Economics for Management. The Prisoners Dilemma

A prisoners Dilemma is a situation where the parties involved are engaged in a non-cooperative game. As there is no negotiation and cooperation between the parties involved, the best option for the parties is to adopt a maximin strategy where they will be able to maximize their minimum gain. The concept arises from the dilemma of two prisoners who are interrogated separately. Here they have two options, first is to confess and minimize their jail time, or not confess. If one does not confess and the other does, then the first gets maximum jail time. As there is no cooperation among prisoners, they are forced to opt for a maximin strategy and confess.

As the first prisoner knows the best option for him is to confess and minimize his jail time becomes his dominant strategy. So is the case for the second prisoner. Similarly, the dominant strategy for the second prisoner too is to confess and get the minimum jail term. Thus, the dominant strategy for both the prisoners in case of a non-cooperation situation is to opt for their dominant strategy i.e. to confess.

A Nash equilibrium is defined as a set of strategies, such that, none of the participants are in a position to improve their game given the strategies of the other participant. In this case, if the first prisoner chooses not to confess, and the second prisoner does, then the former will have maximum jail term and vice versa. But if both the parties confess, then both will minimize their jail term. Thus, confessing is the stable Nash strategy of both the prisoners.

Let us consider the case of advertising for Coca-Cola and Pepsi (Saporito & Reese 23 March 1992; Derby 6 December 2003). In this case, the soft drinks market is oligopolistic in nature with the two most dominating players. If both Coca-Cola and Pepsi choose not to advertise or get into a price war, they will have a much higher profit. However, as they are in a non-cooperative situation, they choose to advertise extensively in order to attain their best possible profit. Now if Coca-Cola chooses not to advertise, and the other chooses to advertise extensively, Pepsi will have higher profit, and Coca-Cola has its minimum profit. Therefore, the best option for both companies is to maximize their minimum profit.

A prisoners dilemma-like situation arose in 1998 in the PC wares market (Schonfeld 13 April 1998). Compaq declared that its profits might be going down, which reduced its share prices considerably. The case arose when Hewlett-Packard (HP) had a manageable inventory for 2 weeks, a similar problem faced by other wares companies like Compaq, IBM, and other PC makers. If the companies could cooperate to bring down the inventory in the reseller channel to around 2 weeks, all of them would benefit equally. However, they were in a noncooperation situation. So if HP reduces its inventories with distributors that increase the place for Compaq with distributors which might allow Compaq to reduce price and gain market share, while HP will have to match.

a classic case of prisoners dilemma can be observed in case of prisoners dilemma arose in case of Microsofts bidding of Yahoo (Tech Biz 29 April 2008). If Yahoo would have said that it would receive a higher bid, Microsoft would have given a higher bid. And had Microsoft provided a higher bid in the beginning Yahoo would have taken it. It was a deliberate move from Microsoft, to make an average bid on Yahoo, to drive down the stock prices and eventually reduce its bid. However, the situation failed and Microsoft failed to acquire Yahoo. This shows that any company in real life will adopt a dominant strategy it has in order to employ a maximin strategy in a Prisoners Dilemma situation.