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The regret-scaling used by algorithms to determine acceptance criteria for epsilon-Nash equilibria was inconsistent. Specifically, the (min, max) range of payoffs in an extensive form is in general different than that range for its reduced strategic form, when there are chance moves. This establishes consistency that scaling is done by the range of attainable expected payoffs, which ensures the same criterion is applied whether a game is implicitly or explicitly converted to reduced strategic form. Because this range can be efficiently computed in the extensive game directly as long as there are no absent-minded information sets, the implementation of computing this range checks this (and throws on the absent-minded case as equivalence does not hold between the forms in that case). As additional tidiness checks for perfect recall have consistently been added to all relevant solvers (rather than in some cases relying on exceptions being raised in called code).
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@rahulsavani This also involved thinking a bit carefully about how imperfect recall and absent-mindedness should be handled, so the solution is a bit more subtle than we discussed. Please check my thinking is OK on this! |
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The regret-scaling used by algorithms to determine acceptance criteria for epsilon-Nash equilibria was inconsistent. Specifically, the (min, max) range of payoffs in an extensive form is in general different than that range for its reduced strategic form, when there are chance moves.
This establishes consistency that scaling is done by the range of attainable expected payoffs, which ensures the same criterion is applied whether a game is implicitly or explicitly converted to reduced strategic form.
Because this range can be efficiently computed in the extensive game directly as long as there are no absent-minded information sets, the implementation of computing this range checks this (and throws on the absent-minded case as equivalence does not hold between the forms in that case). As additional tidiness checks for perfect recall have consistently been added to all relevant solvers (rather than in some cases relying on exceptions being raised in called code).