Time-dependent cooperation in games.

*(English)*Zbl 0677.90101
Differential games and applications, Proc. 3rd Int. Symp., Sophia- Antipolis/Fr. 1988, Lect. Notes Control Inf. Sci. 119, 157-169 (1989).

[For the entire collection see Zbl 0663.00020.]

Situations where players have an option to play cooperatively or noncooperatively during the game are considered for two-person linear- quadratic dynamic games. If at least one player rejects cooperation, the game will evolve according to the Nash equilibrium concept. If both players accept cooperation, the game will develop according to the Pareto solution. It is assumed that the i-th player being in the position (x,t) chooses cooperation if and only if \(V^ c_ i(x,t)\geq V^ N_ i(x,t)\) where \(V^ N_ i(x,t)\) and \(V^ c_ i(x,t)\) are gains of the i-th player when both players confine themselves to the Nash equilibrium solution and Pareto solution, respectively. It is shown that there can exist switches from the cooperative to the noncooperative mode of play and vice versa. A finite horizon differential game in which the decision whether to cooperate or not has a stochastic component is considered.

Situations where players have an option to play cooperatively or noncooperatively during the game are considered for two-person linear- quadratic dynamic games. If at least one player rejects cooperation, the game will evolve according to the Nash equilibrium concept. If both players accept cooperation, the game will develop according to the Pareto solution. It is assumed that the i-th player being in the position (x,t) chooses cooperation if and only if \(V^ c_ i(x,t)\geq V^ N_ i(x,t)\) where \(V^ N_ i(x,t)\) and \(V^ c_ i(x,t)\) are gains of the i-th player when both players confine themselves to the Nash equilibrium solution and Pareto solution, respectively. It is shown that there can exist switches from the cooperative to the noncooperative mode of play and vice versa. A finite horizon differential game in which the decision whether to cooperate or not has a stochastic component is considered.

Reviewer: A.Kleimenov

##### MSC:

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

91A10 | Noncooperative games |

91A12 | Cooperative games |

91A15 | Stochastic games, stochastic differential games |

91A20 | Multistage and repeated games |