Non-Cooperative Dynamic Games with General Utility Functions

Abstract

The present paper is concerned with a general non-cooperative two-person dynamic game with Borel state and action spaces, non-Markovian transition law and with utility functions depending on the whole sequence of states and actions. The motivation for a general utility function is that in several problems in economic theory, additivity or separability of the utility function is a restrictive assumption and hard to justify, e.g. in problems of consumption and production choices over time and in the closely related problems of optimal economic growth. Dynamic games with additive utility functions have been introduced by Shapley [22] and have then been investigated by many authors (see the survey paper of Parthasarathy and Stern [16] or Kiienle [9]). In recent years several authors have considered dynamic games with more general utility functions, e.g. Sengupta [21], Iwamoto [7], Schäl [19].