Computation of Characteristic Function Values for Linear-State Differential Games

2003 ◽  
Vol 117 (1) ◽  
pp. 183-194 ◽  
Author(s):  
G. Zaccour
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Linear State

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 Cooperative optimality principals in differential games on networks

2020 ◽  
Vol 12 (4) ◽  
pp. 93-111
Author(s):  
Анна Тур ◽  
Anna Tur ◽  
Леон Аганесович Петросян ◽  
Leon Petrosyan
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Network Structure ◽  
Shapley Value ◽  
The Core ◽  
Investment Game ◽  
The Shapley Value ◽  
Research Investment ◽  
Optimality Principles

The paper describes a class of differential games on networks. The construction of cooperative optimality principles using a special type of characteristic function that takes into account the network structure of the game is investigated. The core, the Shapley value and the tau-value are used as cooperative optimality principles. The results are demonstrated on a model of a differential research investment game, where the Shapley value and the tau-value are explicitly constructed.

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.

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.

scholarly journals Superadditive extension of characteristic functions for cooperative differential games

2020 ◽  
Vol 12 (4) ◽  
pp. 40-61
Author(s):  
Екатерина Викторовна Громова ◽  
Ekaterina Gromova ◽  
Екатерина Марова ◽  
Ekaterina Marova
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Differential Game ◽  
Characteristic Functions ◽  
Cooperative Differential Games

The paper provides a constructive theorem that allows one to construct a superadditive characteristic function in a differential game based on a non-superadditive one. As an example, a differential game is considered in which the delta - and eta - characteristic functions are not superadditive. An additional construction is carried out and it is shown that the obtained functions satisfy superadditivity  

scholarly journals On a class of linear-state differential games with subgame individually rational and time consistent bargaining solutions

2020 ◽  
Vol 5 (1) ◽  
pp. 79-97
Author(s):  
Simon Hoof ◽  
Keyword(s):  
Differential Games ◽  
Environmental Economics ◽  
Time Horizon ◽  
Time Instant ◽  
Infinite Time ◽  
Cooperative Solution ◽  
Original Solution ◽  
Bargaining Solutions ◽  
Cooperative Strategies ◽  
Linear State

We consider n-person pure bargaining games in which the space of feasible payoffs is constructed via a normal form differential game. At the beginning of the game the agents bargain over strategies to be played over an infinite time horizon. An initial cooperative solution (a strategy tuple) is called subgame individually rational (SIR) if it remains individually rational throughout the entire game and time consistent (TC) if renegotiating it at a later time instant yields the original solution. For a class of linear-state differential games we show that any solution which is individually rational at the beginning of the game satisfies SIR and TC if the space of admissible cooperative strategies is restricted to constants. We discuss an application from environmental economics.

Sign in / Sign up

Export Citation Format

Share Document