Sunday 19 December 2010
Last Sunday we had a sort of workshop on "negotiation" for some of the Mozilla managers. Part of this workshop was an exercise amounting to playing Iterated Prisoner's Dilemma, with some twists which aren't relevant here. There were three independent games, each with two players, each player being a team of three or four people. We were instructed to maximise our own score without regard to the other player's score.
My approach was to observe that if both teams behave perfectly rationally, they will use the same strategy. Then the optimal strategy is obviously to always cooperate. If the other team defects then you know the rationality assumption doesn't hold, so the game gets more difficult (probably devolving to the game-theoretic equilibrium of always defecting, but then asymptotically it doesn't matter what you did before detecting defection). Fortunately for us the other team was in fact rational enough to always cooperate and we played a perfect game. (If the number of iterations is known in advance, defecting on or before the last round might make sense, but we couldn't be sure how many rounds there were going to be so this didn't matter.) This approach is known as superrationality although I wasn't aware of that at the time...
One surprise for me was that at least three of the six teams did not always cooperate. I was a bit disappointed to find that not all my colleagues think like me :-). I don't think that was supposed to be the lesson of this exercise, though :-).
Another surprise was that some people expected me to play the game according to "Christian principles". In fact, I was purely trying to optimize the objective function we were given, regardless of what God would want. This raises a very interesting question: is it OK to disobey God's commands within the framework of an artificial game? In many games, especially games with more than two players that involve alliances, lies and betrayal are an essential part of the game. Is it OK for a Christian to lie and betray in such games?
I think the answer depends on the context. If everyone understand it's "just a game", the diabolical behaviour is demanded by the framework of the game, and there are absolutely no hard feelings about such behaviour, it seems harmless. But in any context where others might expect you to be obeying God even within the framework of the game, I think we have to follow Paul and play it safe so we do not "cause others to stumble". So I think in hindsight I was wrong to ignore Christian considerations in our negotiation exercise, although I think they lead to the same results anyway.
So what would Jesus do in a real-life Iterated Prisoner's Dilemma? It seems obvious: "do to others what you would have them do to you", which leads to the same analysis as I had before --- cooperate. If the other player defects, the Sermon on the Mount still applies --- "turn the other cheek --- and also "forgive seventy times seven times": we are asked to cooperate in the face of repeated defection.
Interestingly, in this game, belief in the trustworthiness of the other player --- or even belief in divine justice --- lead to superior joint outcomes on average even if the belief is false. Most people think it's obvious we should believe only what is true, but I don't think that principle is obvious at all in (for example) materialist utilitarian frameworks. It should be obvious to Christians.