Jim writes >yes, but do three- or four-person games ever produce useful results? are >other game metaphors used besides "I move" and "you move" of the standard >prisoner's dilemma box?
Re the first question: for the most part, analyses of games that generically feature several players are not limited to the "three- or four-person" case. Re the second question, yes, abundantly. Game theory has provided the microfoundation for much, maybe most, of modern microeconomics, and as such has been developed way, way beyond its simple roots. >I know about games such as "the dollar auction," which probably can be >modelled using standard game-theory tools, but it's hardly ever mentioned >outside of books such as Poundstone's PRISONER'S DILEMMA. That book also >mentions various other games, including one invented by John Nash that >involved movement of pieces on boards divided into hexagonal spaces. (It was >sold commercially for awhile and seems the basis of Avalon-Hill-type war >games.) Are any of these various non-standard games given any kind of >attention? How about, as I mentioned in my original missive in this thread, >card games such as solitaire? >Am I right to say that game theorists concentrate only on the simplest >possible games, because those are the easiest to analyze? In general, no. They may start with the simplest cases, but usually extend the results to the most general case possible. For example, the analysis of "strategic bargaining" models started with the bilateral, 2-player case, but now has been extended to the n-player case. Grab any recent graduate text on game theory, Jim (Fudenberg and Tirole, and Myerson, are two good ones), you'll see how general the development has been. Gil
