Racy Cases 19 The Prisoners’ dilemma


First published in HBL

A V Vedpuriswar and V Pattabhi Ram

Professor Shondeep Chatterjee was known just as Chatshow. “Chat” being short for Chatterjee and “Show” being reflective of his talk-show style of delivery. Chatshow who was teaching game theory began: “The tool that economists use to analyze strategies and outcomes taking into account the expected behavior of others and the mutual recognition of interdependence is called game theory”. The girl in the middle row yawned! It was sounding like Stephen Covey. “Dependence. Independence. Interdependence”.

Chatshow continued: “Game theory is intended to understand games of all types, including the games people play in business.” Flowers (because he always wore a flowered shirt) felt like screaming. Even income tax provisions would have been easier to understand, he felt.

The professor realized that he was losing the class. And so he decided to engage them in one of his stories. It had never failed him in the past. “Two men, Appu and Raja, have been caught on camera robbing a house,” he began. Flowers whispered: “What’s new? Being caught on camera is the in-thing”. Chatshow ignored the barb. “The Assistant Commissioner of Police (ACP), who is the Chief Investigating Officer, now suspects that the duo could also be responsible for a bank heist that had its trail in both Chennai and Hyderabad. What should he do?”

Flowers thought, “Give a dog a bad name and hang it”. The girl in the middle row (She always sat there and so was acronymed GITMR) interrupted, “Sir, it is simple. The ACP has to just get them to confess”. Someone asked, “How?” She said, “Apply third degree.” The class roared. Chatshow wasn’t amused. He wasn’t in the mood for wisecracks.

Chatshow continued: “The ACP is an honest officer, English style. Third degree isn’t his cup of tea. He places each prisoner in a separate room, so that they cannot communicate with each other. And then tries to make them confess. If both Appu and Raja confess to the larger crime (the bank robbery), each will receive a sentence of 3 years. If Appu alone confesses and Raja does not, Appu will receive a short sentence of 1 year for having helped the police solve the crime while Raja will receive a 10-year sentence. If Raja alone confesses and Appu does not, Raja will receive a short sentence of 1 year, while Appu will have to cool his heels for 10 years”. And with a majestic swish of his mane, Chatshow asked, “What do you think will happen?”

Flowers: “Each prisoner has two choices. One, confess to the bank robbery. Two, deny it.”

Chatshow: “Good. What are the possible outcomes?”

GITMR: There are two players, each with two strategies. So there are four possible outcomes: Neither confesses. Both confess. Raja confesses but Appu does not. Appu confesses but Raja does not.

Chatshow noticed a few boys and girls rapidly drawing a two by two matrix. He was happy that the class was getting into the thick of action.

Chatshow: What will be the punishment in each case?

Class: “If both prisoners confess, each gets a term of 3 years. If Raja confesses but Appu denies, Appu gets 10 years and Raja gets 1 year. If Appu confesses and Raja denies, Appu gets 1 year and Raja gets 10. And if both of them deny, neither can be convicted of the bank robbery charge but both will be sentenced for the house burglary. Both will get a 2-year sentence.”

The last statement impressed Chatshow. That if both of them denied, neither could be convicted of the larger crime. Consciously he hadn’t expressed it. But the class had spotted it. Clearly they were quick on the uptake. He continued: “The equilibrium will occur when Appu takes the best possible action given the action of Raja. And Raja takes the best possible action given the action of Appu.” He gave the class a few moments to think and then asked, “How do you think Appu and Raja should act?”

A girl in the front row put her hand up. “Let’s assume Raja confesses. If Appu too confesses, Appu gets 3 years. If he denies he gets 10. It therefore pays for Appu to confess. Now let’s assume Raja does not confess. If Appu confesses, Appu will get only one year. If he does not confess, Appu will get two years. It still pays to confess. Clearly the best action for Appu, regardless of what Raja does is to confess”. Boka looked bored.

Happy at the reasoning, Chatshow asked, “How does Raja view the problem?” “Ditto” screamed the class.

“If Appu confesses, Raja can either confess or deny. If Raja also confesses, he gets 3 years; if he doesn’t, he gets 10 years. It therefore pays to confess. If Appu does not confess, Raja can either confess or deny. If Raja confesses, he gets one year. If he does not, he gets two years. It again pays to confess. Clearly the best action, independent of what Appu does is for Raja to confess”. Boka continued to look bored.

Chatshow summed up. “Neither Appu nor Raja had committed the bank robbery. But both see that, regardless of what the other does, the best action is to confess. Each will get a 3-year prison term. This is the equilibrium of the game.”

Flowers ¬remarked: “That’s the prisoner’s dilemma. Should I deny and rely on my accomplice to deny so that we both get only 2 years? Or should I confess hoping to get just 1 year (provided my accomplice denies) but knowing that if he also confesses, we will both get 3 years? If only each knew how the other would respond. If only each trusted the other. In the absence of these, each walks a path that effectively delivers a bad outcome for both.”

Chatshow decided to move forward: “Today, we are witnessing a price war between Hindustan Lever and P&G in the detergents market. The war isn’t helping any of them. It isn’t the best outcome for either party. What should they do?” Suddenly there was a spark in Boka’s eyes. He looked like an enlightened Buddha. Still rooted to the prisoner’s dilemma he asked, “Does it not mean that those who confess may not have necessarily committed the crime?” Wacky question indeed. “Satyamevajayathe” roared a backbencher, obviously in support. Chatshow ignored him and asked “Any answers?”

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About Pattabhi Ram

A chartered accountant by profession, a writer by passion and a teacher by accidental choice.
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