Asset pricing under ambiguous information: an empirical game-theoretic analysis

  • Ben-Alexander CassellEmail author
  • Michael P. Wellman
SI: Agent-Directed Simulation


In a representative agent model, the behavior of a social system is described in terms of a single aggregate decision maker. Such models are popular in economic and finance research, largely due to their analytic tractability, but fail to account for real-world agent heterogeneity, and may ignore effects of market microstructure. Agent-based simulation models naturally incorporate agent heterogeneity, and can account for any particular market microstructure; however, such models have gained only limited acceptance by the mainstream economic research community, due to concerns over how much general insight can be gleaned from simulating a particular configuration of agent behaviors. We address such concerns by employing game-theoretic criteria in behavior selection. We present a case study investigating a recent model from the finance literature proposed by Epstein and Schneider (ES), and its ability to explain the classic equity premium puzzle in risky asset pricing. For all market configurations that we examined, ambiguity-averse pricing was played with little or no probability in equilibrium. Moreover, none of the market configurations exhibited significant equity premia. Both our use of strategic equilibrium as a market composition concept, and the actions of our simulated market microstructure contribute to removing any equity premium. These findings underscore the value of checking that results from abstract representative-agent models are supportable in a higher-fidelity model where heterogeneity and strategic interactions are taken into account.


Empirical game theory Agent-based modeling Market simulation Equity premium 



This research was supported in part by Grant CCF-0905139 from the U.S. National Science Foundation, and the Army Research Laboratory Collaborative Technology Alliance in Network Science.


  1. Chapman DA, Polkovnichenko V (2009) First-order risk aversion, heterogeneity, and asset market outcomes. J Finance 64(4):1863–1887 CrossRefGoogle Scholar
  2. Chen S-H, Duffy J, Yeh C-H (2002) Equilibrium selection via adaptation: using genetic programming to model learning in a coordination game. Electron J Evol Model Econ Dyn Google Scholar
  3. DeLong JB, Magin K (2009) The US equity return premium: past, present, and future. J Econ Perspect 23(1):193–208 CrossRefGoogle Scholar
  4. Ellison G, Fudenberg D (1993) Rules of thumb for social learning. J Polit Econ 101(4):612–643 CrossRefGoogle Scholar
  5. Epstein LG, Schneider M (2008) Ambiguity, information quality, and asset pricing. J Finance 63(1):197–228 CrossRefGoogle Scholar
  6. Exley J, Mehta S, Smith A (2004) Mean reversion. In: Finance and investment conference, Brussels Google Scholar
  7. Fama EF, French KR (2002) The equity premium. J Finance 57:637–659 CrossRefGoogle Scholar
  8. Friedman D (1991) Evolutionary games in economics. Econometrica 59(3):637–666 CrossRefGoogle Scholar
  9. Friedman D, Rust J (eds) (1993) The double auction market: institutions, theories, and evidence. Addison-Wesley, Reading Google Scholar
  10. Gilboa I, Schmeidler D (1989) Maxmin expected utility with non-unique prior. J Math Econ 18(2):141–153 CrossRefGoogle Scholar
  11. Halevy Y (2007) Ellsberg revisited: an experimental study. Econometrica 75:503–536 CrossRefGoogle Scholar
  12. Hu J, Wellman MP (2003) Nash Q-learning for general-sum stochastic games. J Mach Learn Res 4:1039–1069 Google Scholar
  13. Jordan PR, Kiekintveld C, Wellman MP (2007) Empirical game-theoretic analysis of the TAC supply chain game. In: Sixth international joint conference on autonomous agents and multi-agent systems, Honolulu, pp 1188–1195 Google Scholar
  14. Jordan PR, Vorobeychik Y, Wellman MP (2008) Searching for approximate equilibria in empirical games. In: Seventh international conference on autonomous agents and multi-agent systems, Estoril, Portugal, pp 1063–1070 Google Scholar
  15. Lavenberg SS, Welch PD (1981) A perspective on the use of control variables to increase the efficiency of Monte Carlo simulations. Manag Sci 27(3):322–335 CrossRefGoogle Scholar
  16. LeBaron B (2006) Agent-based computational finance. In: Tesfatsion L, Judd KL (eds) Handbook of agent-based computational economics. Elsevier, Amsterdam Google Scholar
  17. Leombruni R, Richiardi M (2005) Why are economists sceptical about agent-based simulations? Physica A 355(1):103–109 CrossRefGoogle Scholar
  18. Littman ML (1994) Markov games as a framework for multi-agent reinforcement learning. In: Eleventh international conference on machine learning, pp 157–163 Google Scholar
  19. Longstaff FA (2006) Asset pricing in markets with illiquid assets. In: American finance association 2006 Boston meetings Google Scholar
  20. Mehra R, Prescott EC (1985) The equity premium: a puzzle. J Monet Econ 15(2):145–161 CrossRefGoogle Scholar
  21. Raberto M, Teglio A, Cincotti S (2008) Integrating real and financial markets in an agent-based economic model: an application to monetary policy design. Comput Econ 32:147–162 CrossRefGoogle Scholar
  22. Rothschild M, Stiglitz JE (1970) Increasing risk. I. A definition. J Econ Theory 2:225–243 CrossRefGoogle Scholar
  23. Schuster P, Sigmund K (1983) Replicator dynamics. J Theor Biol 101:19–38 CrossRefGoogle Scholar
  24. Thurner S (2011) Systemic financial risk: agent based models to understand the leverage cycle on national scales and its consequences. Technical report ifp/wkp/fgs (2011) 1, Organisation for Economic Co-operation and Development (OECD) Google Scholar
  25. Vorobeychik Y, Wellman MP, Singh S (2007) Learning payoff functions in infinite games. Mach Learn 67:145–168 CrossRefGoogle Scholar
  26. Weitzman ML (2007) Subjective expectations and asset-return puzzles. Am Econ Rev 97:1102–1130 CrossRefGoogle Scholar
  27. Wellman MP (2006) Methods for empirical game-theoretic analysis. In: Twenty-first national conference on artificial intelligence, pp 1552–1555 (abstract) Google Scholar
  28. Wellman MP, Estelle J, Singh S, Vorobeychik Y, Kiekintveld C, Soni V (2005a) Strategic interactions in a supply chain game. Comput Intell 21:1–26 CrossRefGoogle Scholar
  29. Wellman MP, Reeves DM, Lochner KM, Cheng S-F, Suri R (2005b) Approximate strategic reasoning through hierarchical reduction of large symmetric games. In: Twentieth national conference on artificial intelligence, Pittsburgh, pp 502–508 Google Scholar
  30. White M, Bowling M (2009) Learning a value analysis tool for agent evaluation. In: Twenty-first international joint conference on artificial intelligence, pp 1976–1981 Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.University of MichiganAnn ArborUSA

Personalised recommendations