Cooperative equilibria in differential games.

*(English)*Zbl 0607.90097This 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 J. Nash [Econometrica 18, 155-162 (1950); ibid. 21, 128-140 (1953; Zbl 0050.14102)] was extended to differential games by P. T. Liu [J. Optimization Theory Appl. 11, 284-292 (1973; Zbl 0251.90061)]. The question of acceptability of such solutions was raised by A. Haurie [J. Optimization Theory Appl. 18, 31-39 (1976; Zbl 0321.90062)].

The use of memory strategies was first suggested by 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.

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 J. Nash [Econometrica 18, 155-162 (1950); ibid. 21, 128-140 (1953; Zbl 0050.14102)] was extended to differential games by P. T. Liu [J. Optimization Theory Appl. 11, 284-292 (1973; Zbl 0251.90061)]. The question of acceptability of such solutions was raised by A. Haurie [J. Optimization Theory Appl. 18, 31-39 (1976; Zbl 0321.90062)].

The use of memory strategies was first suggested by 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.

Reviewer: St.Jørgensen

##### MSC:

91A23 | Differential games (aspects of game theory) |

##### Keywords:

acceptable equilibria; non-cooperative differential games; memory strategies; threat; continuous time setting##### Citations:

Zbl 0298.90075; Zbl 0241.90073; Zbl 0050.14102; Zbl 0251.90061; Zbl 0321.90062; Zbl 0482.90094
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\textit{B. Tolwinski} et al., J. Math. Anal. Appl. 119, 182--202 (1986; Zbl 0607.90097)

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