Learning in Games with Cumulative Prospect Theoretic Preferences
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We consider repeated games where players behave according to cumulative prospect theory (CPT). We show that a natural analog for the notion of correlated equilibrium in the CPT case, as defined by Keskin, is not enough to guarantee the convergence of the empirical distribution of action play when players have calibrated strategies and behave according to CPT. We define the notion of a mediated CPT calibrated equilibrium via an extension of the game to a so-called mediated game. We then show, along the lines of Foster and Vohra's result, that under calibrated learning the empirical distribution of play converges to the set of all mediated CPT correlated equilibria. We also show that, in general, the set of CPT correlated equilibria is not approachable in the Blackwell approachability sense.
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