Game theory covers different scenarios of cooperation and competition in 2 person contests where one player’s gain is another player’s loss. The objective always being to identify an equilibrium position i.e where both persons are satisfied with their strategies given the opposite party’s choices.

The equilibrium position is not necessarily the best outcome for the players, best example is the game theory’s most famous, provocative, and controversial 2-player game: “the prisoner’s dilemma”.

What is the Prisoner’s dilemma?

Imagine that you and a co-conspirator have been arrested after robbing a bank (USD 1M) and are being held in separate jail cells. Now you must decide whether to “cooperate” with each other—by remaining silent and admitting nothing—or to “defect” from your partnership by ratting out the other to the police.

Options:

1.      Cooperate: both cooperate, both walk free, split loot (0.5M)

2.      One defects, other silent: the informer goes free, gets 1M, silent one gets 10-year sentence

3.      Both defect: share blame, and each gets 5 years sentence

Here’s the problem. No matter what your accomplice does, it’s always better for you to defect i.e this is the equilibrium strategy. The paradox is that if both do the rational thing then both of you end up serving 5 years sentence compared to freedom and 0.5M (if they cooperate).

This has emerged as one of the major insights of traditional game theory: the equilibrium for a set of players, all acting rationally in their own interest, may not be the outcome that is best for those players

Solution:

Applying reverse game theory identify what rules will generate the desired behavior.

1.      We will make one crucial addition to the prisoner’s dilemma: the Godfather!

2.      Now you and your fellow thief are members of a crime syndicate, and the don has made it all too clear that any informants will sleep with the fishes.

3.      This alteration of the game’s payoffs while limiting the actions you can take, ironically makes it far more likely that things will end well, both for you and your partner.

4.      Since defection is now less attractive (to put it mildly), both prisoners must now cooperate, and both will confidently walk away half a million dollars richer. Minus, of course, a nominal payoff to the don!