Saturday, April 11, 2009

Prisoner's Dilemma



And that's why you should never trust women!

What the woman did, however, makes complete sense. If the man had decided to steal, it would make no difference to the amount of money she would take back (which would be zero) whether she splits or steals. If on the other hand the man had decided to split, it would obviously be favorable for her to steal. Thus whatever the man might have chosen to do, split or steal, the outcome is more favorable to the woman if she chooses to steal.

But what if the man had also done this simple calculation before taking his decision? The outcome would be the worst possible for either of the participants! Thus if both players are rational and try to maximize their own payoffs they lose everything. Thus sometimes altruism can be more beneficial than selfishness. This is a version of the prisoner's dilemma (PD) (although there are subtle differences). The wikipedia article mentions that in experiments 40 % of people choose to trust each other and cooperate. Thus people do not always make the selfish, rational choice.

I read about a similar paradox called the traveler's dilemma (TD) in an article written in Scientific American by Kaushik Basu who used this paradox to argue that

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.

You might wonder (as I did when I first read the above article) when in real life do people have to make such decisions (other than contrived situations in game shows)? Let me give you two examples,

1)A recession like the current one is worsened due to a lack of confidence. Consumers because of lower income and out of fear of unemployment choose to spend less which leads to companies doing badly which leads to further unemployment and lowering of incomes. Thus although it may be rational for each individual to save money in a recession, this leads to a situation which is bad for the population as a whole. This is called the paradox of thrift.

2) In an arms race between two countries both the countries have the choice to invest more in weapons or reduce arms. For either country military expansion is the 'rational' choice irrespective of what the other country does. This leads to a situation which makes both countries less safe than if both had chosen to reduce arms.

As the second example suggests PD is not limited to just economics. In fact the iterated PD (a version where two players play PD many times) has been used to explain among other things morality and the evolution of altruism (subscription required)!

6 comments:

  1. Since you mention iterative prisoner's dilemma, there can be a form where the decision making in subsequent games take into account the outcomes of the previous game.

    This can lead to a very effective algorithm for negotiation, depending on how much someone co-operates subsequent decisions in the negotiation is taken. Surprisingly the best strategy in situations like these have been found to be tit for tat. Despite its simplicity and obviousness, it _is_ the most effective algorithm to follow.

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  2. @ suvayu
    ya the nature link (on the evolution of altruism) actually mentions that.... but if i understood it correctly (of which i am not sure) if we want to understand the behavior of animals in a more realistic way (the game assumes animals meet multiple times and can choose to either cooperate or defect each time) the optimal strategy is "generous tit for tat (GTFT)" where the animals always cooperate in response to past cooperation but sometimes forgive cases of past defection...

    @ dip
    tor blog ta jano kom antel!

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  3. I have heard game theoreticians/ behavioural economists talk about experiments on repeated games that they have conducted. Say the no. of times the game is to be repeated is 100. They observed that people tend to co operate for the bulk of the game and then try to defect before the other person does. Many times this results in co operation till anywhere between first 70 and first 80 rounds and then lack of co operation. (Apologies for not being able to point out any paper or article capturing these! Not in the habit of reading such.)

    Repeated games is also in my mind applicable to human relationships. One would accept and forgive a family member for something which hurts one in any form because you know you have to keep on interacting for a long term and it is best not to disturb the balance. A mere acquaintance or even better a stranger causing similar hurt would not be treated as generously I am sure. So it is not mere love and affection for the family member which protects them from ire. May be. :)

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  4. @sandeepan
    Ya, there are many variations to the tit for tat strategy, but in the end all essentially come down to the same basic idea. As you pointed out, its a variation that is most efficient rather than the vanilla.

    @dip
    antel #1 onyoke bolchhe!

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  5. @gaurav

    I don't know whether it is the optimal solution mathematically but that does seem to make sense intuitively- Gain the other person's trust in the first 80 rounds and then try to outsmart her/him toward the end!

    I hope the same behavioral pattern does not extend to the relationship analogy you mentioned !

    @suvayu

    ya its amazing how the optimal strategy may be such a simple, intuitive one!

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