Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Game Theory and Strategic Complexity

  • Kalyan ChatterjeeEmail author
  • Hamid Sabourian
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_241-3

Definition

The subject of this entry is at the intersection of economics and computer science and deals with the use of measures of complexity obtained from the study of finite automata to help select among multiple equilibria and other outcomes appearing in game-theoretic models of bargaining, markets, and repeated interactions. The importance of the topic lies in the ability of concepts that employ bounds on available resources to generate more refined predictions of individual behavior in markets.

Introduction

This entry is concerned with the concept of strategic complexity and its use in game theory. There are many different meanings associated with the word “complexity,” as the variety of topics discussed in this volume makes clear. In this entry, we shall adopt a somewhat narrow view, confining ourselves to notions that measure, in some way, constraints on the ability of economic agents to behave with full rationality in their interactions with other agents in dynamic...

Keywords

Nash Equilibrium Equilibrium Strategy Competitive Equilibrium Finite Automaton Repeated Game 
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.

Notes

Acknowledgments

We wish to thank an anonymous referee and Jihong Lee for valuable comments that improved the exposition of this entry. We would also like to thank St. John’s College, Cambridge, and the Pennsylvania State University for funding Dr. Chatterjee’s stay in Cambridge at the time this entry was written.

Bibliography

  1. Abreu D, Rubinstein A (1988) The structure of Nash equilibria in repeated games with finite automata. Econometrica 56:1259–1282CrossRefzbMATHMathSciNetGoogle Scholar
  2. Anderlini L (1990) Some notes on church’s thesis and the theory of games. Theory Decis 29:19–52CrossRefzbMATHMathSciNetGoogle Scholar
  3. Anderlini L, Sabourian H (1995) Cooperation and effective computability. Econometrica 63:1337–1369CrossRefzbMATHMathSciNetGoogle Scholar
  4. Aumann RJ (1981) Survey of repeated games. In: Essays in game theory and mathematical economics in honor of Oskar Morgenstern. Bibliographisches Institut, Mannheim/Vienna/Zurich, pp 11–42Google Scholar
  5. Banks J, Sundaram R (1990) Repeated games, finite automata and complexity. Games Econ Behav 2:97–117CrossRefzbMATHMathSciNetGoogle Scholar
  6. Ben Porath E (1986) Repeated games with bounded complexity. Mimeo, StanfordUniversity, Stanford, CalifGoogle Scholar
  7. Ben Porath E (1993) Repeated games with finite automata. J Econ Theory 59:17–32CrossRefzbMATHMathSciNetGoogle Scholar
  8. Binmore KG (1987) Modelling rational players I. Econ Philos 3:179–214CrossRefGoogle Scholar
  9. Binmore KG, Samuelson L (1992) Evolutionary stability in repeated games played by finite automata. J Econ Theory 57:278–305CrossRefzbMATHMathSciNetGoogle Scholar
  10. Binmore KG, Piccione M, Samuelson L (1998) Evolutionary stability in alternating-offers bargaining games. J Econ Theory 80:257–291CrossRefzbMATHMathSciNetGoogle Scholar
  11. Birkhoff GD (1933) Aesthetic measure. Harvard University Press, Cambridge, MACrossRefzbMATHGoogle Scholar
  12. Bloise G (1998) Strategic complexity and equilibrium in repeated games. Unpublished doctoral dissertation, University of CambridgeGoogle Scholar
  13. Busch L-A, Wen Q (1995) Perfect equilibria in a negotiation model. Econometrica 63:545–565CrossRefzbMATHGoogle Scholar
  14. Chatterjee K (2002) Complexity of strategies and multiplicity of Nash equilibria. Group Decis Negot 11:223–230CrossRefGoogle Scholar
  15. Chatterjee K, Sabourian H (2000a) Multiperson bargaining and strategic complexity. Econometrica 68:1491–1509CrossRefzbMATHMathSciNetGoogle Scholar
  16. Chatterjee K, Sabourian H (2000b) N-person bargaining and strategic complexity. Mimeo, University of Cambridge and the Pennsylvania State University, Cambridge, UK and University Park, Pa., USAGoogle Scholar
  17. Debreu G (1959) Theory of value. Yale University Press, New Haven/LondonzbMATHGoogle Scholar
  18. Fernandez R, Glazer J (1991) Striking for a bargain between two completely informed agents. Am Econ Rev 81:240–252Google Scholar
  19. Fudenberg D, Maskin E (1990) Evolution and repeated games. Mimeo, Harvard University, Cambridge, MassGoogle Scholar
