Professor Hugo F. Sonnenschein of the University of Chicago explains the famous prisoner’s dilemma differently.
There are two players, A and B, and a moderator. The moderator hands A and B a dollar each and an envelope. Players can keep the dollar in their pocket or leave it inside the envelope. Players then return the envelope to the moderator; the moderator can’t see what each has done. The moderator then looks at the envelopes and doubles the amount she sees inside them. In other words, if she sees a dollar inside the envelope, she makes it two; she doesn’t add anything if she sees nothing.
The moderator then switches the envelopes (envelope A to B and B to A) and gives them back to the players. What is the best strategy for the players to do in the first place—keep the dollar inside the envelope or hold it with them?
Player A can do two things with four possible outcomes; one guarantees a profit.
Keep the dollar in the pocket and return an empty envelope. This guarantees $1 if the other player does the same, or A gets two more dollars if player B is magnanimous (returning her envelope with a dollar in it).
The second option for player A is to return the envelope with one dollar in it. Again, there are two possible outcomes: A gets nothing if player B follows A’s first strategy (keeping a dollar in her pocket) or two if the other returns with a dollar in the envelope.
If you want to be formal with the payoff matrix, here it is.
While it is perfectly understandable that corporation (by each putting their dollars inside the envelope) brings prosperity to both (2 dollars each), the game theory doesn’t work that way. It will give you a strategy that guarantees you a profit irrespective of what the other person would do. In other words, the rational approach is to be selfish.
Game Theory and Negotiation: Becker Friedman Institute University of Chicago
