Advertisement

Bargaining Model of Mutual Deterrence Among Three Players with Incomplete Information

Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 758)

Abstract

The tripartite bargaining problem of mutual deterrence has been investigated from the perspective of Rubinstein indefinite bargaining and cooperative game theory. Considering the situation of incomplete information in reality, this paper established a tripartite mutual deterrence bargaining model with unilateral and bilateral incomplete information by introducing incomplete information into the model and defining a discount factor. And particularly, the formula is furnished for calculating the Nash equilibrium distribution of every player under the incomplete information. Finally, an illustrative example is presented to show that the established model is feasible and effective and can provide a new way and method to analyze and solve multi mutual deterrence or conflict problems with incomplete information.

Keywords

Deterrence Bargaining Incomplete information Game theory 

Notes

Acknowledgement

This work was supported by the Key Project of Natural Science Foundation of China (Grant Nos. 71231003).

References

  1. 1.
    Schelling, T.: Arms and Influence, pp. 120–123. Yale University Press, New Haven (1966)Google Scholar
  2. 2.
    Nash, J.F.: The bargaining problem. Econometrica 18, 155–162 (1950)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Rubinstein, A.: Perfect equilibrium in a bargaining model. Econometrica 50, 97–109 (1982)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Kalandrakis, A.: A three-player dynamic majoritarian bargaining game. J. Econ. Theor. 116(2), 194–322 (2004)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Calvo-Armengol, A.: A note on three players noncooperative bargaining with restricted pairwise meetings. Econ. Lett. 65(1), 47–54 (1999)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Xiang, G.H., Wang, Y.X.: A bargaining model of mutual deterrence with incomplete information. Oper. Res. Manag. Sci. 17(6), 16–19 (2009)Google Scholar
  7. 7.
    Gong, Z.Q., Xie, Z., Dai, L.: A bargaining model of mutual deterrence between three players. J. Quant. Econ. 32(2), 87–92 (2015)MathSciNetGoogle Scholar
  8. 8.
    Harsanyi, J.C.: Games with incomplete information played by “Bayesian” players. Manag. Sci. 14(3), 159–182 (1967)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Yu, W.S.: Game Theory and Economy, pp. 115–127. Higher Education Press, Beijing (2007)Google Scholar
  10. 10.
    Li, D.F.: Fuzzy Multiobjective Many-Person Decision Makings and Games. National Defense Industry Press, Beijing (2003)Google Scholar
  11. 11.
    Zagare, F.C., Kilgour, D.M.: Alignment patterns, crisis bargaining, and extended deterrence: a game-theoretic analysis. Int. Stud. Q. 47(4), 587–615 (2003)CrossRefGoogle Scholar
  12. 12.
    Zhang, Z.Y., Li, Z.Y., Long, Y.: Empirical study on enterprise bargaining power in skill-based competitive strategic alliances. J. Syst. Eng. 22(2), 148–155 (2007)MATHGoogle Scholar
  13. 13.
    Zhou, J.X., Wang, Y.: Research on bargaining problem between a disadvantaged wholesaler and a supplier under asymmetric information. J. Syst. Eng. 31(4), 481–493 (2016)MATHGoogle Scholar
  14. 14.
    Li, D.-F.: Multiattribute group decision-making methods with intuitionistic fuzzy sets. In: Li, D.-F. (ed.) Decision and Game Theory in Management With Intuitionistic Fuzzy Sets. SFSC, vol. 308, pp. 251–288. Springer, Heidelberg (2014). doi: 10.1007/978-3-642-40712-3_6 CrossRefGoogle Scholar
  15. 15.
    Fontenay, C.C.D., Gans, J.S.: Bilateral bargaining with externalities. J. Ind. Econ. 62(4), 756–788 (2014)CrossRefGoogle Scholar
  16. 16.
    Bayati, M., Borgs, C., Chayes, J., et al.: Bargaining dynamics in exchange networks. J. Econ. Theor. 156(2), 417–454 (2015)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Aghadadashli, H., Wey, C.: Multiunion bargaining: tariff plurality and tariff competition. J. Inst. Theor. Econ. (JITE) 171(4), 666–695 (2015)CrossRefGoogle Scholar
  18. 18.
    Collard-Wexler, A., Gowrisankaran, G., Lee, R.S.: “Nash-in-Nash” bargaining: a microfoundation for applied work. Eur. J. Pharm. Biopharm. 71(2), 339–345 (2014)Google Scholar
  19. 19.
    An, B., Gatti, N., Lesser, V.: Alternating-offers bargaining in one-to-many and many-to-many settings. Ann. Math. Artif. Intell. 77(1), 1–37 (2016)MathSciNetMATHGoogle Scholar
  20. 20.
    Abreu, D., Pearce, D., Stacchetti, E.: One-sided uncertainty and delay in reputational bargaining. Theor. Econ. 10(3), 719–773 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.College of Economics and ManagementFuzhou UniversityFuzhouChina

Personalised recommendations