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Prisoner's dilemma

By Lawrence B. Ebert, Esq.

In a post titled Health Reform: A Prisoner's Dilemma , KAREN TUMULTY uses the imagery of the game theory problem "the prisoner's dilemma" to get across the point:

The parallel here is that, in purely political terms, the easiest choice for endangered Democrats in swing districts is to vote against the bill--but only if it passes

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]

Relative to issues in patenting the industry standard, note of coordination games: An example of a coordination game is the setting where two technologies are available to two firms with compatible products, and they have to elect a strategy to become the market standard. If both firms agree on the chosen technology, high sales are expected for both firms. If the firms do not agree on the standard technology, few sales result. Both strategies are Nash equilibria of the game. [from wikipedia]

Of game theory and Nash, Nash's first paper EQUILIBRIUM POINTS IN N-PERSON GAMES is available on the internet. It's in PNAS and it's less than two pages long. The punchline is

In the two-person zero-sum case the "main theorem"2 and the existence
of, an equilibrium point are equivalent. In this case any two equilibrium
points lead to the-same expectations for the players, but this need not occur
in general.

Of note, the work was sponsored by the A.E.C. (the Atomic Energy Commission), Nash's short proof was facilitated by someone else ( The author is indebted to Dr. David Gale for suggesting the use of Kakutani's theorem to simplify the proof and to the A. E. C. for financial support. ) and the paper was communicated to PNAS by Solomon Lefschetz, the chairman of the mathematics department of Princeton)

**Of the prisoner's dilemma as an argument AGAINST plea bargaining

The theoretical conclusion of PD is one reason why, in many countries, plea bargaining is forbidden. Often, precisely the PD scenario applies: it is in the interest of both suspects to confess and testify against the other prisoner/suspect, even if each is innocent of the alleged crime. Arguably, the worst case is when only one party is guilty ? here, the innocent one is unlikely to confess, while the guilty one is likely to confess and testify against the innocent. [from wikipedia]

**
Health Care: Beyond Prisoner's Dilemma

Full post as published by IPBiz on March 05, 2010 (boomark / email).