Some aspects of nonzero-sum differential games

Some properties of nonzero-sum differential games are explored. A differential game is defined in extensive form, and the set of attainable payoffs is defined. Various subsets of which are useful in discussing solutions are identified. The concept of signaling in discrete games is interpreted as dynamic bargaining in continuously evolving games. Via these concepts a player can, at little expense to himself, attempt to induce the other players to adopt a strategy more favorable to himself. Several examples are given to illustrate the definitions and developments. Interpreting some classical matrix games as continuously evolving games helps to clarify that there can be cooperation or threatening without pregame or explicit negotiation and bargaining. A simple two-player differential game which has been programmed on a hybrid computer and for which some limited experimental results are presented is also described.