Cooperative equilibria in differential games (Q1086180)

This paper defines and characterizes a certain class of equilibria for non-cooperative differential games. Using memory strategies, instead of feedback strategies, yields a wider class of equilibria. When the players are allowed to cooperate, then the usual equilibrium concept is the Pareto solution, and there are several schemes devised for picking a particular Pareto outcome as the solution. The axiomatic approach of \textit{J. Nash} [Econometrica 18, 155-162 (1950); ibid. 21, 128-140 (1953; Zbl 0050.14102)] was extended to differential games by \textit{P. T. Liu} [J. Optimization Theory Appl. 11, 284-292 (1973; Zbl 0251.90061)]. The question of acceptability of such solutions was raised by \textit{A. Haurie} [J. Optimization Theory Appl. 18, 31-39 (1976; Zbl 0321.90062)]. The use of memory strategies was first suggested by \textit{B. Tolwinski} [Automatica 18, 431-441 (1982; Zbl 0482.90094)] in a multistage bargaining game. Memory strategies incorporate a threat which will be used if the opponent does not observe the agreement, and the memory permits each player to recall a possible deviation from the agreement. The paper extends the work by Tolwinski to a continuous time setting. The work is purely theoretical; no examples or applications are given.