Properties of Nash Solutions of a Two-Stage Nonzero-Sum Game

This paper contains exact expressions for the complete class of uncountably many globally optimal affine Nash equilibrium strategies for a two-stage two-person nonzero-sum game problem with quadratic objective functionals and with dynamic information for both players. Existence conditions for each of these Nash equilibrium solutions are derived and it is shown that a recursive Nash solution is not necessarily globally optimal. Cost-uniqueness property of the derived Nash strategies is investigated and it is proven that the game problem under consideration admits a unique Nash cost pair if and only if it can be made equivalent to either a team problem or a zero-sum game. It is also shown that existence conditions of a globally optimal Nash solution will be independent of the parameters characterizing the nonuniques of the Nash strategies only if the game problem can be made equivalent to a team problem.