Geodesic
Strategic Support of Cooperative Solutions in 2-Person Differential Games with Dependent Motions
Contributions to game theory and management, Tome 6 (2013), pp. 388-394.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of strategically supported cooperation in 2-person differential games with integral payoffs is considered. Based on initial differential game the new associated differential game (CD-game) is designed. In addition to the initial game it models the players actions connected with transition from the strategic form of the game to cooperative with in advance chosen principle of optimality. The model provides possibility of refusal from cooperation at any time instant $t$ for each player. As cooperative principle of optimality the Shapley value is considered. In the bases of CD-game construction lies the so-called imputation distribution procedure described earlier in (Petrosjan and Zenkevich, 2009). The theorem established by authors says that if at each instant of time along the conditionally optimal (cooperative) trajectory the future payments to each player according to the imputation distribution procedure exceed the maximal guaranteed value which this player can achieve in CD-game, then there exist a Nash equilibrium in the class of recursive strategies first introduced in (Chistyakov, 1981) supporting the cooperative trajectory. In the present paper the results similar to (Chistyakov and Petrosyan, 2011) are obtained without the requirement of independent motions and for the more general type of payoff functions.
Keywords: strong Nash equilibrium, time-consistency, core, cooperative trajectory. 
@article{CGTM_2013_6_a29,
     author = {Leon Petrosyan and Sergey Chistyakov},
     title = {Strategic {Support} of {Cooperative} {Solutions} in {2-Person} {Differential} {Games} with {Dependent} {Motions}},
     journal = {Contributions to game theory and management},
     pages = {388--394},
     publisher = {mathdoc},
     volume = {6},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2013_6_a29/}
}
TY  - JOUR
AU  - Leon Petrosyan
AU  - Sergey Chistyakov
TI  - Strategic Support of Cooperative Solutions in 2-Person Differential Games with Dependent Motions
JO  - Contributions to game theory and management
PY  - 2013
SP  - 388
EP  - 394
VL  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2013_6_a29/
LA  - en
ID  - CGTM_2013_6_a29
ER  - 
%0 Journal Article
%A Leon Petrosyan
%A Sergey Chistyakov
%T Strategic Support of Cooperative Solutions in 2-Person Differential Games with Dependent Motions
%J Contributions to game theory and management
%D 2013
%P 388-394
%V 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2013_6_a29/
%G en
%F CGTM_2013_6_a29
Leon Petrosyan; Sergey Chistyakov. Strategic Support of Cooperative Solutions in 2-Person Differential Games with Dependent Motions. Contributions to game theory and management, Tome 6 (2013), pp. 388-394. http://geodesic.mathdoc.fr/item/CGTM_2013_6_a29/

[1] Petrosjan L. A., Zenkevich N. A., “Principles of stable cooperation”, The mathematical games theory and its applications, 1:1 (2009), 102–117 (in Russian)

[2] Chistyakov S. V., “To the solution of game problem of pursuit”, Prikl. Math. i Mech., 41:5 (1977), 825–832 (in Russian) | MR

[3] Chistyakov S. V., Value Operators in Two-Person Zero-Sum Differential Games, St. Petersburg Univ. Press, St. Petersburg, 1999

[4] Chistyakov S. V., Petrosyan L. A., “Strong Strategic Support of Cooperative solutions in Differential Games”, Contributions to Game Theory and Management, 4, 2011, 105–111 | MR | Zbl

[5] Chentsov A. G., “On a game problem of convering at a given instant time”, Math. USSR Sbornic, 28:3 (1976), 353–376 | DOI

[6] Soviet Math. Dokl., 24:1 (1981), 166–169 | MR | Zbl

[7] Petrosjan L. A., Differential Games of Pursuit, World Scientific, Singapore, 1993 | MR

[8] Pschenichny B. N., “E-strategies in differential games”, Topics in Differential Games, New York–London–Amsterdam, 1973, 45–56 | MR

[9] Fridman A., Differential Games, John Wiley and Sons, New York, NY, 1971 | MR

[10] Petrosjan L. A., Danilov N. N., “Stability of Solutions in nonzero-sum Differential Games with Integral Payoffs”, Viestnik Leningrad University, 1979, no. 1, 52–59 | MR

[11] Petrosjan L. A., “The Shapley Value for Differential Games”, Annals of the International Society of Dynamic Games, 3, ed. Geert Jan Olsder, Birkhauser, 1995, 409–417 | MR | Zbl