This note revisits the problem of how to select an equilibrium in a differential game in the case of multiplicity of Nash equilibria. Most of the previous applied dynamic games literature has considered preplay negotiations between players, implicitly or explicitly, with the aim of reaching an agreement on the selection of the pair of strategies. The main objective of this note is to analyze which would be the most likely equilibrium without preplay communications. We study the linear and nonlinear Markov perfect Nash equilibria for a class of well-known models in the literature if preplay communications are eliminated. We analyze both symmetric and nonsymmetric strategies. We show that the nonlinear strategies are not always the optimal strategies implemented when cheap talk is removed. We conclude that in the presence of multiple equilibria and without cheap talk the most likely equilibria are symmetric piecewise linear Markov perfect Nash equilibria at least for a range of initial values of the state variable.
Published October 2017 , 15 pages