TURNPIKE PROPERTIES AND COMPARATIVE DYNAMICS OF GENERAL CAPITAL ACCUMULATION GAMES

Publisher Summary This chapter discusses the solutions for a general class of capital accumulation games with stability properties of Nash equilibrium. It focuses on the application of turnpike theory to dynamic games. The turnpike results known from the theory of optimal economic growth can be used to derive a general convergence result. They also yield comparative statics and dynamics properties. The key result is the global convergence of the Nash trajectories to a unique steady state provided that the matrix of second order derivatives of the profit functions has a dominant diagonal. This result implies that the block diagonal assumption introduced by Araujo and Scheinkman is satisfied. Thus, comparative statics and dynamics analyses are possible. The chapter presents a model, which is very general in nature and can be applied to various market situations. The chapter discusses the relationship between the equilibrium path of the finite and infinite-horizon games. The finite horizon eqilibrium path stays within a closed neighborhood of the stationary equilibrium.