Dynamic production output adjustment with sticky prices: A mean field game approach

This paper presents an application of mean field games to dynamic production competition. We first introduce a market of a large number of agents (firms) with sticky prices and adjustment costs. The cost functional of each agent has indefinite state weights. By solving a limiting optimal control problem subject to consistent mean field approximations, a set of decentralized strategies is obtained and further shown to be an ε -Nash equilibrium.

[1]  Benjamin Van Roy,et al.  Markov Perfect Industry Dynamics with Many Firms , 2005 .

[2]  Ji-Feng Zhang,et al.  Mean Field Games for Large-Population Multiagent Systems with Markov Jump Parameters , 2012, SIAM J. Control. Optim..

[3]  Robert Driskill,et al.  Dynamic duopoly with adjustment costs: A differential game approach , 1989 .

[4]  R. Hall,et al.  Industry Dynamics with Adjustment Costs , 2002 .

[5]  Minyi Huang,et al.  Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria , 2007, IEEE Transactions on Automatic Control.

[6]  Sean P. Meyn,et al.  Synchronization of Coupled Oscillators is a Game , 2010, IEEE Transactions on Automatic Control.

[7]  Ronnie Sircar,et al.  Bertrand and Cournot Mean Field Games , 2015 .

[8]  P. Lions,et al.  Mean field games , 2007 .

[9]  Peter E. Caines,et al.  Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle , 2006, Commun. Inf. Syst..

[10]  Quanyan Zhu,et al.  Risk-Sensitive Mean-Field Games , 2012, IEEE Transactions on Automatic Control.

[11]  Martino Bardi,et al.  Explicit solutions of some linear-quadratic mean field games , 2012, Networks Heterog. Media.

[12]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[13]  Luca Lambertini,et al.  Dynamic Oligopoly with Sticky Prices: Closed-Loop, Feedback, and Open-Loop Solutions , 2004 .

[14]  Diogo A. Gomes,et al.  Mean Field Games Models—A Brief Survey , 2013, Dynamic Games and Applications.

[15]  Ji-Feng Zhang,et al.  Hierarchical Mean Field Games for Multiagent Systems With Tracking-Type Costs: Distributed $\varepsilon $-Stackelberg Equilibria , 2014, IEEE Transactions on Automatic Control.

[16]  Minyi Huang,et al.  Large-Population LQG Games Involving a Major Player: The Nash Certainty Equivalence Principle , 2009, SIAM J. Control. Optim..

[17]  Tao Li,et al.  Asymptotically Optimal Decentralized Control for Large Population Stochastic Multiagent Systems , 2008, IEEE Transactions on Automatic Control.

[18]  J. Willems Least squares stationary optimal control and the algebraic Riccati equation , 1971 .

[19]  Andrew E. B. Lim,et al.  Stochastic optimal LQR control with integral quadratic constraints and indefinite control weights , 1999, IEEE Trans. Autom. Control..

[20]  Peter E. Caines,et al.  Mean Field Stochastic Adaptive Control , 2012, IEEE Transactions on Automatic Control.

[21]  Ronnie Sircar,et al.  Bertrand & Cournot Mean Field Games , 2014 .

[22]  Agnieszka Wiszniewska-Matyszkiel,et al.  Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis , 2015, Dyn. Games Appl..

[23]  René Carmona,et al.  Probabilistic Analysis of Mean-field Games , 2013 .

[24]  Ramesh Johari,et al.  Equilibria of Dynamic Games with Many Players: Existence, Approximation, and Market Structure , 2010, J. Econ. Theory.

[25]  Minyi Huang,et al.  Linear-Quadratic-Gaussian Mixed Games with Continuum-Parametrized Minor Players , 2012, SIAM J. Control. Optim..

[26]  Peter E. Caines,et al.  Epsilon-Nash Mean Field Game Theory for Nonlinear Stochastic Dynamical Systems with Major and Minor Agents , 2012, SIAM J. Control. Optim..

[27]  Ji-Feng Zhang,et al.  Distributed control of multi-agent systems with random parameters and a major agent , 2012, Autom..

[28]  A. Bensoussan,et al.  Mean Field Games and Mean Field Type Control Theory , 2013 .

[29]  Xavier Vives,et al.  Strategic incentives in dynamic duopoly , 2004, J. Econ. Theory.

[30]  C. Fershtman,et al.  Dynamic Duopolistic Competition with Sticky Prices , 1987 .

[31]  Marwan A. Simaan,et al.  Game theory applied to dynamic duopoly problems with production constraints , 1978, Autom..

[32]  Naresh K. Sinha,et al.  Modern Control Systems , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[33]  P. Caines,et al.  Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).