Dynamic Bargaining and Time-Consistency in Linear-State and Homogeneous Linear-Quadratic Cooperative Differential Games

2021 ◽  
Author(s):  
Jesús Marín-Solano
Keyword(s):  
Differential Games ◽  
Time Consistency ◽  
Discount Rates ◽  
Solution Concepts ◽  
Linear Quadratic ◽  
Equilibrium Strategies ◽  
Dynamic Bargaining ◽  
Linear State ◽  
Homogeneous Linear ◽  
Cooperative Differential Games

Three different solution concepts are reviewed and computed for linear-state and homogeneous linear-quadratic cooperative differential games with asymmetric players. Discount rates can be nonconstant and/or different. Special attention is paid to the issues of time-consistency, agreeability and subgame-perfectness, both from the viewpoint of sustainability of cooperation and from the credibility of the announced equilibrium strategies.

Agreeability and Time Consistency in Linear-State Differential Games

2003 ◽  
Vol 119 (1) ◽  
pp. 49-63 ◽  
Author(s):  
S. Jørgensen ◽  
G. Martín-Herrán ◽  
G. Zaccour
Keyword(s):  
Differential Games ◽  
Time Consistency ◽  
Linear State

scholarly journals Feedback based strategies for autonomous linear quadratic cooperative differential games with continuous updating

2020 ◽  
Vol 13 ◽  
pp. 244-251
Author(s):  
Ildus Kuchkarov ◽  
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Shapley Value ◽  
Linear Quadratic ◽  
Cooperative Solution ◽  
Cooperative Strategies ◽  
The Shapley Value ◽  
Cooperative Differential Games

In the paper the class of linear quadratic cooperative differential games with continuous updating is considered. Here the case of feedback based strategies is used to construct cooperative strategies with continuous updating. Characteristic function with continuous updating, cooperative trajectory with continuous updating and cooperative solution are constructed. For the cooperative solution we use the Shapley value.

SUSTAINABILITY OF COOPERATION OVERTIME IN LINEAR-QUADRATIC DIFFERENTIAL GAMES

2005 ◽  
Vol 07 (04) ◽  
pp. 395-406 ◽  
Author(s):  
STEFFEN JØRGENSEN ◽  
GUIOMAR MARTÍN-HERRÁN ◽  
GEORGES ZACCOUR
Keyword(s):  
Differential Games ◽  
Quadratic Differential ◽  
Time Consistency ◽  
Individual Rationality ◽  
Linear Quadratic ◽  
Special Linear ◽  
Linear Quadratic Differential Games ◽  
Fair Sharing

This note deals with time-consistency and agreeability, two dynamic individual rationality concepts, in special linear-quadratic differential games. Conditions ensuring their satisfaction are derived and a link between sustainability of cooperation and fair sharing of cooperation surplus is established.

Linear-State Differential Games in Partition Function Form

2019 ◽  
Vol 21 (04) ◽  
pp. 1950006
Author(s):  
Simon Hoof
Keyword(s):  
Partition Function ◽  
Differential Games ◽  
Coalition Structure ◽  
Function Form ◽  
Equilibrium Payoff ◽  
Noncooperative Equilibrium ◽  
Pollution Accumulation ◽  
Linear State ◽  
Partition Function Form ◽  
Cooperative Differential Games

We introduce a partition function for [Formula: see text]-player linear-state cooperative differential games. The value of a coalition within a given coalition structure is defined as its noncooperative equilibrium payoff of a game played between the coalitions. We also define two core notions, namely, the cautious and the singleton core. If the game is convex, then the cores are nonempty. In order to illustrate the approach, we consider a symmetric game of pollution accumulation.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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