For the Weekend: John Donne

The first write-up of the Prisoner's (or is it Prisoners'?) Dilemma: Merrill Flood (1958): Some Experimental Games: "Summary: Two players non-cooperatively choose rows and columns of their payoff matrices in a series of 100 plays of a non-constant sum game. The purpose of this experimental game is to determine which of several theories best describes their behavior. The players, being familiar with zero-sum game theory, happen to choose a poor solution for their non-constant-sum game...

...The experiment suggests the hypothesis that people tend to start near an equilibrium point and then try to find a better equilibrium if there is one. At the end of the series of plays the players appear to be converging to a cooperative split-the-difference principle, or a cooperatiive von Neumann-Morgenstern solution, in this formally non-cooperative game. The social relationship between players appears to be an important factor. (January 1950)

There are now several theories for various special classes of games, some of which are not formally games in the von Neumann-Morgenstern sense. One theory that is of interest is that of Nash for games in which coalitions are prohibited, called non-cooperative games. One brief experiment was conducted with a two-person positive-sum non-cooperative game in order to find whether or not the subjects tended to behave as they should if the Nash theory were applicable,9 or if their behavior tended more toward the von Neumann-Morgenstern solution, the split-the-difference principle, or some other yet-to-be-discovered principle.

The two subjects AA and JW were familiar with two-person zero-sum game theory. They also knew something of the von Neumann-Morgenstern theory for non-constant sum games, but were not familiar either with the work by Nash or with the split-the-difference principle. It was originally intended that non-cooperation be enforced by keeping each subject in ignorance about the identity of his opponent, but this was not done, due to an accident at the outset; the experiment certainly seemed to be fully non-cooperative since there was no evidence of side payments, but there may well have been some implicit collusion within the rules of the game...