[jukofyork]

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Some kind of "raw" first idea, didnt really think it through yet:
Instead of optimizing the "current" equity (ie, playing maximally exploitative), each player tries to "drag" the strategies in a direction that will give him better equity than the current state - but only as long as his deviation from maximally exploitative play costs the respective opponents more EV than him.

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Yep, this is what I was thinking, but "dragging" the values could be very computationally expensive to try. The basic idea would be to somehow "drag" your own strategy into the space where it is -EV for you and see how that effects your opponents maximally exploitative strategy. The current update rule never considers these -EV calls.

Perhaps rather than "dragging" this could be accomplished by some kind of recursive update rule which is about order O(n) more complex? One idea would be to find the gradient of EV change for you for each variable of the strategy and then update your strategy variable by moving in the direction which increases EV for you (as opposed to updating it based on whether it is +EV or -EV for you to play against the current opposing strategy).

I've still not thought about this much yet so the idea might be flawed or there might be a much simpler way to combine the maximally exploitative strategy with the maximally spiteful strategy and update the rules based on both.

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This should converge to a more "robust" set of strategies. But then, these strategies will be easily exploitable by opponents who simply skip their "spite calls".

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I don't think it could really be exploited, as it's the threat of the spite calls more than the calls itself that's important. The equilibrium should mean that if player A deviates by not spite calling player B anymore then player B won't be making the pushes that are punished by the spite calls anyway so nothing has changed. If the player B decides to push these anyway knowing that he'll be spite called then he's just made his strategy -EV compared to if he respected the player A's spite calls.

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This gets pretty interesting if you think about it. If we draw random players from a population of 50% NE, and 50% "spite callers" and put them into a game, the spite caller population would have a higher expectation in this game, i think.

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That's quite interesting and would make an interesting experiment. What would happen if you tried to train up a maximally exploitative strategy to play against this mixed NE/spite player? Perhaps this would be a more robust strategy than NE alone?

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Need to think it through before posting any more. I hope the above makes any sense, lol.

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Yep, some of my ideas might be totally off here too - I've just woke up and not really thought too carefully about all this yet, but overall it makes for some interesting thinking!

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