Politicians' Dilemma

This is a game with two players, Arboma and Berckle. They are politicians who have agreed not to tap each other’s phones (or otherwise to spy on each other).

Each has a choice between sticking to the agreement, which will call cooperating, or breaking the agreement, which we will call defecting. Each would prefer to be able to make private phone calls. Each would prefer to be able to listen in on the other’s phone calls.

If we assign numbers to the possible outcomes, we can specify the payoff matrix for the game. Each player faces the same decision—cooperate or defect—although it is possible for each to decide differently. For example, if A cooperates and B defects, A gets zero, and B gets five (of whatever unit A and B are playing for).

A cooperates A defects
B cooperates 3 each for A and B 5 for A, Zero for B
B defects Zero for A, 5 for B 1 each for A and B

As A, how would you play? In other words, would you cooperate, or would you defect? Note that B faces exactly the same question, and the same payoffs. You will each choose to cooperate or to defect; you will do so simultaneously and without conferring.

Now you and the same person will play the game again. The only change is that you will now play it three times in succession, rather than just once. How did this change (three rounds) to the game change your thinking? Did it change your decision? What other changes to the game might change the players’ thinking?

You may have recognized the Politician’s Dilemma. It is the Prisoners’ Dilemma, with the prisoners disguised as politicians; I’ll shorten the name of this game to PD.

Why call PD a game? Because the study of models involving interdependent decisions is called game theory. Game theory terms include payoff matrix, used above, and Nash equilibrium. The latter refers to a combination of decisions in which each player’s decision is the best response to the other player’s. Not every game has an equilibrium, but PD does: defection by both players.

One of the interesting things about PD is that its equilibrium does not yield the best outcomes for the players. Both would fare better is they both cooperated. But, as we can see from the payoff matrix, if A cooperates, B will do better by defecting than by cooperating.

A player may think differently if they play PD multiple times against the same other player. (This is known as the iterated Prisoners’ Dilemma.) A player may cooperate, hoping that the other will reciprocate by cooperating in future rounds.

We might think differently about PD if we question the assumption that cooperation is “good”. For example, we can: change the setting of PD to business; have A and B represent firms (Arboma Inc and Berckle Werks?); assume that A and B control the supply of a product (i.e. assume a duopoly); and focus on the form of cooperation known as price-fixing. Then mutual cooperation would constitute collusion; it would maximize the outcome for both firms, at the expense of consumers.

Defection would mean competing on price. This would maximize market share for the price-cutting firm, and would also benefit consumers.

Should government act to prevent collusion between firms? If the answer is “yes”, the government can “change the game.” It can reduce the payoff for collusion in one or both of two ways. First, it can increase the penalties for colluding, by increasing fines. Second, it can increase the probability that collusion will be detected, by allocating more resources to investigation of corporate wrongdoing.

The government can change the game more radically by making sure that there are at least three major competitors in the industry. This moves us beyond PD, to what I’ll call the Peasants’ Problem, and addresss in the next post.

If you want to read more on PD, the classic book is Robert Axlerod’s The Evolution of Cooperation. Note about links: to Amazon; to Kindle edition, where available; I’m an affiliate, so there’s a danger I may earn a commission.

If you want to read more on game theory, I recommend Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life, by Dixit and Nalebuff, as accessible without being superficial. (I understand that their more recent book, The Art of Strategy, is rather similar, but I haven’t read it.)

If you want to read my favorite business book, go for it: Co-Opetition. It’s about the mix of cooperation and competition. Appropriately enough, its two co-authors were at rival universities: Harvard (Adam Brandenburger, now at NYU) and Yale (Barry Nalebuff, still at Yale).

PDjpg.If you want to an illustration of old-school PD, here you are, thanks to Giulia Forsythe, Flickr, and Creative Commons.

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