Advertisement

Journal of Economics

, Volume 97, Issue 3, pp 265–272 | Cite as

Payoff dominance and risk dominance in the observable delay game: a note

  • Toshihiro Matsumura
  • Akira OgawaEmail author
Article

Abstract

We examine whether the payoff dominant sequential-move (Stackelberg) outcome is realized when timing is endogenized. We adopt the observable delay game formulated by Hamilton and Slutsky [Games Econ Behav 2(1):29–46, 1990]. We find that if one sequential-move outcome is payoff dominant, either (i) the outcome both players prefer is the unique equilibrium; or (ii) two sequential-move outcomes are equilibria and the one both players prefer is risk dominant. In other words, no conflict between payoff dominance and risk dominance in the observable delay game exists, in contrast to other games such as (non pure) coordination games. We also find that even if one of two sequential-move outcomes is the unique equilibrium outcome in the observable delay game, it does not imply that the equilibrium outcome is payoff dominant to the other sequential-move outcome.

Keywords

Observable delay Endogenous role Payoff dominance Risk dominance 

JEL Classification

L13 C72 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amir R, Stepanova A (2006) Second-mover advantage and price leadership in Bertrand duopoly. Games Econ Behav 55(1): 1–20CrossRefGoogle Scholar
  2. Bárcena-Ruiz JC (2007) Endogenous timing in a mixed duopoly: price competition. J Econ 91(3): 263–272CrossRefGoogle Scholar
  3. Deneckere RJ, Kovenock D (1992) Price leadership. Rev Econ Stud 59(1): 143–162CrossRefGoogle Scholar
  4. Elberfeld W (1997) Incentive montonicity and equilibrium selection in 2 ×  2 matrix games. J Econ 65(3): 279–290Google Scholar
  5. Fonseca MA, Muller W, Normann H-T (2006) Endogenous timing in duopoly: experimental evidence. Int J Game Theory 34(3): 443–456CrossRefGoogle Scholar
  6. Furth D, Kovenock D (1993) Price leadership in a duopoly with capacity constraints and product differentiation. J Econ 57(1): 1–35Google Scholar
  7. Hamilton JH, Slutsky SM (1990) Endogenous timing in duopoly games: Stackelberg or Cournot equilibria. Games Econ Behav 2(1): 29–46CrossRefGoogle Scholar
  8. Harsanyi JC, Selten R (1988) A general theory of equilibrium selection in games. MIT Press, CambridgeGoogle Scholar
  9. Ishibashi I (2008) Collusive price leadership with capacity constraints. Int J Ind Organ 26(3): 704–715CrossRefGoogle Scholar
  10. Ishibashi I, Matsumura T (2006) R&D competition between public and private sectors. Eur Econ Rev 50(6): 1347–1366CrossRefGoogle Scholar
  11. Itoh M, Ono Y (1982) Tariffs, quotas, and market-structure. Q J Econ 97(2): 295–305CrossRefGoogle Scholar
  12. Jafarey S, Lahiri S (2007) Developing-country borrowing from a monopolist lender: strategic interactions and endogenous leadership. Jpn Econ Rev (forthcoming). doi: 10.1111/j.1468-5876.2008.00436.x
  13. Jinji N (2004) Endogenous timing in a vertically differentiated duopoly with quantity competition. Hitotsubashi J Econ 45(2): 119–127Google Scholar
  14. Lambertini L (1999a) The international coordination of monetary policy: a game-theoretic reformulation. Keio Econ Stud 36(1): 39–49Google Scholar
  15. Lambertini L (1999b) Endogenous timing and the choice of quality in a vertically differentiated duopoly. Res Econ 53(1): 101–109CrossRefGoogle Scholar
  16. Lu Y (2006) Endogenous timing in a mixed oligopoly with foreign competitors: the linear demand case. J Econ 88(1): 49–68CrossRefGoogle Scholar
  17. Matsumura T (1995) Endogenous timing in multi-stage duopoly games. Jpn Econ Rev 46(3): 257–265CrossRefGoogle Scholar
  18. Matsumura T (2003) Stackelberg mixed duopoly with a foreign competitor. Bull Econ Res 55(3): 275–287CrossRefGoogle Scholar
  19. Normann H-T (2002) Endogenous timing with incomplete information and with observable delay. Games Econ Behav 39(2): 282–291CrossRefGoogle Scholar
  20. Ohkawa T, Okamura M, Tawada M (2002) Endogenous timing and welfare in the game of trade policies under international oligopoly. In: Woodland A (ed) Economic theory of international trade: essay in Honor of Murray C. Kemp. Edward Elgar, UKGoogle Scholar
  21. Ono Y (1978) The equilibrium of duopoly in a market of homogeneous goods. Economica 45(179): 287–295CrossRefGoogle Scholar
  22. Ono Y (1982) Price leadership: a theoretical analysis. Economica 49(193): 11–20CrossRefGoogle Scholar
  23. Ono Y (1984) Profitability of export restraint. J Int Econ 16(3–4): 335–343CrossRefGoogle Scholar
  24. Pal D (1998) Endogenous timing in a mixed oligopoly. Econ Lett 61(2): 181–185CrossRefGoogle Scholar
  25. Tasnádi A (2003) Endogenous timing in moves in an asymmetric price-setting duopoly. Portuguese Econ J 2(1): 23–35CrossRefGoogle Scholar
  26. Tomaru Y, Saito M (2009) Mixed duopoly, privatization and subsidization in an endogenous timing framework. Manchester School (forthcoming)Google Scholar
  27. Schoonbeck L (1990) Stackelberg price leadership in the linear heterogeneous duopoly. J Econ 88(1): 49–68Google Scholar
  28. van Damme E, Hurkens S (2004) Endogenous price leadership. Games Econ Behav 47(2): 404–420CrossRefGoogle Scholar
  29. Vives X (2000) Oligopoly pricing: old idea and new tools. The MIT Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Institute of Social ScienceUniversity of TokyoTokyoJapan
  2. 2.College of Liberal ArtsInternational Christian UniversityMitaka, TokyoJapan

Personalised recommendations