Bargaining Between Automata

  • Ken Binmore
  • Michele Piccione
  • Larry Samuelson
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 456)


If the players in an alternating-offers bargaining game are averse to delays in reaching an agreement, then a unique subgame-perfect equilibrium exists. But the rationality requirements of the subgame-perfect equilibrium concept are too severe for this celebrated result of Ariel Rubinstein [21] to be relevant to the design of automated agents capable of negotiating on behalf of their clients. This paper therefore studies the play of bargaining games with alternating offers by finite automata.


Nash Equilibrium Finite Automaton Repeated Game Bargaining Game Subgame Perfection 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. Abreu and A. Rubinstein. The structure of Nash equilibrium in repeated games with finite automata. Econometrica, 56: 1259–1282, 1988.CrossRefGoogle Scholar
  2. [2]
    J. Banks and R. Sundaram. Repeated games, finite automata and complexity. Games and Economic Behavior, 2: 97–117, 1990.CrossRefGoogle Scholar
  3. [3]
    David Baron and Ehud Kalai. The simplest equilibrium of a majority-rule division game. Journal of Economic Theory, 61: 290–301, 1993.CrossRefGoogle Scholar
  4. [4]
    Ken Binmore. Modelling rational players: I and II. Economics and Philosophy,3 and 4:179–214 and 9–55, 1987–88.Google Scholar
  5. [5]
    Ken Binmore, Michele Piccione, and Larry Samuelson. Evolutionary stability in alternating-offers bargaining games. SSRI Working Paper 9603, University of Wisconsin, 1996.Google Scholar
  6. [6]
    Ken Binmore and Larry Samuelson. Evolutionary stability in repeated games played by finite automata. Journal of Economic Theory, 57: 278–305, 1992.CrossRefGoogle Scholar
  7. [7]
    Immanul M. Bomze and Jörgen Weibull. Does neutral stability imply Lyapunov stability? Games and Economic Behavior, 11: 173–192, 1995.CrossRefGoogle Scholar
  8. [8]
    Colin F. Camerer, Eric J. Johnson, Talia Rymon, and Sankar Sen. Cognition and framing in sequential bargaining for gains and losses. In Ken Binmore, Alan Kirman, and Piero Tani, editors, Frontiers of Game Theory, pages 27–48. MIT Press, Cambridge, Massachusetts, 1993.Google Scholar
  9. [9]
    Kalyan Chatterjee and Hamid Sabourian. Multilateral bargaining and strategic complexity. Mimeo, Penn State University and Cambridge University, 1995.Google Scholar
  10. [10]
    W. Güth, R. Schmittberger, and B. Schwarze. An experimental analysis of ultimatumbargaining. Journal of Economic Behavior and Organization, 3: 367–388, 1982.CrossRefGoogle Scholar
  11. [11]
    Werner Güth and Reinhard Tietz. Ultimatum bargaining behavior: A survey and comparison of experimentalresults. Journal of Economic Psychology, 11: 417–49, 1990.CrossRefGoogle Scholar
  12. [12]
    John Maynard Smith. Evolution and the Theory of Games. Cambridge University Press, Cambridge, 1982.CrossRefGoogle Scholar
  13. [13]
    John Maynard Smith and G. R. Price. The logic of animal conflict. Nature, 246: 15–18, 1973.CrossRefGoogle Scholar
  14. [14]
    Roger B. Myerson. Game Theory: Analysis of Conflict. Harvard University Press, Cambridge, Mass, 1991.Google Scholar
  15. [15]
    Alejandro Neme and Luis Quintas. Subgame perfect equilibrium of repeated games with implementation costs. Journal of Economic Theory, 66: 599–608, 1995.CrossRefGoogle Scholar
  16. [16]
    Martin J. Osborne and Ariel Rubinstein. A Course in Game Theory. MIT Press, Cambridge, 1994.Google Scholar
  17. [17]
    Motty Perry and Philip J. Reny. A non-cooperative bargaining model with strategically timed offers. Journal of Economic Theory, 59: 55–77, 1993.CrossRefGoogle Scholar
  18. [18]
    Michele Piccione. Finite automata equilibria with discounting. Journal of Economic Theory, 56: 180–193, 1992.CrossRefGoogle Scholar
  19. [19]
    Michele Piccione and Ariel Rubinstein. Finite automata play a repeated extensive game. Journal of Economic Theory, 61: 160–168, 1993.CrossRefGoogle Scholar
  20. [20]
    Alvin E. Roth. Bargaining experiments. In John Kagel and Alvin E. Roth, editors, Handbook of Experimental Economics, pages 253–348. Princeton University Press, 1995.Google Scholar
  21. [21]
    Ariel Rubinstein. Perfect equilibrium in a bargaining model. Econometrica, 50: 97–109, 1982.CrossRefGoogle Scholar
  22. [22]
    Ariel Rubinstein. Finite automata play the repeated prisoners’ dilemma. Journal of Economic Theory, 39: 83–96, 1986.CrossRefGoogle Scholar
  23. [23]
    Ariel Rubinstein. On the interpretation of two theoretical models of bargaining. Sackler Institute of Economic Studies Working Paper 7–92, Tel Aviv University, 1992.Google Scholar
  24. [24]
    Eric van Damme, Reinhard Selten, and Eyal Winter. Alternating bid bargaining with a smallest money unit. Games and Economic Behavior, 2: 188–201, 1990.CrossRefGoogle Scholar
  25. [25]
    Peyton Young. An evolutionary model of bargaining. Journal of Economic Theory, 59: 145–168, 1993.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ken Binmore
    • 1
  • Michele Piccione
    • 2
  • Larry Samuelson
    • 3
  1. 1.Economics DepartmentUniversity CollegeLondonUK
  2. 2.Economics DepartmentUniversity of British ColumbiaVancouverCanada
  3. 3.Economics DepartmentUniversity of WisconsinMadisonUSA

Personalised recommendations