...except for me and my monkey! "Everything we see hides another thing. We always want to see what is hidden by what we see." -Rene Magritte

Tuesday, November 22, 2005

Game Theory on my mind

I keep thinking about this problem we analyzed in Game Theory last spring. Let me see if I can explain it (Christine, feel free to jump in in the comments): There are two players, you and some artificial intelligence entity (which could also be called God; in any case, it´s omniscent. I´ll call it God for simplicity´s sake). Each player has two options, A or B. You are the first player (you choose A or B, then God chooses A or B). For you, playing A is the ´´safest´´ option; if you play A, no matter what God does (ie regardless of whether God plays A or B), you´ll get a good payoff. Playing B is riskier: If you play B and God plays A, then you get a low payoff. But if you play B and God plays B, then you get the highest payoff of all.

Basically what the problem boils down to is whether or not you trust God to act in your best interests: whether you´re willing to bet the possibility of a low payoff (you play B, God plays A) against the possibility of a high payoff (you play B, God plays B). Extrapolating the consequences even further, the problem is supposed to indicate whether you believe in free will or determination. The person who believes in free will will play A, getting a decent payoff regardless of what God does (ie they don´t trust God to maximize their payoffs). The person who believes in determination will play B, because they trust that God will also play B, giving them a high payoff.

With me? The reason this has been on my mind is that it´s a pretty good model for the Pedro Montt vs. Errázuriz bus dilemma.

See, there are two buses I can take to get into Valparaíso from Viña del Mar: the Pedro Montt buses, and the Errázuriz buses. The Errázuriz buses always follow the same route and drop me off about a block and a half from the university. That´s a decent payoff; it´s a quick walk. The Pedro Montt buses, approaching Valparaíso, follow two distinct routes: they either get on the overpass and stop at the corner of Pedro Montt, about three or four blocks from the university, or they stay on the main street and stop right at the door of the U. In other words: a crappy payoff (especially when I have classes in Gimpert, I end up having to walk about seven blocks) or the best payoff of all (a walk of a few meters). I always ask the drivers of the Pedro Montt buses to let me off at the university, and about 50% of them do. At first I thought that whether they went on the overpass or not depended on the traffic lights near the U, but more and more I´m convinced that it´s random.

In this case, the Errázuriz buses are option A: they´re safe; I get a decent payoff no matter what. The Pedro Montt buses are option B: I can get either a high payoff (driver stays on the road) or a low payoff (driver gets on the overpass and continues to Pedro Montt). The dilemma is: do I trust the driver of a Pedro Montt bus (God, in this case) to act in my best interest and drop me off by the university? And, based on my answer, should I take an Errázuriz bus or a Pedro Montt bus? What do you think? What would you do?

If you´re interested, post your thoughts in the comments section, and I´ll edit this blog later to add the solution I´ve come up with to the problem!