However the outcome changes slightly when given the chance to play more than one game, known as the ‘Iterated prisioner’s dilemma’. If the players have memory of at least one previous game, a co-operative outcome can eventually be reached as shown by Robert Aumann in 1959. With outcomes judged solely on self interest of both parties, it is shown that greed stratergies are much less effective than those of co-operation and fogiveness. Staergies that lead to success in this long game are being ‘nice’ in that you should not defect before your opponant does, ‘retailiating’ as if you are up against a greedy competitor you must fight back or risk loss, ‘forgiving’ in that if they retailiate second chances must be given, else it will lead to both constantly defecting which is in neither’s best interests, and lastly a ‘non-envious’ stratergy, as you should not focus on scoring more than your opponant, only focus on scoring the best that you can in yourself. The conclusion of the iterated game therefore is that the most selfish and greedy thing to do it to be nice, non-envious and forgiving. The end result therefore is that both parties have the opportunity to ‘punish’ the other for previous non-cooperative play. The threat of future punishment overrides the incentive and desire to defect leading to the possibility of a cooperative equilibry where everyone is better off.
Another solution concept for the prisioners dilemma is the ‘nash equailibrium’ developed by John Nash in 1950. This states that “If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium”(Nash, 1951).
The prisoner’s dilemma is a practical application of the mathematics of game theory. This studies stratergy of competion between sellers in a market to maximise their return and it provides a ‘formal modelling approach to social situations’. Due to this fact, game theory has played a huge role in modern social sciences, politics and has even been applied to animal behavior and ethics.
The prisoner’s dilemma can be seen to have large significance in understanding economic behavior, for example in reference to an oligopoly market. An oligopoly is a market dominated by a few large suppliers, with large barriers to entry, and larely similar products. There is also assumed to exist independence between firms meaning that each firm must take into account the likely reactions of the other firms in the market when making pricing decisions. This leads to uncertainity in the market and therefore the desire for prediction and the use of game theory. It can be seen that two oligopolistic firms in a market will both loose out as per the prisoner’s dilemma unless there is colusion occuring. Colluision is illeagal as it leads to a monopoly style market and means the consumer looses out whislt the firms make super-normal profit. This is unfair to the consumer and means that all the problems of a monopoly such as large barriers to entry and lack of competition become prevelent in this type of market too.
An example of oligopolies relating to the prisioner’s dilemma is within the supermarket industry. This industry is made up of a few very large sellers with homogeoneous products and huge barriers to entry through non-price competition for example advertising and brand loyalty. The prisioner’s dilemma can be illustrated very well in this circumstance for example with relevence to the price of milk sold in Tescos and Asda. The two stores are directly competative it terms of milk price, and each store sells the milk at 40p a pint with the store making 10p as profit from each pint sold and with around 200 pints sold a day at each store. Each store is considering lowering the price of the milk from 40p to 38p on one given day however if one store lowers its price and the other doesn’t the higher priced store will loose 50% of its milk sales. It can be seen in the matrix below the different permutations of profit outcomes available.
Figue 2- Matrix to show milk price changes
As it can be seen in figure 2 above it is in the overall best interest of both parties to maintain their prices however they can make more short term profit by adopting the dominant and aggressive stratergy of slashing their prices. In the long run however both will have to take prices down to the equilibrium point of £16 profit and both parties will loose out, maybe even leading the store into a price war which would be benificial to no-one except for the consumer. This happens due to the assumption of the rationality of the consumer as it is shown that this is achieved by maximising profit where possible in the short term. In the long term iterated game though the stores may learn that they can benefit more by being forgiving with less short term greed for more long term profits.
In cases such as this there is an opportunity for colluision for example if both Asda and Tescos both decided to set their milk prices at 45p. This would mean the consumers would have less choice and it would be removing their right to be price-makers in the market and leading to a simulation of a monopoly situation. This would mean super-normal profits for the supermarkets and an unfair price for the consumers to pay esspecially as it is a basic good without substitues. Cases such as these are normally investigated by the Office of Fair Trading as has happened in this case which has been in the news recently. Tesco are estimated to have cost consumers £270 million in the milk price fixing scam and are currently being fined £116 million for breaking these laws.
In conclusion using the prisoner’s dilemma as an economic illustration of game theory, it can be seen that it is more benifical for firms to co-operate rather than betray or defect. This means more profit for all, it is however at odds with one of economic’s broadest and most widely accepted assumptions of rationality. If the firm is assumed rational it will never cooperate as rationality states that profit must be maximised not compromised. The only other definate way of profiting is for firms to collude, which means that all will make super-normal profit and only the consumer will suffer.
References
Axelrod, R. (1984). The Evolution of Cooperation.
Poundstone, W. (1992) Prisoner's Dilemma Doubleday, NY
http://www.tutor2u.net/economics/content/topics/monopoly/oligopoly_notes.htm
Fudenberg, Drew and Jean Tirole (1991) Game Theory MIT Press.
Nash, John (1951) "Non-Cooperative Games" The Annals of Mathematics 54(2):286-295.
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