Prisoner’s Dilemma and Economics

ECONOMICS E-COLUMNIST

“The hazards of the generalised prisoner’s dilemma are removed by the match between the right and the good.” – John Rawls

The prisoner’s dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, although it will result in an optimal outcome. The prisoner’s dilemma was framed by Merrill Flood and Melvin Dresher while working at RAND in 1950, reflecting a paradox in decision analysis. The background to this is illustrated by the scenario where two members of a criminal gang are arrested. These two members are interrogated separately and offered a deal. If both of the members confessed to the charges, both will serve two years in jail. If one confesses whereas the other remain silent, the confessor will be freed while the other will serve three years in jail. Lastly, if both remains silent, then both will serve a year in jail. Essentially, one can choose to cooperate with the partner (staying silent) or to defect and betray the the other (confessing). This can be better visualised in a payoff matrix.

  B stays silent B confesses
A stays silent A: +1 , B: +1 A: +3 , B: 0
A confesses A: 0 , B: +3 A: +2 , B: +2

Prisoner’s dilemma payoff matrix

The eventual outcome depends on each individual’s decision. In the case whereby both participants seek their self-interests by defecting, it will result in a less optimal outcome than when they have cooperated, meaning that their self-interest do not coincide with their best interest. The prisoner’s dilemma is normally used to help us in understanding the cooperation between two individuals.

In prisoner’s dilemma, each player’s decisions affects the other. The decision a player makes depends on what the player believe is best for him. In rational choice theory, each player will choose to defect as that has the best outcome. This is therefore the dominant strategy to employ. However, this will instead land them in the worst position. This concept is known as the Nash equilibrium, where no participant in a stable system can gain with a unilateral decision. The concept states an incentive for a player deviate from his original strategy after considering the other player’s decisions. Importantly, cooperation in prisoner’s dilemma stems from trust between the two parties. Both parties do not know the intention of the other and they usually do not have the chance retaliate after that decision. This tends to result in a stronger motivation to defect.

We may be unaware, but prisoner’s dilemma is in fact seen frequently in our daily lives.  One of the more commonly stated examples is in international relations. The recent trade war between China and America encapsulates this theory. Due to the trade imbalance with China, America feels incentivized to impose additional trade tariffs on Chinese goods, with the belief that it can change the balance of trade and put America in a better position than before. However, when it led to a retaliation from China, both sides suffer.

Another example will be on advertising strategy by different companies. When Company A advertises and Company B does not, Company A is likely to see an increase in its sales and Company B will probably see a decrease. Vice versa. However, should both companies advertise at the same period, both will likely retain the same sales figures but seeing an increase in expenditure on advertising. This means they are defecting. Yet if both adopt a cooperative behaviour by advertising less, they will have a win-win situation.

A more detailed example is prisoner’s dilemma as a model for oligopoly. Firms in an oligopoly can increase their profits by colluding and fixing prices to be (far) higher than market-clearing prices. The pursuit of self-interest and increasing individual outputs however, will result in smaller profits than monopolising. Hence, these firms are incentivized to monopolize the market through reducing output collectively. Despite so, collusive arrangements are inherently unstable. Individual firms are often enticed to lower their prices to increase their market share, therefore breaking the monopoly. In other cases instead of monopoly, firms in an oligopoly agree to have a “price leader” with other firms following so as to allow for generation of more revenues for all. Prisoner’s dilemma explains the breakdown in these price-fixing agreements, illustrating the difficulties in maintaining cooperation despite mutual benefits. This can be better understood in studying the case study of Organisation of Petroleum Exporting Countries (OPEC) as an Oligopoly.

As this essay concludes, perhaps today we can reconsider whether cooperation depends on the “complicated dynamics of environments where people challenge, betray and then trust each other over and over again or an internal sense of morality” (The New York Times, 1986). And some of you may be happy to know that in 2013, a real-life study done by 2 University of Hamburg economists on prisoner’s dilemma showed that inmates cooperated 56% of the time, far more than expected.

Bibliography

https://www.businessinsider.com/prisoners-dilemma-in-real-life-2013-7/?IR=T

http://www.open.edu/openlearn/history-the-arts/culture/philosophy/the-prisoners-dilemma

Oligopoly in Practice

Lai Yi Qian (18-O5)