The time consistency of the optimality principles in non-zero sum differential games

2005 ◽  
pp. 299-311 ◽  
Author(s):  
L. A. Petrosjan
Keyword(s):  
Differential Games ◽  
Time Consistency ◽  
Optimality Principles ◽  
Zero Sum

Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games

2011 ◽  
Vol 153 (3) ◽  
pp. 662-687 ◽  
Author(s):  
Beatris Escobedo-Trujillo ◽  
Daniel López-Barrientos ◽  
Onésimo Hernández-Lerma
Keyword(s):  
Differential Games ◽  
Stochastic Differential Games ◽  
Zero Sum

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

DETERMINISTIC DIFFERENTIAL GAMES UNDER PROBABILITY KNOWLEDGE OF INITIAL CONDITION

2008 ◽  
Vol 10 (01) ◽  
pp. 1-16 ◽  
Author(s):  
P. CARDALIAGUET ◽  
M. QUINCAMPOIX
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Random Distribution ◽  
Uniqueness Result ◽  
Initial Condition ◽  
Initial State ◽  
Lack Of Information ◽  
In The Beginning ◽  
Zero Sum ◽  
Future Work

We study a zero-sum differential game where the players have only an unperfect information on the state of the system. In the beginning of the game only a random distribution on the initial state is available. The main result of the paper is the existence of the value obtained through an uniqueness result for Hamilton-Jacobi-Isaacs equations stated on the space of measure in ℝn. This result is the first step for future work on differential games with lack of information.

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.

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