dilemma

One of my heroes is Howard Raiffa, a pioneer in decision science and game theory. Before he passed away in 2016, Professor Raiffa held a joint chair at Harvard Business School and the Kennedy School of Government.  His expertise spanned statistical decision theory, game theory, behavioral decision theory, risk analysis, and (of particular interest to me) negotiation analysis.  His seminal book The Art and Science of Negotiation is a classic text in the field of conflict resolution.  It is a foundational text that integrates the fields of game theory and negotiation in innovative ways.

One of the examples of this synthesis of game theory and negotiation theory discussed in Prof. Raiffa’s book is the Prisoners’ Dilemma.  In case you haven’t come across the Prisoners’ Dilemma before, it’s outlined in the graphic above and in the description below (written by Albert Tucker, who gave it its name):

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:

  • If A and B each betray the other, each of them serves 2 years in prison
  • If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
  • If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge). 

This simple model is a neat representation of one of the central challenges of negotiation. If the prisoners trust each other, they’re better off overall.  But if the trust is undermined, they are tempted to betray the other, and they’re potentially much worse off. Extrapolate this to any negotiation partnership and you understand the importance of trust between negotiators. Once trust is undermined, there is always a temptation to betray, which can be worse for everyone.

A later classic book in the conflict resolution field is Axelrod’s Evolution of Cooperation, which leverages the Prisoners’ Dilemma extensively.  Axelrod invited game theorists to write algorithms to play the Prisoners’ Dilemma, and then to come to the University of Michigan (where Axelrod is a Professor in Political Science) to play in a Prisoners’ Dilemma tournament with multiple rounds.  In a field of competing algorithms, some with very complex rules for when to betray and when to remain silent, the winning algorithm across all the matches was a simple approach titled “tit for tat.”

Tit for tat works this way: it starts out trusting on the first round, and subsequently copies the other side’s prior move.  The core idea is that good behavior is rewarded by reciprocating with good behavior, but bad behavior is immediately punished.  In practice, tit for tat cooperates when the other party has an immediate history of cooperating and betrays when the other party previously betrayed.

Now my goal is not not to give you a Spark Notes version of a degree in game theory and negotiation — so let me cut to the point.  As Megan McArdle explained in the Washington Post last week, our nation is having a tit for tat moment.  As Prof. Raiffa would have probably argued, our national nervous breakdown can be modeled in game theory, which can generate insights about how to start to recover.  As Megan put it in her piece:

“…both sides think they have legitimate grievances, and both are hurting themselves as they try to punish the other. At this point, the only way out is for everyone to put themselves in timeout — to think hard about whether their behavior reflects the kind of people they want to be, or the kind of country they want to live in. And then try to find some common set of rules that will let us cooperate instead of mindlessly punishing each other.”

It’s not going to happen all at once, and there are sure to be fits and starts as we try to work our way back to cooperation.  But the good news is, a) people respond to incentives, and b) tit for tat shows us it’s not really that complicated.  We just have to keep our responses proportional and forgive quickly to get things back on track.  But someone has to take the first step by trusting the other side.