Beyond myopic best response (in Cournot competition)

The Nash equilibrium as a prediction myopically ignores the possibility that deviating from the equilibrium could lead to an avalanche of beneficial changes by other agents. We consider a non-myopic version of Cournot competition, where each firm selects either profit maximization (as in the classical model) or revenue maximization (by masquerading as a firm with zero production costs). We consider many non-identical firms with linear demand functions and show existence of pure Nash equilibria, that simple dynamics will produce such an equilibrium, and that some natural dynamics converge within linear time. Furthermore, we compare the outcome of the non-myopic Cournot competition with that of the standard Cournot competition. Prices in the non-myopic game are lower and the firms, in total, produce more and have a lower aggregate utility. We also briefly consider a non-myopic version of Bertrand competition, and find that prices increase relative to the classical model. © 2013 Elsevier Inc

Blind Deblurring Using Internal Patch Recurrence

Abstract. Recurrence of small image patches across different scales of a natural image has been previously used for solving ill-posed problems (e.g., superresolution from a single image). In this paper we show how this multi-scale property can also be used for “blind-deblurring”, namely, removal of an unknown blur from a blurry image. While patches repeat ‘as is ’ across scales in a sharp natural image, this cross-scale recurrence significantly diminishes in blurry images. We exploit these deviations from ideal patch recurrence as a cue for recovering the underlying (unknown) blur kernel. More specifically, we look for the blur kernel k, such that if its effect is “undone ” (if the blurry image is deconvolved with k), the patch similarity across scales of the image will be maximized. We report extensive experimental evaluations, which indicate that our approach compares favorably to state-of-the-art blind deblurring methods, and in particular, is more robust than them