Mixed Nash continued

Following up on the four-person game analyzed in the previous post...

Memo to self: If the Pascal-Bentham-Whitman-Nash type that optimizes in two-player games and holds its own against egoists is a truly groovy type, it should also optimize and be an evolutionarily stable type in the four-player game in which you play either 2 or 10 and get either $2 or $10 except that if all four choose 10 no one gets anything.

As a two-person game, this is a leadership game, and I'm morally sure (that is, I think I know but don't really know) that P-B-W-N will optimize because the game is similar enough to ones I have analyzed.

As a four-player game...well, I haven't really thought about multi-player games for P-B-W-N purposes, basically because the tech gets out of my league...

A note or two...the .928 probability of playing 10 that is mixed Nash for four egoists is decidedly suboptimal...a little SAT-style plug-in suggests that the optimal level of playing 10 is somewhere between .5 and .75...so P-B-W-N if it is an optimizing type in the 4-player game should play 10 at that lower level...to meet the criterion of being an evolutionarily stable strategy, it should also be resistant to egoism...

I'm genuinely interested (i.e., no moral certainty here) as to whether P-B-W-N is optimizing and an ESS in the 4-player game...a to-do for when some time opens up after getting my SBE paper for 3/1 done...

 

 

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