email@example.com (Malcolm Ryan) wrote in message news:<firstname.lastname@example.org>... > A question about game theory: > > In a classic n-player simultaneous move matrix game (eg, the > Prisoner's dilemma) better outcomes can be obtained if you have some > way of making a binding (or believable) promise that you will choose a > particular action. > > Eg: Say you and I are about to play Prisoner's Dilemma. But we are > given the opportunity to communicate before the game, and I swear upon > my life that I will cooperate, if you promise to do likewise. Now it > is in your best interest to agree. We both promise to cooperate, and > as people of our word, we both maintain our promises. For each of us > the payoff is better than it could have been without having made the > promises before the game. > > Alternatively, promises can be regarded as threats. Consider the game > of Chicken: > YOU > Drive Swerve > ME Drive (0,0) (3,1) > Swerve (1,3) (2,2) > > There are two equilibria for this game, either combination of > Drive/Swerve or Swerve/Drive. If I can make a binding promise to you, > before the game, that I will not swerve (perhaps by throwing my > steering wheel out the window) then your only rational decision is to > swerve. So I guarantee a favourable outcome for me by making an > appropriate promise/threat. > > My question is: has anyone done a full analysis of this kind of > promise-making? It seems fairly elementary to me. I'm interested in > doing some research in this area, but I'm rather new to game-theory. > I'm familiar with most of the standard text-book stuff, but text-books > are always behind the times. Is anyone out there up with the state of > play? Are there any papers I ought to read? > > Malcolm
Very interesting. However, in both of these cases you assume that the promise is kept. While I will admit that in the Chicken game throwing the steering wheel out the window would be a binding promise, what if simultaneously the other player did the same thing? Your reward drops from 3 to 0 immediately. In the Prisoner Dilemma, a similar effect happens. Prisoner A can make a promise to the B, in order to recieve a promise from B that B will not sell A out. Then, A will sell out B in case B might sell out A. The idea of that could nullify all effects of a previous promise. However, it is an interesting concept, and I am not very experienced in game theory. Some papers you might like to read are anything by John Nash. Yes, I know that it is nothing new, but he was a pioneer in the field and it would be good to read anything by him. I hope you have success in working out your theory.