Evolutionary stability and tenable strategy blocks

Abstract We analyze relationships between evolutionary stability and the tenable strategy blocks of Myerson and Weibull (Econometrica 83(3): 943–976). In finite two-player games, we prove that strategies robust against equilibrium entrants (Swinkels, J. Econ. Theory 57(2):306–332) are fully settled in the sense of Myerson and Weibull. Based on this, we propose new evolutionary stability concepts that characterize tenable strategy blocks directly. These characterizations are formulated solely in terms of primitives without relying on tenability’s meta game framework, simplifying the application of tenability and comparisons with other concepts. For instance, we prove that every coarsely tenable block contains a strategically stable set (Kohlberg and Mertens, Econometrica 54(5):1003–1037). Finally we show that in finite and symmetric two-player games, established evolutionary stability notions imply a symmetric variant of coarse tenability.