Mean field equilibrium in dynamic games with strategic complementarities

Operations Research

Volumn 61, Issue 4, 2013, Pages 971-989

  Adlakha, Sachin ^a   Johari, Ramesh ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION METHODOLOGY; EMPIRICAL DISTRIBUTIONS; EQUILIBRIUM STRATEGY; EXISTENCE THEOREM; MONOTONICITY PROPERTY; STOCHASTIC DYNAMICS; STOCHASTIC GAME; STRATEGIC COMPLEMENTARITY;

OPERATIONS RESEARCH;

COMPUTER APPLICATIONS;

EID: 84883739204     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.2013.1192     Document Type: Article

References (56)

1. Acemoglu D, Jensen MK (2013) Aggregate comparative statics. Games Econom. Behav. 81: 27-49.
2. Adlakha S, Johari R, Weintraub GY (2013) Equilibria of dynamic games with many players: Existence, approximation, and market structure. J. Econom. Theory. http://dx.doi.org/10.1016/j.jet.2013.07.002.
3. Amir R (2002) Complementarity and diagonal dominance in discounted stochastic games. Ann. Oper. Res. 114(1-4): 39-56.
4. Amir R (2005) Discounted supermodular stochastic games: Theory and applications. Technical report, Mimeo, University of Arizona, Tucson.
5. Bergin J, Bernhardt D (1995) Anonymous sequential games: Existence and characterization of equilibria. Econom. Theory 5(3): 461-489.
6. Bertsekas DP (2001) Dynamic Programming and Optimal Control, Vol. 2 (Athena Scientific, Nashua, NH).
7. Bertsekas DP (2009) Convex Optimization Theory (Athena Scientific, Nashua, NH).
8. Bertsekas DP, Shreve SE (1978) Stochastic Optimal Control: The Discrete-Time Case (Academic Press, New York).
9. Billingsley P (1968) Convergence of Probability Measures (John Wiley & Sons, Inc., New York).
10. Blume LE (1993) The statistical mechanics of best-response strategy revision. Games Econom. Behav. 11(2): 111-145.
11. Bodoh-Creed A (2012) Approximation of large games with applications to uniform price auctions. Auctions, Market Mechanisms, and Their Applications (Springer, Berlin), 54.
12. Chakrabarti SK (2003) Pure strategy Markov equilibrium in stochastic games with a continuum of players. J. Math. Econom. 39(7): 693-724.
13. Curtat L (1996) Markov equilibria in stochastic games with complementaries. Games Econom. Behav. 17: 177-199.
14. Diamond P (1982) Aggregate demand management in search equilibrium. J. Political Econom. 90: 881-894.
15. Doraszelski U, Pakes A (2007) A framework for applied dynamic analysis in IO. Handbook of Industrial Organization, Vol. 3 (Elsevier), 1887-1966.
16. Duffie D, Malamud S, Manso G (2009) Information percolation with equilibrium search dynamics. Econometrica 77(5): 1513-1574.
17. Dutta PK, Majumdar MK, Sundaram RK (1994) Parametric continuity in dynamic programming problems. J. Econom. Dynam. Control 18(6): 1069-1092.
18. Echenique F (2003) Mixed equilibria in games of strategic complementarities. Econom. Theory 22(1): 33-44.
19. Filar J, Vrieze K (1996) Competitive Markov Decision Processes (Springer-Verlag, New York).
20. Friesz TL, Bernstein D, Smith TE, Tobin RL, Wie BW (1993) A variational inequality formulation of the dynamic network user equilibrium problem. Oper. Res. 41(1): 179-191.
21. Fudenberg D, Tirole J (1991) Game Theory (MIT Press, Cambridge, MA).
22. Garcia CE, Prett DM, Morari M (1989) Model predictive control: Theory and practice - A survey. Automatica 25(3): 335-348.
23. Glynn P (2004) Distributed algorithms for wireless networks. Presentation, Conf. Stochastic Networks, Montréal, Québec.
24. Hopenhayn HA (1992) Entry, exit, and firm dynamics in long run equilibrium. Econometrica 60(5): 1127-1150.
25. Hopenhayn HA, Prescott EC (1992) Stochastic monotonicity and stationary distributions for dynamic economies. Econometrica 60(6): 1387-1406.
26. Horst U (2005) Stationary equilibria in discounted stochastic games with weakly interacting players. Games Econom. Behav. 51(1): 83-108.
