Journal of Logic, Language and Information

, Volume 21, Issue 1, pp 117–139 | Cite as

Bidirectional Optimization from Reasoning and Learning in Games

  • Michael Franke
  • Gerhard Jäger


We reopen the investigation into the formal and conceptual relationship between bidirectional optimality theory (Blutner in J Semant 15(2):115–162, 1998, J Semant 17(3):189–216, 2000) and game theory. Unlike a likeminded previous endeavor by Dekker and van Rooij (J Semant 17:217–242, 2000), we consider signaling games not strategic games, and seek to ground bidirectional optimization once in a model of rational step-by-step reasoning and once in a model of reinforcement learning. We give sufficient conditions for equivalence of bidirectional optimality and the former, and show based on numerical simulations that bidirectional optimization may be thought of as a process of reinforcement learning with lateral inhibition.


Bidirectional optimality theory Signaling games Game theory Iterated best response Reinforcement learning 


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  1. Aloni M. (2007) Expressing ignorance or indifference. Modalimplicaturesinbi-directionaloptimalitytheory. In: B. Ten Cate, Zeevat H. (eds) Logic, language and computation: Papers from the 6th international Tbilisi symposium (Vol. 4363). Springer, Berlin, pp 1–20Google Scholar
  2. Argiento R., Pemantle R., Skyrms B., Volkov S. (2009) Learning to signal: Analysis of a micro-level reinforcement model. Stochastic Processes and their Applications 119: 373–390CrossRefGoogle Scholar
  3. Barrett J. A. (2009) The evolution of coding in signaling games. Theory and Decision 67: 223–237CrossRefGoogle Scholar
  4. Benz A., van Rooij R. (2007) Optimal assertions and what they implicate. Topoi—an International Review of Philosophy 27(1): 63–78Google Scholar
  5. Blutner R. (1998) Lexical pragmatics. Journal of Semantics 15(2): 115–162CrossRefGoogle Scholar
  6. Blutner R. (2000) Some aspects of optimality in natural language interpretation. Journal of Semantics 17(3): 189–216CrossRefGoogle Scholar
  7. Blutner, R., Zeevat, H. (eds) (2004) Optimality theory and pragmatics. Palgrave MacMillan, BasingstokeGoogle Scholar
  8. Blutner, R. & Zeevat, H. (2008). Optimality-theoretic pragmatics. In C. Maienborn, K. von Heusinger & P. Portner (Eds.), Semantics: An international handbook of natural language meaning (to appear).Google Scholar
  9. Dekker P., van Rooij R. (2000) Bi-directional optimality theory: An application of game theory. Journal of Semantics 17: 217–242CrossRefGoogle Scholar
  10. Franke M. (2009). Signal to act: Game theory in pragmatics. PhD thesis, Universiteit van Amsterdam.Google Scholar
  11. Franke M. (2011) Quantity implicatures, exhaustive interpretation, and rational conversation. Semantics & Pragmatics 4(1): 1–82Google Scholar
  12. Grice P.H. (1975) Logic and conversation. In: Cole P., Morgan J.L. (eds) Syntax and semantics (Vol. 3). Speech Acts. Academic Press, London, pp 41–58Google Scholar
  13. Hendriks P., de Hoop H. (2001) Optimality theoretic semantics. Linguistics and Philosophy 24: 1–32CrossRefGoogle Scholar
  14. Hendriks P., de Hoop H., Krämer I., de Swart H., Zwarts J. (2010) Conflicts in interpretation. Equinox Publishing, LondonGoogle Scholar
  15. Horn L. (1984) Towards a new taxonomy for pragmatic inference: Q-based and R-based implicatures. In: Schiffrin D. (eds) Meaning, Form, and Use in Context. Georgetown University Press, Washington, pp 11–42Google Scholar
  16. Jäger G. (2002) Some notes on the formal properties of bidirectional optimality theory. Journal of Logic, Language and Information 11(4): 427–451CrossRefGoogle Scholar
  17. Jäger, G. (2008). Game theory in semantics and pragmatics. Manuscript, University of Bielefeld.Google Scholar
  18. Levinson S. C. (2000) Presumptive Meanings. The Theory of Generalized Conversational Implicature. MIT Press, Cambridge, MassachusettsGoogle Scholar
  19. Lewis D. (1969) Convention. Harvard University Press, Cambridge, MassGoogle Scholar
  20. Mühlenbernd, R. (2011). Learning with neighbors: Emergence of convention in a society of learning agents. Synthese (online first).Google Scholar
  21. Parikh P. (1987) Language and strategic inference. PhD thesis, Stanford University (unpublished).Google Scholar
  22. Prince, A., Smolensky, P. (1993). Optimality theory: Constraint interaction in generative grammar. Technical report TR-2. New Brunswick, NJ: Rutgers University Cognitive Science Center.Google Scholar
  23. Roth A. E., Erev I. (1995) Learning in extensive form games: Experimental data and simple dynamical models in the intermediate term. Games and Economic Behavior 8(1): 164–212CrossRefGoogle Scholar
  24. Selten R. (1998) Features of experimentally observed bounded rationality. European Economic Review 42(3-5): 413–436CrossRefGoogle Scholar
  25. Skyrms B. (2010) Signals. Oxford University Press, OxfordCrossRefGoogle Scholar
  26. Stalnaker R. (2006) Saying and meaning, cheap talk and credibility. In: Benz A., Jäger G., van Rooij R. (eds) Game theory and pragmatics. Palgrave MacMillan, Hampshire, pp 83–100Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of LinguisticsUniversity of TübingenTubingenGermany

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