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Abstract
This paper studies linear quadratic games with set up costs monotonic on the number of active players, namely, players whose action is non-null. Such games arise naturally in joint replenishment inventory systems. Building upon a preliminary analysis of the properties of the best response strategies and Nash equilibria for the given game, the main contribution is the study of the same game under large population. We also analyze the influence of an additional disturbance in the spirit of the literature onH∞ control. Numerical illustrations are provided.
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References
Bagagiolo F, Bauso D (2011) Objective function design for robust optimality of linear control under state-constraints and uncertainty. ESAIM Control Optim Calc Var 17:155–177
Bardi M (2012) Explicit solutions of some linear-quadratic mean field games. Netw Heterog Media 7(2):243–261
Başar T, Bernhard P (1991)H∞-optimal control and related minimax design problems: a dynamic game approach. Birkhäuser, Basel
Bauso D, Giarrè L, Pesenti R (2008) Consensus in noncooperative dynamic games: a multiretailer inventory application. Trans Autom Control 53(4):998–1003
Bauso D, Tembine H, Başar T (2012) Robust mean field games with application to production of an exhaustible resource. In: Proceedings of 7th IFAC symposium on robust control design, Aalborg, Denmark, pp 454–459
Bauso D, Zhu Q, Başar T (2012) Mixed integer optimal compensation: decompositions and mean-field approximations. In: Proceedings of 2012 American control conference, Montreal, Montreal, Canada, pp 2663–2668
Elliot NJ, Kalton N (1972) The existence of value in differential games of pursuit and evasion. J Differ Equ 12:504–523
Gueant O, Lasry JM, Lions PL (2010) Mean field games and applications. Paris-Princeton lectures
Huang M, Caines P, Malhamé R (2007) Population cost-coupled lqg problems with non-uniform agents: individual-mass behaviour and decentralizedϵ-Nash equilibria. Trans Autom Control 52(9):1560–1571
Lachapelle A, Salomon J, Turinici G (2010) Computation of mean field equilibria in economics. Math Models Methods Appl Sci 20:1–22
Lasry JM, Lions PL (2007) Mean field games. Jpn. J. Math. 2
Milchtaich I (1996) Congestion games with player-specific payoff functions. Games Econ Behav 13:111–124
Pesenti R, Bauso D (2011) Mean field linear quadratic games with set up costs. In: Proceedings of NetGCoop 2011, Paris, France, pp 1–6
Roxin E (1969) The axiomatic approach in differential games. J Optim Theory Appl 3:153–163
Soulaimani AS, Quincampoix M, Sorin S (2009) Approchability theory, discriminating domain and differential games. SIAM J Control Optim 48(4):2461–2479
Tembine H, Zhu Q, Basar T (2011) Risk-sensitive mean field stochastic games. In: Proceedings of IFAC world congress, Milan, Italy, pp 3222–3227
Varaiya P (1967) The existence of solution to a differential game. SIAM J Control Optim 5:153–162
Watts A (2002) Uniqueness of equilibrium in cost sharing games. J Math Econ 37:47–70
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DICGIM, Università di Palermo, 90128, Palermo, Italy
Dario Bauso
Dipartimento di Management, Università di Venezia-Ca’ Foscari, Venezia, Italy
Raffaele Pesenti
- Dario Bauso
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- Raffaele Pesenti
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Correspondence toRaffaele Pesenti.
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Bauso, D., Pesenti, R. Mean Field Linear Quadratic Games with Set Up Costs.Dyn Games Appl3, 89–104 (2013). https://doi.org/10.1007/s13235-012-0069-0
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