Computational Management Science

, Volume 12, Issue 1, pp 5–33 | Cite as

Game Theory Explorer: software for the applied game theorist

Original Paper


This paper presents the “Game Theory Explorer” software tool to create and analyze games as models of strategic interaction. A game in extensive or strategic form is created and nicely displayed with a graphical user interface in a web browser. State-of-the-art algorithms then compute all Nash equilibria of the game after a mouseclick. In tutorial fashion, we present how the program is used, and the ideas behind its main algorithms. We report on experiences with the architecture of the software and its development as an open-source project.


Game theory Nash equilibrium Scientific software 



We are indebted to Mark Egesdal, Alfonso Gómez-Jordana and Martin Prause for their invaluable contributions as programmers of GTE. Mark Egesdal designed the main program structure and coined the name “Game Theory Explorer”, with financial support from a STICERD research grant at the London School of Economics in 2010. Alfonso Gómez-Jordana and Martin Prause were funded by the Google Summer of Code in 2011 and 2012 for the open-source Gambit project, and continue as contributing volunteers. Karen Bletzer wrote conversion programs between GTE and Gambit file formats. Wan Huang implemented the enumeration of Nash equilibria based on the sequence form. We thank Theodore L. Turocy for inspiring discussions and for his support of GTE as part of Gambit. David Avis has written the lrsNash code for computing all Nash equilibria of a two-player game. All contributions and financial support are gratefully acknowledged.


  1. Audet C, Belhaiza S, Hansen P (2009) A new sequence form approach for the enumeration of all extreme Nash equilibria for extensive form games. Int Game Theory Rev 11:437–451Google Scholar
  2. Audet C, Hansen P, Jaumard B, Savard G (2001) Enumeration of all extreme equilibria of bimatrix games. SIAM J Sci Comput 23:323–338CrossRefGoogle Scholar
  3. Avis D (2000) Lrs: a revised implementation of the reverse search vertex enumeration algorithm. In: Kalai G, Ziegler G (eds) Polytopes-combinatorics and computation. DMV Seminar Band 29. Birkhäuser, Basel, pp 177–198Google Scholar
  4. Avis D (2006) User’s guide for lrs. Accessed 2 April 2014
  5. Avis D, Rosenberg G, Savani R, von Stengel B (2010) Enumeration of Nash equilibria for two-player games. Econ Theory 42:9–37CrossRefGoogle Scholar
  6. Bagwell K (1995) Commitment and observability in games. Games Econ Behav 8:271–280CrossRefGoogle Scholar
  7. Balthasar AV (2009) Geometry and equilibria in bimatrix games. PhD Thesis, London School of Economics, LondonGoogle Scholar
  8. Barnes N (2010) Publish your computer code: it is good enough. Nature 467:753–753CrossRefGoogle Scholar
  9. Belhaiza SJ, Mve AD, Audet C (2010) XGame-solver software. Accessed 2 April 2014
  10. Bron C, Kerbosch J (1973) Finding all cliques of an undirected graph. Commun ACM 16:575–577CrossRefGoogle Scholar
  11. Conitzer V, Sandholm T (2008) New complexity results about Nash equilibria. Games Econ Behav 63:621–641CrossRefGoogle Scholar
  12. Datta RS (2010) Finding all Nash equilibria of a finite game using polynomial algebra. Econ Theory 42:55–96CrossRefGoogle Scholar
  13. Gilboa I, Zemel E (1989) Nash and correlated equilibria: some complexity considerations. Games Econ Behav 1:80–93CrossRefGoogle Scholar
  14. Govindan S, Wilson R (2004) Computing Nash equilibria by iterated polymatrix approximation. J Econ Dyn Control 28:1229–1241CrossRefGoogle Scholar
  15. Harsanyi JC, Selten R (1988) A general theory of equilibrium selection in games. MIT Press, CambridgeGoogle Scholar
  16. Hauk E, Hurkens S (2002) On forward induction and evolutionary and strategic stability. J Econ Theory 106:66–90CrossRefGoogle Scholar
  17. Huang W (2011) Equilibrium computation for extensive games. PhD Thesis, London School of Economics, LondonGoogle Scholar
  18. Jiang AX, Leyton-Brown K, Bhat NAR (2011) Action-graph games. Games Econ Behav 71:141–173CrossRefGoogle Scholar
  19. Kohlberg E, Mertens J-F (1986) On the strategic stability of equilibria. Econometrica 54:1003–1037CrossRefGoogle Scholar
  20. Kuhn HW (1953) Extensive games and the problem of information. Contributions to the theory of games II. In: Kuhn HW, Tucker AW (eds) Annals of mathematics studies, 28th edn. Princeton University Press, Princeton, pp 193–216Google Scholar
  21. Langlois J-P (2006) GamePlan, a windows application for representing and solving games. Accessed 2 April 2014
  22. Lemke CE (1965) Bimatrix equilibrium points and mathematical programming. Manag Sci 11:681–689CrossRefGoogle Scholar
  23. Lemke CE, Howson JT Jr (1964) Equilibrium points of bimatrix games. J Soc Ind Appl Math 12:413–423CrossRefGoogle Scholar
  24. McKelvey RD, McLennan AM, Turocy TL (2010) Gambit: software tools for game theory, version 0.2010.09.01. Accessed 2 April 2014
  25. Nash J (1951) Noncooperative games. Ann Math 54:286–295CrossRefGoogle Scholar
  26. Osborne MJ (2004) An introduction to game theory. Oxford University Press, OxfordGoogle Scholar
  27. Quint T, Shubik M (1997) A theorem on the number of Nash equilibria in a bimatrix game. Int J Game Theory 26:353–359CrossRefGoogle Scholar
  28. Savani R (2005) Solve a bimatrix game. Interactive website. Accessed 2 April 2014
  29. Savani R, von Stengel B (2004) Exponentially many steps for finding a Nash equilibrium in a bimatrix game. In: CDAM research report LSE-CDAM-2004-03Google Scholar
  30. Savani R, von Stengel B (2006) Hard-to-solve bimatrix games. Econometrica 74:397–429CrossRefGoogle Scholar
  31. Shapley LS (1974) A note on the Lemke–Howson algorithm. In: Mathematical programming study 1: pivoting and extensions, pp 175–189Google Scholar
  32. van der Laan G, Talman AJJ, van der Heyden L (1987) Simplicial variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using a general labelling. Math Oper Res 12:377–397CrossRefGoogle Scholar
  33. von Stengel B (1996) Efficient computation of behavior strategies. Games Econ Behav 14:220–246CrossRefGoogle Scholar
  34. von Stengel B (1999) New maximal numbers of equilibria in bimatrix games. Discret Comput Geom 21:557–568CrossRefGoogle Scholar
  35. von Stengel B (2002) Computing equilibria for two-person games. In: Aumann RJ, Hart S (eds) Handbook of game theory, vol 3. North-Holland, Amsterdam, pp 1723–1759Google Scholar
  36. von Stengel B et al (2007) Equilibrium computation for two-player games in strategic and extensive form. In: Nisan N (ed) Algorithmic game theory. Cambridge University Press, Cambridge, pp 53–78CrossRefGoogle Scholar
  37. von Stengel B (2012) Rank-1 games with exponentially many Nash equilibria. Preprint. arXiv:1211.2405
  38. von Stengel B, van den Elzen AH, Talman AJJ (2002) Computing normal form perfect equilibria for extensive two-person games. Econometrica 70:693–715CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpool UK
  2. 2.Department of MathematicsLondon School of EconomicsLondon UK

Personalised recommendations