Game Theory: Prisoner's Dilemma and Tag Team Tic Tac Toe

What is game theory? It is the science of strategic thinking:

• Branch of mathematics used in economics, military strategy, politics, and most important, relationships.

• Best decision possible based on the way you expect other people to act.

• Players have to be rational.

• Try to understand the perspective of the other player (not what you would do in their shoes but what you think they would do).

zero sum game: a situation in which one person's gain is equivalent to another's loss, so the net change in wealth or benefit is zero. Examples are chess, tennis, poker, flipping a coin, etc. We have one winner and one loser. Rock, paper, scissors is a great example.

win-win game: opposite of a zero sum game where both players can gain a benefit. One example is splitting a cake between two people fairly so one cuts and one chooses. What about splitting the cake fairly between three people? (player 1 cuts the cake in half, player 2 chooses one of the halves, players 1 and 2 both try to cut their half into three equal parts, and player 3 chooses one of each of player 1 and 2's thirds). Most famous example is the:

Prisoner's Dilemma: Two people, who are suspected to have been involved in a serious crime, are being interrogated separately by the police. The police inform each man that they know that they were involved in a serious crime but don’t have enough evidence to convict them. They also inform the suspects that they know that they were involved in a more minor crime and that they could easily convict them of this one. They offer each suspect the following deal. If one of them confesses but the other one. doesn’t, the one who confessed will be freed and the one who did not will do 20 years in prison. If neither of them confesses, they will be easily convicted of the minor crime and both will do 1 year in prison. If both of them confess to the more serious crime, they will each do 5 years, instead of the full 20 years, as a reward for their cooperation. Assuming the suspects would rather do less time in prison than more time, they would both be better off if they both kept quiet. But some simple tools of game theory can show that each prisoner is under compelling pressure to confess.

the children: their discussion of the prisoner’s dilemma surprised me greatly. Many of them analyzed this exactly like a mathematician would. First they looked at the two possible scenarios if the prisoner confessed: either get 5 years in jail if the other prisoner also confesses or they go free if the other prisoner remains silent; a net cost of 5 years (5 + 0). Second, they looked at the two possible scenarios if the prisoner remained silent: either get 20 years in jail if the other prisoner confesses or they get 1 year in jail if the other prisoner remains silent; a net cost of 21 years (20 + 1). The decision was easy, you must confess. Many of the children really wanted to look at a scenario where the two prisoners could somehow communicate to signal to each other to remain silent to get the 1 year sentence only. Of course, this model breaks down when you consider that the decision to remain silent is too risky given the lack of integrity of criminals: they lie.

Tag Team Tic Tac Toe: for the last 17 years, I have conducted an exercise with thousands of students, from young children to seasoned executives while teaching negotiation skills. If you are interested, you can read an article I published in 2004 called THE LOST ART OF ETHICS AND COLLABORATION: WHERE DID WE GO WRONG? http://faculty.washington.edu/janegf/ethicsinnegotiation.pdf.

I introduced this game theory exercise to the Mathletes this week and they were able to see a mathematical proof that collaboration produces a significant gain over self-interest. Please read the write up in the attached pdf which has the rules of the game and a script for the children to take you and their teachers through the exercise. It would be great if they were just able to take you through the proof. I am trying to convince them that the majority of life’s “games” are win-win and require a collaborative mindset to yield the highest return, whether in education, relationships, and someday, business.