First Report on a Project Studying the Analysis
of Cooperation in Games Through Modeling in Terms
of Formally Non-Cooperative Action in a Repeated
Game Context
A few years ago I gave a talk on the topic of the use
of the "Prisoner's Dilemma" game, in a context of repetition and evolution of strategies, by theoretical biologists
who were interested in studying the natural evolution of cooperative adaptations. And after giving the talk I thought more about the concept of studying a game by studying it as a repeated game and through this viewpoint I got an idea of how to eliminate all of the "verbal" complications that could become involved in the consideration of coalitions
and coalition formation.
In principle, coalitions, and specifically coalitions
as considered by Von Neumann and Morgenstern in "Theory of Games and Economic Behavior", are things that could be implemented by contracts, like contracts in roman law. But of course a contract is quite intrinsically a "verbal" thing because indeed it could (or should!) be written down in words.
On the other hand, if in Nature a form of cooperation has evolved, like with a species of insects providing fertilization for a flowering species of plants, then the cooperation exists and is maintained, not by the enforcement of a verbal contract but presumably by the action of "natural selection" affecting the genetics of both species as time passes.
My idea was that in a repeated game context that the players could be given the right to vote for "agencies" or "agents" among themselves. Thus at a first step a player, say player ...