CronoDAS comments on Mixed strategy Nash equilibrium - Less Wrong

40 Post author: Meni_Rosenfeld 16 October 2010 04:00PM

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Comment author: CronoDAS 17 October 2010 05:41:26AM *  0 points [-]

A Nash equilibrium is frequently not Pareto efficient; if everyone changed their strategy at once, everyone could do better.

The Traveler's Dilemma is a game that's similar to the Prisoner's Dilemma, and humans usually don't play the Nash Equilibrium strategy.

In other words,

This notion of mechanism design, and more generally of rational play, is certainly interesting mathematics, but in practice it often leads to mechanisms that consistently perform very badly (sometimes it gives good mechanisms, but that is no thanks to the formalism)

means "people often don't behave the way game theory says they should, and assuming that they will is often foolish."

Comment author: Perplexed 17 October 2010 02:06:12PM 3 points [-]

A Nash equilibrium is frequently not Pareto efficient; if everyone changed their strategy at once, everyone could do better.

If everyone does better at a different Nash equilibrium, then that just shows that being a NE is necessary, but not sufficient for mutual rationality.

If everyone does better at a joint strategy that is not an NE (PD, for example), then one of the players is not playing rationally - he could do better with another strategy, assuming the other player stands pat.

... people often don't behave the way game theory says they should, and assuming that they will is often foolish.

Assuming that they won't be rational can often be foolish too.

Rational-agent game theory is not claimed to have descriptive validity; its validity is prescriptive or normative. Or, to be more precise, it provides normatively valid advice to you, under the assumption that it is descriptively valid for everyone else. And yes, I do appreciate that this is a very weird kind of validity for a body of theory to claim for itself.

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