Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Minority Games

  • Chi Ho Yeung
  • Yi-Cheng Zhang
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_332-3

Definition of the Subject

The minority game (MG) refers to the simple adaptive multi-agent model of financial markets with the original formulation introduced by Challet and Zhang in 1997. In this model of repeated games, agents choose between one of the two decisions at each round of the game, using their own simple inductive strategies. At each round, the minority group of agents win the game, and rewards are given to those strategies that predict the winning side. Daily examples of minority game include drivers choosing a less crowded road or people choosing a less crowded restaurant. Unlike most economic models or theories that assume investors are deductive in nature, a trial-and-error inductive thinking approach is implicitly implemented in the process of decision making when agents choose their choices in the games. In this original formulation, the history or the information given to agents is a string of binary bits that is composed of the winning sides in the past few rounds.


Financial Market Symmetric Phase Volatility Cluster Replica Symmetry Cumulate Payoff 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.


Primary Literature

  1. Andersen JV, Sornette D (2003) The $-game. Eur Phys J B 31:141ADSCrossRefGoogle Scholar
  2. Arthur WB (1994) Inductive reasoning and bounded rationality: the El Farol problem. Am Econ Assoc Pap Proc 84:406–411Google Scholar
  3. Bouchaud J-P, Giardina I, Mezard M (2001) On a universal mechanism for long-range volatility correlations. Quant Financ 1:212–216CrossRefGoogle Scholar
  4. Burgos E, Ceva H (2000) Self organization in a minority game: the role of memory and a probabilistic approach. Physica A 284:489ADSCrossRefGoogle Scholar
  5. Cavagna A (1999) Irrelevance of memory in the minority game. Phys Rev E 59:R3783–R3786ADSCrossRefGoogle Scholar
  6. Cavagna A (2000) Comment on adaptive competition, market efficiency, and phase transitions. Phys Rev Lett 84:1058ADSCrossRefGoogle Scholar
  7. Cavagna A, Garrahan JP, Giardina I, Sherrington D (1999) A thermal model for adaptive competition in a market. Phys Rev Lett 83:4429–4432ADSCrossRefGoogle Scholar
  8. Cavagna A, Garrahan JP, Giardina I, Sherrington D (2000) Reply to comment on thermal model for adaptive competition in a market. Phys Rev Lett 85:5009ADSCrossRefGoogle Scholar
  9. Challet D (2008) Inter-pattern speculation: beyond minority, majority and $-games. J Econ Dyn Control 32:85CrossRefzbMATHMathSciNetGoogle Scholar
  10. Challet D, Marsili M (1999) Symmetry breaking and phase transition in the minority game. Phys Rev E 60:R6271ADSCrossRefGoogle Scholar
  11. Challet D, Marsili M (2003) Criticality and finite size effects in a simple realistic model of stock market. Phys Rev E 68:036132ADSCrossRefGoogle Scholar
  12. Challet D, Zhang Y-C (1997) Emergence of cooperation and organization in an evolutionary game. Physica A 246:407ADSCrossRefGoogle Scholar
  13. Challet D, Zhang Y-C (1998) On the minority game: analytical and numerical studies. Physica A 256:514ADSCrossRefGoogle Scholar
  14. Challet D, Marsili M, Zhang Y-C (2000a) Modeling market mechanisms with minority game. Physica A 276:284ADSCrossRefMathSciNetGoogle Scholar
  15. Challet D, Marsili M, Zecchina R (2000b) Statistical mechanics of heterogeneous agents: minority games. Phys Rev Lett 84:1824–1827ADSCrossRefGoogle Scholar
  16. Challet D, Chessa A, Marsili M, Zhang Y-C (2000c) From minority games to real markets. Quant Financ 1:168CrossRefMathSciNetGoogle Scholar
  17. Challet D, Marsili M, Zecchina R (2000d) Comment on thermal model for adaptive competition in a market. Phys Rev Lett 85:5008ADSCrossRefGoogle Scholar
  18. Challet D, Marsili M, Zhang Y-C (2001) Stylized facts of financial markets in minority games. Physica A 299:228ADSCrossRefzbMATHGoogle Scholar
  19. Coolen ACC, Heimel JAF (2001) Dynamical solution of the on-line minority game. J Phys A Math Gen 34:10783ADSCrossRefzbMATHMathSciNetGoogle Scholar
  20. De Martino AD, Marsili M (2001) Replica symmetry breaking in the minority game. J Phys A Math Gen 34:2525–2537ADSCrossRefzbMATHGoogle Scholar
  21. Gabaix X, Gopikrishnan P, Plerou V, Stanley HE (2003) A theory of power-law distributions in financial market fluctuations. Nature 423:267ADSCrossRefGoogle Scholar
