The refined best-response correspondence in normal form games

This paper provides an in-depth study of the (most) refined best-response correspondence introduced by Balkenborg et al. (Theor Econ 8:165–192, 2013 ). An example demonstrates that this correspondence can be very different from the standard best-response correspondence. In two-player games, however, the refined best-response correspondence of a given game is the same as the best-response correspondence of a slightly modified game. The modified game is derived from the original game by reducing the payoff by a small amount for all pure strategies that are weakly inferior. Weakly inferior strategies, for two-player games, are pure strategies that are either weakly dominated or are equivalent to a proper mixture of pure strategies. Fixed points of the refined best-response correspondence are not equivalent to any known Nash equilibrium refinement. A class of simple communication games demonstrates the usefulness and intuitive appeal of the refined best-response correspondence. Copyright Springer-Verlag Berlin Heidelberg 2015