In the Part I of this series, we made the assertion that the right strategy is to always cooperate. In this post, I will lay out the reasoning behind that assertion using Prisoner’s Dilemma construct used in Game Theory.
Prisoner’s Dilemma (PD)
The central concept of Prisoner’s Dilemma resides in the fact that each party has a choice between only two options, cooperate or defect, but cannot make a good decision without knowing what the other one will do.
Classically, PD is stated as “Imagine two criminals arrested under the suspicion of having committed a crime together. However, the police does not have sufficient proof in order to have them convicted. The two prisoners are isolated from each other, and the police visit each of them and offer a deal: a) Provide evidence and you are free to go (Defect on your partner) or b) Keep your mouth shut and you get a small punishment (Cooperate with your partner)”
One can generalize PD argument to real-world interactions related to working with others on a project, a business contract, etc. Below is a sample pay-off matrix that represents a PD-like scenario:
The numbers in the boxes represent units of satisfaction. For instance, if you cooperate and other party cooperates as well – cooperate-cooperate scenario, then each of you can derive two units of satisfaction. However, if you defect and other party cooperates – cooperate-defect scenario, then you get four units of satisfaction, while other party gets negative one units. Other way to look at this payoffs –
Payoff of two = Reward (R) for mutual cooperation
Payoff of four = Temptation to defect (T)
Payoff of zero = Punishment for mutual defection (P)
Payoff of negative one = Sucker’s Payoff (S)
For payoff matrix to represent PD, two conditions need to hold:
- T > R > P > S (in our case, 4 > 2 > 0 > -1)
- (T+S)/2 < R (in our case, 4 – 1/ 2 (=1.5)< 2)
According to first condition, it’s always better to defect since we get the maximum units of satisfaction (four). And this creates huge temptation to defect. However, the key to answer to the question “Why always cooperate” lies in the second condition.
According to the second condition, the payoff for Cooperate-Defect (C-D) scenario (with average payoff of 1.5) will always be less then Reward points (2). This ensures that in the long run, Cooperate-Defect (C-D) scenario will always yield lower average payoff (1.5) compared to average payoff (of 2 points) for Cooperate-Cooperate (C-C) scenario.
In other words, one can take a short-view and defect because the temptation is so high, however, over multiple iterations (or transactions), the average pay-off for C-D scenario is lower compared to C-C. Our defection the first time around, might very well lead to defection from the other party in the next iteration and even worse, total loss of opportunity to work together with the other individual.
As they say, grow the pie and not slice the pie. And Game Theory with the PD model tries to convey the same mathematically.
In the next installment of this series, I will articulate the reasoning behind why “tit-for-tat” is the best strategy in the event there is defection from the other party.