27. Huang M, Caines PE, Malhamé RP (2007) Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized .-Nash equilibria. IEEE Trans. Automatic Control 52(9): 1560-1571.
28. Huang M, Malhamé RP, Caines PE (2005) Nash equilibria for largepopulation linear stochastic systems of weakly coupled agents. Boukas EK, Malhame RP, eds. Analysis, Control and Optimization of Complex Dynamic Systems (Springer), 215-252.
29. Huang M, Malhamé RP, Caines PE (2006) Large population stochastic dynamic games: Closed-loop Mckean-Vlasov systems and the Nash certainty equivalence principle. Comm. Inform. Systems 6(3): 221-251.
30. Jovanovic B, Rosenthal RW (1988) Anonymous sequential games. J. Math. Econom. 17: 77-87.
31. Kamae T, Krengel U, O'Brien GL (1977) Stochastic inequalities on partially ordered spaces. Ann. Probab. 5(6): 899-912.
32. Kleene SC (1971) Introduction to Metamathematics (American Elsevier Publishing Co., New York).
33. Kunreuther H, Heal G (2003) Interdependent security. J. Risk Uncertainty 26(2): 231-249.
34. Lasry JM, Lions PL (2007) Mean field games. Japanese J. Math. 2(1): 229-260.
35. Maitra A (1968) Discounted dynamic programming on compact metric spaces. Sankhya: The Indian J. Statist., Ser. A 30(2): 211-216.
36. Maskin E, Tirole J (1988) A theory of dynamic oligopoly, I and II. Econometrica 56(3): 549-570.
37. Mézard M, Montanari A (2009) Information, Physics, and Computation (Oxford University Press, Oxford, UK).
38. Milgrom P, Roberts J (1990) Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica 58: 1255-1277.
39. Morris S (2000) Contagion. Rev. Econom. Stud. 67(1): 57-78.
40. Nowak AS (2007) On stochastic games in economics. Math. Methods Oper. Res. 66(3): 513-530.
41. Pakes A, McGuire P (2001) Stochastic algorithms, symmetric Markov perfect equilibrium, and the "curse" of dimensionality. Econometrica 69(5): 1261-1281.
42. Shapley LS (1953) Stochastic games. Proc. Natl. Acad. Sci. 39: 1095-1100.
43. Sleet C (2001) Markov perfect equilibria in industries with complementarities. Econom. Theory 17(2): 371-397.
44. Smith JE, McCardle KF (2002) Structural properties of stochastic dynamic programs. Oper. Res. 50(5): 796-809.
45. Stokey NL, Lucas RE Jr, Prescott EC (1989) Recursive Methods in Economic Dynamics (Harvard University Press, Cambridge, MA).
46. Tarski A (1955) A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math. 5: 285-309.
47. Tembine H, Le Boudec J-Y, El-Azouzi R, Altman E (2009) Mean field asymptotics of Markov decision evolutionary games and teams. Proc. GameNets '09, 140-150.
48. Topkis DM (1998) Supermodularity and Complementarity (Princeton University Press, Princeton, NJ).
49. Vives X (1990) Nash equilibrium with strategic complementarities. J. Math. Econom. 19: 305-321.
50. Vives X (2009) Strategic complementarity in multi-stage games. Econom. Theory 40(1): 151-171.
51. Weintraub GY, Benkard CL, Van Roy B (2008) Markov perfect industry dynamics with many firms. Econometrica 76(6): 1375-1411.
52. Weintraub GY, Benkard CL, Van Roy B (2011) Industry dynamics: Foundations for models with an infinite number of firms. J. Econom. Theory 146(5): 1965-1994.
53. Wiecek P, Altman E, Hayel Y (2011) Stochastic state dependent population games in wireless communication. IEEE Trans. Automatic Control 56(3): 492-505.
54. Wunderlich KE, Kaufman DE, Smith RL (2000) Link travel time prediction for decentralized route guidance architectures. IEEE Trans. Intelligent Transportation Systems 1(1): 4-14.
55. Yin H, Mehta PG, Meyn SP, Shanbhag UV (2010) Synchronization of coupled oscillators is a game. IEEE Conf. Decision and Control (IEEE, Piscataway, NJ).
56. Zhou L (1994) The set of Nash equilibria of a supermodular game is a complete lattice. Games Econom. Behav. 7: 295-300.