Okay, geeks, this one’s for you.
I hereby concede that I am out of my depth with regard to the complex processes that could determine the outcome of the upcoming health care vote. Particularly when it comes to my grad-school understanding of game theory.
At his blog IPBiz, Lawrence B. Ebert looks at my Prisoner’s Dilemma post from yesterday and makes the argument that another, potentially more relevant exercise to look at is Nash’s Equilibrium:
IPBiz notes that long before game theory and the prisoner’s dilemma, strategic voting existed. In the case of the vote of Edmund Ross in the impeachment trial of Andrew Johnson in 1868: But Ross’ vote wasn’t the lone act of bravery it was later made out to be. At least four other senators were prepared to oppose conviction had their votes been needed–a fact that has been forgotten [from Slate] More recently, strategic voting has been discussed in the healthcare saga: One lone House Republican voting for the reviled Democrat healthcare bill.
Of Nash equilibria: The Nash equilibrium concept is used to analyze the outcome of the strategic interaction of several decision makers. In other words, it is a way of predicting what will happen if several people or several institutions are making decisions at the same time, and if the decision of each one depends on the decisions of the others. The simple insight underlying John Nash’s idea is that we cannot predict the result of the choices of multiple decision makers if we analyze those decisions in isolation. Instead, we must ask what each player would do, taking into account the decision-making of the others. (…) The contribution of John Forbes Nash in his 1951 article Non-Cooperative Games was to define a mixed strategy Nash Equilibrium for any game with a finite set of actions and prove that at least one (mixed strategy) Nash Equilibrium must exist.(…) Of the prisoner’s dilemma, the globally optimal strategy is unstable; it is not an equilibrium.[from wikipedia]
And from the incomparable Swampland comments section come two other arguments:
This is not the Prisoner’s Dilemma (because I should also tell the police in a one shot game, but play tit-for-tat in an infinite repeated game (see Axelrod’s tournament) ), but rather it is best explained by the Lighthouse story. Imagine a fishing community by a rocky shore. They all want to build a lighthouse to keep the boats safe. The lighthouse will cost $15, and there are 25 fishermen. So if each pays $1 they get the lighthouse. Now, if I pay the money and the lighthouse is not built I lose a dollar (imagine a nasty builder). If I pay the dollar and get the lighthouse I benefit from the lighthouse but I still have lost a dollar. If I don’t pay the dollar, but 15 others do, I also get to benefit from the lighthouse. Should I pay the dollar? Well only if 14, and only 14 others, pay a dollar. Otherwise I waste a dollar, either by paying and not getting the lighthouse, or by paying and the community collect more that $15. The real problem is that if I don’t know what the others are doing should I gamble and pay the money. I have played this game in about 10 classes, and the lighthouse has NEVER been built.
Commenter rimmyrimrim comes at this from pretty much the same direction, citing a game theory exercise called Volunteer’s dilemma.
Of course, this is not a game we are talking about here; it is a big decision that will affect the lives of millions and millions of people. Nonetheless, it is sort of interesting and thought-provoking to take it, at least for a moment, out of the partisan realm, and into the academic one.
Any game theory exercises we are missing?