game theory

Jim Farmelant farmelantj at juno.com
Tue Mar 19 06:35:08 PST 2002


It should be noted that the concept of an iterative Prisoners Dilemma game has been used by evolutionary biologists for understanding the evolution of reciprocal altruism. In an iterative Prisoners Dilemma game, the prisoners still cannot communicate directly with one another but since the game is repeated iteratively, each prisoner knows whether or not the other has defected in past rounds of the game, and so is free to adjust his or her strategy accordingly. In experiements by William Hamilton and Robert Axelrod, it was found that people tend over time to adopt tit-for-tat type strategies, where they will cooperate as long as the other person reciprocates, and will defect, if the person has done so previously.

In economics, the notion of an iterative Prisoners DIlemma game has been used in the study of imperfect competition and oligopolies, where presumably direct communication between companies over such matters as prices would be in violation of price-fixing laws and antitrust laws.

Jim F.

On Tue, 19 Mar 2002 03:15:54 -0600 "Daniel Davies" <dsquared at al-islam.com> writes:
> >Date: Mon, 18 Mar 2002 22:38:47 -0600
> >From: Carrol Cox
> >Subject: Re: game theory fails a test
>
> >But doesn't the prisoner's dilemma depend on the >prisoner's (a)
> not
> >communicating and (b) a fortiori, not going through a >process of
> >struggle and self-criticism to work out the principles of
> >collaboration?
> >That seems to rather separate from the world of actual >human
> experience,
> >either today or 60,000 BP.
>
> Game theory is very useful for things like, for example, designing
> auctions
> aimed at making people pay top dollar for mobile telephone licenses.
> Most
> of the practical uses are in this sort of area. (thinking about
> this, it
> relates back to an earlier conversation about the usefulness of
> maths in
> economics; auction design is probably the only area of economics
> where it's
> absolutely impossible to understand it at all if you don't
> understand it
> mathematically).
>
> More generally, there are real-world situations where the prisoners'
> dilemma results are valid. Also note that the PD doesn't really
> need the
> non-communication stipulation. you can let the two prisoners
> communicate
> as much as you like right up until the instant that they have to
> decide;
> they can make as many promises as they like that they'll co-operate,
> but
> these promises are not credible if you assume that the prisoners are
> moderately self-interested (ie, self-interested enough that there is
> some
> number of years in jail which they would sell out a buddy to avoid,
> which
> isn't all that restrictive or unrealistic).
>
> The argument is the basis of the concept of a Nash equilibrium. A
> Nash
> equilibrium is defined (loosely) as a set of strategies under which
> each
> player is doing as well as he can given the other players'
> strategies. The
> analogy to a Pareto optimum is close; you can't be at a Nash
> equilibrium if
> player could do better for himself by changing his (taking other
> players' strategies as given). So (co-operate, co-operate) is not a
> Nash
> equilbrium because either player can improve on it by moving their
> strategy
> to "defect", while (defect, defect) is a Nash equilibrium because at
> that
> point, neither player can improve on it by moving their strategy to
> "co-operate".
>
> I'd also note that Nash equilibrium is a much less compelling and
> interesting property of strategy sets than it is commonly conceived
> to be
> (for example, by the Nobel committee). There is no force pulling
> you
> toward a Nash equilibrium in the way that there is toward a
> competitive
> equilibrium or a no-arbitrage condition. It's just the mathematical
> tractability of the Nash condition in a few cases of interest, plus
> its
> superficial resemblance to the Pareto condition, that makes people
> try to
> identify Nash equilibria as necessary rational choice outcomes,
> which they
> aren't.
>
> dd
>
>
> Get Your Free Email at http://www.al-islam.com
>
>

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