Prisoner’s Dilemma — A Game Theory Simulation
In one of our classes in Entrepreneurship at MBA, we had an interesting classroom game conducted on Game theory. Students were divided into four separate Groups. (Group A, Group B, Group C and Group D) each having a representative. All groups were given the same goal — “To accumulate as many points as possible without helping or hindering the other group.” In practice, I found that the point incentive generally faded away as groups just focused on their perception of “winning.”
The Game
There were two coins- black and red, which were given to every team, at the end of every round each team had to decide to keep either a black or a red coin based upon the discussions among the teammates and other team’s representatives. There were different outcomes based on the combination of coins kept by the teams-
Outcome 1- 2 black 2 red — +1(for the team keeping black)(-1 for team keeping red)
Outcome 2- 3 red 1 black- -2(for the teams keeping red)
Outcome 3- 1 red 3 black- +1 for the teams keeping black
Outcome 4- 4 blacks- +1 to all of them
Outcome 5- 4 red- -1 to all teams
The number of possible outcomes was 5. For every outcome there were either a positive or a negative or no point. Teams need to take decisions wisely so that they gain maximum points at the end of the game. This went on for 10 rounds, with every round lasted for 10 mins for discussion with other team representatives and with our team mates. As the decision rounds accumulated, players faced the results of cooperation and betrayal.
The teams that betrayed, earned points in the beginning and then gradually ended up losing points in the end. The teams that stood by their commitment, cooperated all along the way with the other teams, and had survived to a certain extent when compared to the teams who have betrayed. If all teams would have worked together and co-operated then all teams would gain or bear less loss from what they are bearing now.
The Concept of Prisoner’s Dilemma-Game Theory
Two doubts are detained by the police. The police have lacking proof for a conviction and having separated the prisoners; visit each other to offer the same deal. If one bear witness for the hearing against the other’s defects and the other remains silent (cooperates), the defector goes free and the quiet accomplice receives the full ten years sentence. If both remain quiet, both prisoners are sentenced to only 6 months in jail for a petty charge. If they betray each other, each receives a 5 years sentence. Each jailbird must choose to betray the other or to remain silent. Each one is guaranteed that the other would not know about the betrayal before the end of the investigation.
· If X and Y each betray the other, each of them serves two years in prison
· If X betrays Y but Y remains silent, X will be set free and Y will serve three years in prison (and vice versa)
· If X and Y both remain silent, both of them will only serve 1 year in prison (on the lesser charge)
It is implied that the jailbirds will have no chance to punish or reward their partner other than the prison sentences they get, and that their choice will not affect their standing in the coming future because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested jailbirds would betray the other, and so the only possible outcome for two purely rational jailbirds is for them to betray each other. The exciting part of this outcome is that tracking individual reward logically leads both of the jailbirds to betray, when they would get a better reward if they both kept quiet. In actual fact, individuals display a systematic bias towards cooperative conduct in this and alike games, much more so than predicted by simple models of “rational” self-interested action. A model based on a different kind of level-headedness, where individuals estimate how the game would play if they formed coalitions and then make best use of their predictions which has been shown to make better predictions of the rate of cooperation in this and similar games, given only the settlements of the game.
Key Learnings
The game helped students understand how negotiation matters in business. The prisoner’s dilemma game can be used as a model for many real world situations involving cooperative behaviour. It mainly helped us understand the kinds of decisions to be made by a manager and an Entrepreneur.
References- https://en.wikipedia.org/wiki/Prisoner%27s_dilemma, http://www.people.virginia.edu/~cah2k/pdtr.pdf
