Saturday, January 22, 2022

538 Prisoner’s dilemma

 The prisoner’s dilemma is as follows. Two prisoners get a reduced sentence when confessing to their joint crime. If they both persist in denial, there is not enough evidence, and they are both released. For them, that is the best action, but they are each tempted to confess, accuse the other, and get a reduced sentence, fearing that the other might do so. The result is that they both confess, to prevent a one-sided heavy sentence.

A comparable situation may occur in the economy. A classic example is the tobacco industry. Advertising did not increase sales much, and seemed wasteful, but was needed not to lose market share, if the company reduced advertising but competitors did not. The government intervened for health reasons, limiting advertising, and this imposed a profitable solution for the firms.

In banking, regulation should have been imposed in the 2008 financial crisis, but the governments were also in a prisoner’s dilemma: if they imposed controls, and other countries  did not, this might lure banks to move elsewhere. So, the EU tried to impose restrictions that were common at least in Europe.

Such situations of collaboration versus defection have been investigated by game theory, which is not a theory but a tool for analysing strategic action, anticipating actions of others. There can be several players of the game. An example is bubbles on the stock market, where people assume that others will keep on buying the share, raising its value.

The situation of a game changes when it is repeated. Then one may try to build a reputation of honouring agreements, and keep to them. Game theory yielded the strategy of tit-for tat, where you collaborate as long as the other does, and retaliate when he/she defects. However, then you run the serious risk of getting locked in in mutual defection. An improvement is forgiving tit-for tat, where in case of defection you try out collaboration again, to see if the counterpart may be so wise as to follow. Trust can yield mutually beneficial outcomes, by discounting the risk of defection.

            Another example is that of the game of hawk and dove. Hawks prey on doves, but if that is so successful that doves become extinct, that is not in the interest of the hawks, and it is beneficial to both if doves learn to hide or escape better.

            Another famous game is where A has to decide how much money he/she gives to B, and B has to decide how much to give in return. Often, people are inclined to the fair solution that B returns half and they both have 50%. It has been used in many experiments, to find out how much it matters when an outside gamekeeper gives both players a bonus when they share more or less, the effect of building a favourable reputation by giving a fair return in a repeated game, and what then happens at the last play, and the difference if they have contact and could deliberate.

 There are many useful applications of game theory, but it has its limits. It assumes that the options for strategic choice and the outcomes of combinations of choice are known, but this is often not the case. There, one discovers the options for choice and the value of outcomes only after the action. Here, trust comes in again: are you willing to accept that uncertainty, on the basis of an assessment of someone’s trustworthiness or a leap of faith?

           There are models of search in the form of travelling across a hilly landscape in the mist, in search the highest summit. There, the situation may be that treading on the land causes earthquakes, shifting the hills.


-          As a prisoner would you confess, getting a reduced sentence, or would you deny, risking a high sentence, why, and what would change your choice

-          Have you ever experienced a prisoner’s dilemma

-          When or why would you not use game theory

-          How was the weapons race stopped


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