This is the first of the multiple entries in the series “Explain like I am five”. What I aim to do through this series is to walk the readers through some of the indispensable concepts in Economics, exploring them in a manner that a “five-year-old” can understand. Well, not really a five-year old, but the title sure has an instant appeal to it. It has indeed caught your attention now, hasn’t it? I will kick-start this series by discussing Prisoner’s Dilemma, one of the well-known games analysed in Game theory.

As someone who does Game theory for a living, I have occasionally found myself battling this notion, prevalent among some social scientists, that Game theory belongs more to Mathematics than to Economics or Political Science. When we look at the theoretical development of the subject, we might be tempted to think so. Several Mathematicians such as Von Neumann, John Nash etc. have been the frontrunners in expanding research in this field. But let’s not forget that Neumann did pioneering work in this field with Oskar Morgenstern, an economist by profession. They co-authored the book *Theory of Games and Economic Behaviour* in the late 1940s which is considered the seminal work in areas of game theory. More so, John Nash, who was a brilliant mathematician, is disproportionally famous for his work in Game theory in comparison to his other works in Differential Geometry (which his mathematician colleagues have come to respect greatly). So much so that he won the Nobel Prize in Economics in 1994 for his contribution to non-cooperative games. I have come to understand that anyone who dabbles in games is no longer a mathematician or an economist. He or she simply belongs to a diffused category of what we have come to call them – Game Theorists. Even John Maynard Smith, an evolutionary biologist, is a game theorist for using game theory to explain evolution of sex and theorising signalling theory.

Prisoner’s dilemma is one such example in Game theory that has glaring implications in the social sciences. The story of this game is attributed to a Canadian Mathematician named Albert Tucker. It describes a situation where two prisoners, suspected of a crime, are taken into custody. The prosecutors do not enough evidence to convict them of the principal crime. They are left with the sole option of getting either or both of the prisoners to confess. Now, if none of them confesses to the crime (co-operating with each other), the prosecutors can only charge them for a minor crime and each prisoner gets a lesser sentence of 1 year in prison each. The prosecutors devise a scheme where they question both the prisoners in separate interrogation rooms, cutting off all means of communication between the prisoners. The prosecutors first offer each of them the following bargain offer: If one confesses and the other remains silent, they will be offered a “get out of jail free card”, while the other prisoner will be sentenced to a 30 years of imprisonment. Further, if both the prisoners confess to the crime, each will be sentenced to jail for 10 years. And finally, the prosecutors inform each of them that their partner in crime has been offered the exact same deal.

The accompanying figure (or as we call it in Game theory, the Payoff Matrix) describes what rewards each prisoner receives for the four combinations of possible actions by each player, {(C, C), (C, NC), (NC, C), (NC, NC)}. For e.g., if prisoner 1 chooses to confess and prisoner 2 chooses to not confess, then prisoner 1 goes free (0 jail sentence) and prisoner 2 gets 30 years of jail sentence. Similarly, you can understand payoffs in each cell, depending on the pair of actions taken by both the prisoners.

What do you think each of the prisoner will do? Confess or remain silent? Yes, you guessed it right. They will both confess! The argument is pretty simple, really. Even if either of them is better off by remaining silent than by confessing (less imprisonment by 10 – 1 = 9 years!), both of them are acutely aware that their partner might confess and that could get them 30 – 1 = 29 years of more imprisonment!

Let’s try using the payoff matrix to see this. From prisoner 1’s perspective, if prisoner 2 confesses, prisoner 1 is better off by confessing himself (as 10 < 30). And, if prisoner 2 remains silent, prisoner 1 is again better off by confessing (as 0 < 1). Therefore, it can be concluded that the best response of prisoner 1 to whichever strategy prisoner 2 undertakes, is to confess for the crime. Likewise, prisoner 2, being no different from prisoner 1, will reach the same conclusion, thereby confessing too.

The cell which is highlighted *yellow* in the below figure illustrates the outcome of this game. When you compare the payoffs in the highlighted cells, notice how both the prisoners are choosing to serve more time by confessing. It is the lack of information on what his partner might do, that is forcing either of the prisoners to confess.

Take a look at what our beloved Dilbert is up to when he tries to boast of his knowledge of Prisoner’s Dilemma. Where did you think he went wrong?

Well, he forgot to account for the fact that his office buddies were not aware of the game and were in actual dilemma! They realised soon enough that the best strategy for them in this situation was to confess. While his colleagues were rational (purely self-interested) in their decision-making, Dilbert was smug. If I assume him to be prisoner 1 in the above game, then his payoffs will be according to the cell in second row, first column. That is to say, he will have to serve time in jail, longer than what he would have gotten if he had confessed instead.

The payoff matrix obtained under Prisoner’s Dilemma has been used to model many real-world situations where the players would have been better off had they chosen to cooperate with each other. The imperfect information regarding the actions taken by others makes the players look out for their self-interest and choose a non-cooperative strategy. For e.g., Prisoner’s Dilemma game has been used to explain the strategic reality behind Arms race in Cold war. Even though nuclear disarmament strategy left the countries better off, they still chose to arm. The reason behind this can be argued on the same lines as the argument in Prisoner’s Dilemma. The fear that the opponent country might secretly build an arsenal led the countries to build their own. Prisoner’s dilemma game was used by Hardin to explain what is called as the Tragedy of the Commons. It can be most easily explained by considering the case where multiple people share a house and are supposed to stock a common refrigerator with food items. Now individually, each of them can profit by not doing so. But if that behaviour is adopted by all the residents, then the collective cost is high as there will be no food in the fridge for anybody.

I would like to conclude by emphasising upon two crucial points regarding the game outcome. Firstly, notice how these decisions have been taken simultaneously by both the prisoners. Even in the clip, Dilbert and his colleagues reached their conclusions at the same time, give or take. Secondly, it is important for you to understand that the final decision of the one prisoner cannot alter other prisoner’s decision. It is not like now that Dilbert has seen his friends rat him out, he will be allowed to take the bargain offer and confess.

These are the two fundamental points, that makes the outcome of this game i.e. (Confess, Confess) a Nash Equilibrium. What is a Nash equilibrium? I will try and answer this question and more in the coming articles in this series by picking up few more interesting games along the way.

The author, Shivangi Chandel is lecturer at Meghnad Desai Academy of Economics, Mumbai. For more such articles, follow The Curious Economist on Facebook and Instagram.