  20. Fudenberg D, Tirole J (1991) Game theory. MIT Press, Cambridge, MAGoogle Scholar
  21. Gale D (2000) Strategic foundations of general equilibrium: dynamic matching and bargaining games. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  22. Gale D, Sabourian H (2005) Complexity and competition. Econometrica 73:739–770CrossRefzbMATHMathSciNetGoogle Scholar
  23. Gale D, Sabourian H (2006) Markov equilibria in dynamic matching and bargaining games. Games Econ Behav 54:336–352CrossRefzbMATHMathSciNetGoogle Scholar
  24. Gale D, Sabourian H (2008) Complexity and competition II; endogenous matching. Mimeo, New York University, New York, USA/University of Cambridge, Cambridge, UKGoogle Scholar
  25. Haller H, Holden S (1990) A letter to the editor on wage bargaining. J Econ Theory 52:232–236CrossRefzbMATHGoogle Scholar
  26. Hayek F (1945) The use of knowledge in society. Am Econ Rev 35:519–530Google Scholar
  27. Herrero M (1985) A strategic theory of market institutions. Unpublished doctoral dissertation, London School of EconomicsGoogle Scholar
  28. Kalai E, Neme A (1992) The strength of a little perfection. Int J Game Theory 20:335–355CrossRefzbMATHMathSciNetGoogle Scholar
  29. Kalai E, Stanford W (1988) Finite rationality and interpersonal complexity in repeated games. Econometrica 56:397–410CrossRefzbMATHMathSciNetGoogle Scholar
  30. Klemperer P (ed) (2000) The economic theory of auctions. Elgar, NorthamptonGoogle Scholar
  31. Lee J, Sabourian H (2007) Coase theorem, complexity and transaction costs. J Econ Theory 135:214–235CrossRefzbMATHMathSciNetGoogle Scholar
  32. Maenner E (2008) Adaptation and complexity in repeated games. Games Econ Behav 63:166–187CrossRefzbMATHMathSciNetGoogle Scholar
  33. Miller GA (1956) The magical number seven plus or minus two: Some limits on our capacity to process information. Psychol Rev 63:81–97CrossRefGoogle Scholar
  34. Neme A, Quintas L (1995) Subgame perfect equilibrium of repeated games with implementation cost. J Econ Theory 66:599–608CrossRefzbMATHMathSciNetGoogle Scholar
  35. Neyman A (1985) Bounded complexity justifies cooperation in the finitely-repeated Prisoners’ Dilemma. Econ Lett 19:227–229CrossRefMathSciNetGoogle Scholar
  36. Neyman A (1997) Cooperation, repetition and automata in cooperation: game-theoretic approaches. In: Hart S, Mas-Colell A (eds) NATO ASI series F, vol 155. Springer, Berlin, pp 233–255Google Scholar
  37. Osborne M, Rubinstein A (1990) Bargaining and markets. Academic, New YorkzbMATHGoogle Scholar
  38. Osborne M, Rubinstein A (1994) A course in game theory. MIT Press, Cambridge, MAzbMATHGoogle Scholar
  39. Papadimitriou CH (1992) On games with a bounded number of states. Games Econ Behav 4:122–131CrossRefzbMATHMathSciNetGoogle Scholar
  40. Piccione M (1992) Finite automata equilibria with discounting. J Econ Theory 56:180–193CrossRefzbMATHMathSciNetGoogle Scholar
  41. Piccione M, Rubinstein A (1993) Finite automata play a repeated extensive game. J Econ Theory 61:160–168CrossRefzbMATHMathSciNetGoogle Scholar
  42. Robson A (2003) The evolution of rationality and the Red Queen. J Econ Theory 111:1–22ADSCrossRefzbMATHMathSciNetGoogle Scholar
  43. Rubinstein A (1982) Perfect equilibrium in a bargaining model. Econometrica 50:97–109CrossRefzbMATHMathSciNetGoogle Scholar
  44. Rubinstein A (1986) Finite automata play the repeated Prisoners’ Dilemma. J Econ Theory 39:83–96CrossRefzbMATHGoogle Scholar
  45. Rubinstein A (1998) Modeling bounded rationality. MIT Press, Cambridge, MAGoogle Scholar
  46. Rubinstein A, Wolinsky A (1990) Decentralized trading, strategic behaviour and the Walrasian outcome. Rev Econ Stud 57:63–78CrossRefzbMATHMathSciNetGoogle Scholar
  47. Sabourian H (2003) Bargaining and markets: complexity and the competitive outcome. J Econ Theory 116:189–228CrossRefMathSciNetGoogle Scholar
  48. Selten R (1965) Spieltheoretische Behandlung eines Oligopolmodells mit Nachfrageträgheit. Z gesamte Staatswiss 12:201–324Google Scholar
  49. Shaked A (1986) A three-person unanimity game. In: The Los Angeles national meetings of the Institute of Management Sciences and the Operations Research Society of America, Mimeo, University of Bonn, Bonn, GermanyGoogle Scholar
  50. Zemel E (1989) Small talk and cooperation: a note on bounded rationality. J Econ Theory 49:1–9CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of EconomicsThe Pennsylvania State UniversityUniversity ParkUSA
  2. 2.Faculty of EconomicsUniversity of CambridgeCambridgeUK