prediction of its outcome also contradict economists' ideas. Early economics was firmly tethered to the libertarian presumption that individuals should be left to their own devices because their selfish choices will result in the economy running efficiently. The rise of game-theoretic methods has already done much to cut economics free from this assumption. Yet those methods have long been based on the axiom that people will make selfish rational choices that game theory can predict. TD undermines both the libertarian idea that unrestrained selfishness is good for the economy and the game-theoretic tenet that people will be selfish and rational."
In practice, experiments find that most people would choose a high number near to $100.
Does it mean that the rationality assumption is not valid?
Which leads Bashu to say: "Perhaps altruism is hardwired into our psyches alongside selfishness, and our behavior results from a tussle between the two."
Concluding the article, Bashu said: "If I were to play this game, I would say to myself: "Forget game-theoretic logic. I will play a large number (perhaps 95), and I know my opponent will play something similar and both of us will ignore the rational argument that the next smaller number would be better than whatever number we choose. What is interesting is that this rejection of formal rationality and logic has a kind of meta-rationality attached to it. If both players follow this meta-rational course, both will do well. The idea of behavior generated by rationally rejecting rational behavior is a hard one to formalize. But in it lies the step that will have to be taken in the future to solve the paradoxes of rationality that plague game theory and are codified in Traveler's Dilemma."
The key point in this statement is "I know my opponent will play something similar..."
More recent game theoretic analysis followed this line of reasoning by including knowledge or beliefs about our own rationality or irrationality, and that of the other person rationality or irrationality, into consideration. This field of study is known as interactive epistemics.
The third game, the Ultimatum Game (UG) deals with the concept of fairness.
The games is formulated as follows :
Imagine that somebody offers you $100. All you have to do is agree with some other anonymous person on how to share the sum. The rules are strict.
The two of you are in separate rooms and cannot exchange information. A coin toss decides which of you will propose how to share the money. Suppose that you are the proposer.
You can make a single offer of how to split the sum, and the other person—the responder—can say yes or no. The responder also knows the rules and the total amount of money at stake. If her answer is yes, the deal goes ahead. If her answer is no, neither of you gets anything. In both cases, the game is over and will not be repeated. What will you do?
Instinctively, many people feel they should offer 50 percent, because such a division is
“fair” and therefore likely to be accepted. More daring people, however, think they might
get away with offering somewhat less than half of the sum.
Experiments with people from different countries suggest that there is a concept of fairness, and some people would rather take home nothing than accepting a small amount, which they deem as not fair.
The authors said about the experiments: "Yet despite these cultural variations, the outcome was always far from what rational analysis would dictate for selfish players. In striking contrast to what selfish income maximizers ought to do, most people all over the world place a high value on fair outcomes."
It gets even more interesting when the game is iterated, and the evolution of strategies is studied (Evolutionary Game Theory )
Like in IPD, we can observe the evolution of altruism, cooperation, generosity, punishment of selfish people, sense of fairness, etc.
Nice guys finish first!
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