  22. Garrahan JP, Moro E, Sherrington D (2000) Continuous time dynamics of the thermal minority game. Phys Rev E 62:R9ADSCrossRefGoogle Scholar
  23. Giardina I, Bouchaud J-P (2003) Bubbles, crashes and intermittency in agent based market models. Eur Phys J B 31:421ADSCrossRefMathSciNetGoogle Scholar
  24. Hart ML, Jefferies P, Johnson NF, Hui PM (2000) Generalized strategies in the minority game. Phys Rev E 63:017102ADSCrossRefGoogle Scholar
  25. Hart ML, Jefferies PPM, Hui P, Johnson NF (2001) Crowd-anticrowd theory of multi-agent market games. Eur Phys J B 20:547–550ADSCrossRefMathSciNetGoogle Scholar
  26. Heimel JAF, Coolen ACC (2001) Generating functional analysis of the dynamics of the batch minority game with random external information. Phys Rev E 63:056121ADSCrossRefGoogle Scholar
  27. Heimel JAF, Coolen ACC, Sherrington D (2001) Dynamics of the batch minority game with inhomogeneous decision noise. Phys Rev E 65:016126CrossRefGoogle Scholar
  28. Hod S, Nakar E (2002) Self-segregation versus clustering in the evolutionary minority game. Phys Rev Lett 88:238702ADSCrossRefGoogle Scholar
  29. Jefferies P, Hart ML, Hui PM, Johnson NF (2001) From minority games to real world markets. Eur Phys J B 20:493–502ADSCrossRefMathSciNetGoogle Scholar
  30. Johnson NF, Hart M, Hui PM (1999a) Crowd effects and volatility in a competitive market. Physica A 269:1ADSCrossRefGoogle Scholar
  31. Johnson NF, Hui PM, Johnson R, Lo TS (1999b) Self-organized segregation within an evolving population. Phys Rev Lett 82:3360–3363ADSCrossRefGoogle Scholar
  32. Kay R, Johnson NF (2004) Memory and self-induced shocks in an evolutionary population competing for limited resources. Phys Rev E 70:056101ADSCrossRefMathSciNetGoogle Scholar
  33. Lamper D, Howison SD, Johnson NF (2001) Predictability of large future changes in a competitive evolving population. Phys Rev Lett 88:017902ADSCrossRefGoogle Scholar
  34. Liu Y, Gopikrishnan P, Cizeau P, Meyer M, Peng CK, Stanley HE (1999) Statistical properties of the volatility of price fluctuations. Phys Rev E 60:1390ADSCrossRefGoogle Scholar
  35. Mantegna R, Stanley HE (2005) Scaling behavior in the dynamics of an economic index. Nature 376:46–49ADSCrossRefGoogle Scholar
  36. Marsili M (2001) Market mechanism and expectations in minority and majority games. Phys A 299:93–103CrossRefzbMATHMathSciNetGoogle Scholar
  37. Marsili M, Challet D (2001) Continuum time limit and stationary states of the minority game. Phys Rev E 64:056138ADSCrossRefGoogle Scholar
  38. Marsili M, Challet D, Zecchina R (2000) Exact solution of a modified El Farol’s bar problem: efficiency and the role of market impact. Physica A 280:522ADSCrossRefGoogle Scholar
  39. Savit R (2000) Savit replies on comment on adaptive competition, market efficiency, and phase transitions. Phys Rev Lett 84:1059ADSCrossRefGoogle Scholar
  40. Savit R, Manuca R, Riolo R (1999) Adaptive competition, market efficiency, and phase transitions. Phys Rev Lett 82:2203–2206ADSCrossRefGoogle Scholar
  41. Sherrington D, Moro E, Garrahan JP (2002) Statistical physics of induced correlation in a simple market. Physica A 311:527–535ADSCrossRefzbMATHMathSciNetGoogle Scholar
  42. Slanina F, Zhang Y-C (1999) Capital flow in a two-component dynamical system. Physica A 272:257–268ADSCrossRefGoogle Scholar
  43. Wong KYM, Lim SW, Gao Z (2005) Effects of diversity on multiagent systems: minority games. Phys Rev E 71:066103ADSCrossRefGoogle Scholar
  44. Yeung CH, Wong KYM, Zhang Y-C (2008) Models of financial markets with extensive participation incentives. Phys Rev E 777:026107ADSCrossRefGoogle Scholar
  45. Zhang Y-C (1998) Modeling market mechanism with evolutionary games. Europhys News 29:51Google Scholar
  46. Zhang Y-C (1999) Towards a theory of marginally efficient markets. Physica A 269:30ADSCrossRefGoogle Scholar

Books and Reviews

  1. Challet D, Marsili M, Zhang Y-C (2005) Minority games. Oxford University Press, OxfordzbMATHGoogle Scholar
  2. Coolen AAC (2004) The mathematical theory of minority games. Oxford University Press, OxfordGoogle Scholar
  3. Johnson NF, Jefferies P, Hui PM (2003) Financial market complexity. Oxford University Press, OxfordCrossRefGoogle Scholar
  4. Minority Game’s website. http://www.unifr.ch/econophysics/minority/

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of PhysicsThe Hong Kong University of Science and TechnologyHong KongChina