I just completed at Columbia a game theory course. Of course, I won't try and reproduce all I learned, let a lone all of game theory. There are plenty of good explanations such as Wikipedia, the first two chapters of our textbook by Osborne, and the entire text of A Course in Game Theory. But a basic problem is Prisoner's Dilemma, about which many of you have heard. For us, Dr Clarke reworded the problem as a public goods problem 1. Two neighbors share a yard. It costs $150.00 a year to plant and maintain a nice garden in the yard. Each would get $100.00 worth of enjoyment should the garden be planted. Each neighbor has a choice of contributing to what is a public good or reneging. The payoff matrix is
|Do Not Contribute||Contribute|
|Do not Contribute||0,0||$100,-$50.00|
The mathematical theory says that the same thing would happen if both of our two homeowners knew they would share the yard for fifty years. The Subgame Perfect Equilibria of the finitely repeated game gives the same result. However, if the game is repeated indefintely, then both parties would contribute yielding the net benefit for both of them. The assumption is there is a discount factor that determines how much a garden in the future is worth compared to a garden this syear. If both parties are infinitely patient then the lower right result of both parties contributing to the garden prevails-- exactly opposite the Nash Equilibrium approach! If Party A decides to welch, not contributing while allowing the other party plant the garden, the other party welches the next time--the famous tit-for-tat. If Party A is somewhat impatient, it might take a few more seasons of "punishment" to get Party B to cooperate. The Nash Folk Theorem says that we can get the parties cooperating if the parties are sufficiently patient.
Hotelling used game theory to show that in a two-way election like we have with the two-party system, the parties will say about the same thing. If Candidate A is off to one side of the median position, then Candidate B will go to the median and win the election. And as Theiss-Morse showed, the American people on average think the government is at the right place on the left-right spectrum. (As many people think the government should be further to the left as further to the right.) But they would like to see more participatory democracy.