Abstract
The continuously stable strategy (CSS) concept, originally developed as an intuitive static condition to predict the dynamic stability of a monomorphic population, is shown to be closely related to classical game-theoretic dominance criteria when applied to continuous strategy spaces. Specifically, for symmetric and non symmetric two-player games, a CSS in the interior of the continuous strategy space is equivalent to neighborhood half-superiority which, for a symmetric game, is connected to the half-dominance and/or risk dominance concepts. For non symmetric games where both players have a one-dimensional continuous strategy space, an interior CSS is shown to be given by a local version of dominance solvability (called neighborhood dominance solvable). Finally, the CSS and half-superiority concepts are applied to points in the bargaining set of Nash bargaining problems.
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R. Cressman thanks the referee for pointing out further connections between neighborhood superiority and other dominance concepts in the literature. This research was supported by a Natural Sciences and Engineering Research Council of Canada Individual Discovery Grant.
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Cressman, R. Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy space. Int J Game Theory 38, 221–247 (2009). https://doi.org/10.1007/s00182-008-0148-z
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DOI: https://doi.org/10.1007/s00182-008-0148-z