A Computational Approach to Proving Uniqueness in Dynamic Games

Static and dynamic games are often used to analyze strategic interactions. While existence of equilibrium can often be proved by conventional methods, uniqueness is much more difficult to establish. If a game reduces to solving a system of polynomial equations, then one could use algorithms for finding all solutions to such systems to establish uniqueness of equilibrium. We first illustrate this for a static game. While most dynamic games are far too large for a direct application of this approach, we study a common type of dynamic games where equilibrium can be analyzed as a sequence of small games and apply an all solutions algorithm to each such game. We apply this to an R&D race, a cost-reducing investment game, and a learning curve game to show that this approach is practical given current computational technology.