Prisoner’s Dilemma and the Beach Kiosk Game
The Prisoner’s Dilemma is a mathematical game theory that refers to a game in which the payoff from playing the dominant strategy is not the highest payoff possible and illustrates how self-interest can lead rational individuals and companies to pursue a course leading to mutual self-destruction, even when that destruction is foreseeable or in the case of companies certain decisions could have financial impact for better or worse. It seems that the Prisoner’s Dilemma impacts the many small decisions we consider making. The dilemma provides the logical framework for many situations we face every day in real life. Whether we're competitors conducting business, spouses negotiating understandings our choices are reflected by the prisoner dilemma’s model. The two parties involved will often be better off as a pair if each resists the temptation to go it alone and instead cooperates with or remains loyal to the other person. Both parties' pursuing their own interests exclusively leads to a worse outcome than does cooperation. A situation in which competing firms must make their individual decisions without knowing the decisions of their rivals and arises when all rivals possess dominant strategies, and when both rivals use their dominant strategies, they are worse off than if they had cooperated in making their decisions. The following is the famous scenario (then I’ll share some examples) known as the Prisoner’s Dilemma: Two suspects: Vinny & Tony are arrested by the police. The police have insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other (defects) and the other remains silent (cooperates), the defector goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. Payoff MatrixTony-Cooperate (Don’t Confess)Tony-Defect (Confess) Vinny-Cooperate (Don’t Confess)V&T both get 6 monthsV get 10 years T goes free Vinny-Defect (Confess)V gets 10 years
T go freeV & T both get 5 years
An example in business is about something we have been talking about all through this course: a pizzeria. They both decide to lower their prices. The low price strategy is a dominant strategy for both pizzerias. Both choose to charge low prices, even though the high price/high price alternative is more attractive. This is because it is an unstable equilibrium. One pizzeria could always choose to charge a lower price, to maximize its profits. So they both settle for charging a lower price. The payoff matrix for how many more pizza’s each pizzeria makes a month may look like this: Payoff MatrixSorrento Pizzeria-High PriceSorrento Pizzeria-Low Price Sulmona Pizzeria-High Price400, 400100, 600
Sulmona Pizzeria-Low Price600, 100200, 200
A second example is let’s say that Raquel’s Scented Candles and Rania’s Scented Candles are the producers of candles. Rania’s Candles decides to advertise to differentiate its candles as being Artisan, differnt from Raquel’s candles. If Rania decides to advertise, the payoff in dollar amount profit (or loss) might look like this: Payoff MatrixRania’s Candles-AdvertiseRania’s Candles-Don’t Advertise Raquel’s Candles-Advertise$50,000, $50,000$-25,000, $75,000 Raquel’s Candles-Don’t Advertise$75,000, -$25,000$10,000, $10,000
A third example in recent news is the use of performance-enhancing drugs in professional sports specifically the story of Lance Armstrong. Here the athletes are the players, and the two possible strategies are to use performance-enhancing...