Fictitious play for multi-player games

[jukofyork]

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I guess the challenge here is:
Can we model the "strategy-negotiation process" in a way, such that the Caller eventually "realizes" that its profitable for him to stay at a wider call range, given that the pusher is adopting his ranges?

Even when the pusher is pushing tighter now and switching to a tighter call range would be immediately profitably for the caller - the idea is to simply to "keep" the pusher from loosening up again, because tightening up will eventually end up in a worse state for the caller.

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Ah, I'd forgot that the wider calling, leading to winder pushing, would end up with the caller being able to exploit by calling thinner the the original NE (I was thinking that it would just be like NE+SpiteCall for some reason). So sadly this means that their will be no "spite-call" equilibrium possible.

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OK, I've thought about this some more and how about if we add the extra constraint that the caller is forced to state his exact strategy before the pusher pushes?

This should get round the possibility of the caller to pass up on his spite calls and allow for convergence to a "spite-call" equilibrium?

Juk [img]/images/graemlins/smile.gif[/img]