Refined best reply correspondence and dynamics

Dieter Balkenborg, Josef Hofbauer and Christoph Kuzmics

No 451, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it has a product structure, is upper hemi-continuous, always includes a best reply to any mixed strategy profile, and is convex- and closed-valued. For each generalized best reply correspondence we define a generalized best reply dynamics as a differential inclusion based on it. We call a face of the set of mixed strategy profiles a minimally asymptotically stable face (MASF) if it is asymptotically stable under some such dynamics and no subface of it is asymptotically stable under any such dynamics. The set of such correspondences (and dynamics) is endowed with the partial order of point-wise set-inclusion and, under a mild condition on the normal form of the game at hand, forms a complete lattice with meets based on point-wise intersections. The refined best reply correspondence is then defined as the smallest element of the set of all generalized best reply correspondences. We ultimately find that every Kalai and Samet's (1984) persistent retract, which coincide with Basu and Weibull's (1991) CURB sets based, however, on the refined best reply correspondence, contains a MASF. Conversely, every MASF must be a Voorneveld's (2004) prep set, again, however, based on the refined best reply correspondence.

Keywords: Evolutionary game theory; best response dynamics; CURB sets; persistent retracts; asymptotic stability; Nash equilibrium refinements; learning (search for similar items in EconPapers)
Pages: 28
Date: 2016-02-11
New Economics Papers: this item is included in nep-gth and nep-mic
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Citations: View citations in EconPapers (23)

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