NONZERO-SUM SUBMODULAR MONOTONE-FOLLOWER GAMES: EXISTENCE AND APPROXIMATION OF NASH EQUILIBRIA

Dianetti J, Ferrari G (2020)
SIAM JOURNAL ON CONTROL AND OPTIMIZATION 58(3): 1257-1288.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We consider a class of N-player stochastic games of multidimensional singular control, in which each player faces a minimization problem of monotone-follower type with submodular costs. We call these games monotone-follower games. In a not necessarily Markovian setting, we establish the existence of Nash equilibria. Moreover, we introduce a sequence of approximating games by restricting, for each n is an element of N, the players' admissible strategies to the set of Lipschitz processes with Lipschitz constant bounded by n. We prove that, for each n is an element of N, there exists a Nash equilibrium of the approximating game and that the sequence of Nash equilibria converges, in the Meyer-Zheng sense, to a weak (distributional) Nash equilibrium of the original game of singular control. As a byproduct, such a convergence also provides approximation results of the equilibrium values across the two classes of games. We finally show how our results can be employed to prove existence of open-loop Nash equilibria in an N-player stochastic differential game with singular controls, and we propose an algorithm to determine a Nash equilibrium for the monotone-follower game.
Stichworte
nonzero-sum games; singular control; submodular games; Meyer-Zheng; topology; Pontryagin maximum principle; Nash equilibrium; stochastic; differential games; monotone-follower problem
Erscheinungsjahr
2020
Zeitschriftentitel
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Band
58
Ausgabe
3
Seite(n)
1257-1288
ISSN
0363-0129
eISSN
1095-7138
Page URI
https://pub.uni-bielefeld.de/record/2945133

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Dianetti J, Ferrari G. NONZERO-SUM SUBMODULAR MONOTONE-FOLLOWER GAMES: EXISTENCE AND APPROXIMATION OF NASH EQUILIBRIA. SIAM JOURNAL ON CONTROL AND OPTIMIZATION. 2020;58(3):1257-1288.
Dianetti, J., & Ferrari, G. (2020). NONZERO-SUM SUBMODULAR MONOTONE-FOLLOWER GAMES: EXISTENCE AND APPROXIMATION OF NASH EQUILIBRIA. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 58(3), 1257-1288. doi:10.1137/19M1238782
Dianetti, J., and Ferrari, G. (2020). NONZERO-SUM SUBMODULAR MONOTONE-FOLLOWER GAMES: EXISTENCE AND APPROXIMATION OF NASH EQUILIBRIA. SIAM JOURNAL ON CONTROL AND OPTIMIZATION 58, 1257-1288.
Dianetti, J., & Ferrari, G., 2020. NONZERO-SUM SUBMODULAR MONOTONE-FOLLOWER GAMES: EXISTENCE AND APPROXIMATION OF NASH EQUILIBRIA. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 58(3), p 1257-1288.
J. Dianetti and G. Ferrari, “NONZERO-SUM SUBMODULAR MONOTONE-FOLLOWER GAMES: EXISTENCE AND APPROXIMATION OF NASH EQUILIBRIA”, SIAM JOURNAL ON CONTROL AND OPTIMIZATION, vol. 58, 2020, pp. 1257-1288.
Dianetti, J., Ferrari, G.: NONZERO-SUM SUBMODULAR MONOTONE-FOLLOWER GAMES: EXISTENCE AND APPROXIMATION OF NASH EQUILIBRIA. SIAM JOURNAL ON CONTROL AND OPTIMIZATION. 58, 1257-1288 (2020).
Dianetti, Jodi, and Ferrari, Giorgio. “NONZERO-SUM SUBMODULAR MONOTONE-FOLLOWER GAMES: EXISTENCE AND APPROXIMATION OF NASH EQUILIBRIA”. SIAM JOURNAL ON CONTROL AND OPTIMIZATION 58.3 (2020): 1257-1288.

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