Advertisement

Mutual Rationalizability in Vector-Payoff Games

  • Erella Eisenstadt-Matalon
  • Amiram MoshaiovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11411)

Abstract

This paper deals with vector-payoff games, which are also known as Multi-Objective Games (MOGs), multi-payoff games and multi-criteria games. Such game models assume that each of the players does not necessarily consider only a scalar payoff, but rather takes into account the possibility of self-conflicting objectives. In particular, this paper focusses on static non-cooperative zero-sum MOGs in which each of the players is undecided about the objective preferences, but wishes to reveal tradeoff information to support strategy selection. The main contribution of this paper is the introduction of a novel solution concept to MOGs, which is termed here as Multi-Payoff Mutual-Rationalizability (MPMR). In addition, this paper provides a discussion on the development of co-evolutionary algorithms for solving real-life MOGs using the proposed solution concept.

Keywords

Game theory Non-cooperative games Set-based optimization Set domination Multi-criteria decision-analysis 

Notes

Acknowledgment

The authors would like to thank E. Solan for referring them to the work of Bernheim [7] and of Pearce [8], and to also thank the anonymous reviewers of this paper.

References

  1. 1.
    Blackwell, D.: An analog of the minimax theorem for vector payoffs. Pac. J. Math. 6(1), 1–8 (1956)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Anand, L., Herath, G.: A survey of solution concepts in multicriteria games. J. Indian Inst. Sci. 75(2), 141–174 (1995)MathSciNetGoogle Scholar
  3. 3.
    Nishizaki, I.: Nondominated equilibrium solutions of multiobjective two-person nonzero-sum games in normal and extensive forms. In: Proceedings of Fourth International Workshop on Computational Intelligence & Applications, pp. 13–22 (2008)Google Scholar
  4. 4.
    Eisenstadt, E., Moshaiov, A.: Decision-making in non-cooperative games with conflicting self-objectives. J. Multi-Criteria Decis. Anal. 25, 1–12 (2018)CrossRefGoogle Scholar
  5. 5.
    Eisenstadt, E., Moshaiov, A.: Novel solution approach for multi-objective attack-defense cyber games with unknown utilities of the opponent. IEEE Trans. Emerg. Top. Comput. Intell. 1, 16–26 (2017)CrossRefGoogle Scholar
  6. 6.
    Matalon-Eisenstadt, E., Moshaiov, A., Avigad, G.: The competing travelling salespersons problem under multi-criteria. In: Handl, J., Hart, E., Lewis, P.R., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds.) PPSN 2016. LNCS, vol. 9921, pp. 463–472. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-45823-6_43CrossRefGoogle Scholar
  7. 7.
    Bernheim, B.D.: Rationalizable strategic behavior. Econometrica 52(4), 1007–1028 (1984)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Pearce, D.: Rationalizable strategic behavior and the problem of perfection. Econometrica 52(4), 1029–1050 (1984)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Aumann, R.J.: Backward induction and common knowledge of rationality. Games Econ. Behav. 8(1), 6–19 (1995)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Eisenstadt, E., Moshaiov, A., Avigad, G.: Co-evolution of strategies for multi-objective games under postponed objective preferences. In: Proceedings of IEEE Conference Computational Intelligence and Games, pp. 461–468 (2015)Google Scholar
  11. 11.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  12. 12.
    Żychowski, A., Gupta, A., Mańdziuk, J., Ong, Y.S.: Addressing expensive multi-objective games with postponed preference articulation via memetic co-evolution. Knowl.-Based Syst. 154, 17–31 (2018)CrossRefGoogle Scholar
  13. 13.
    Shapley, L.S.: Equilibrium points in games with vector payoffs. Naval Res. Logistics Q. 6(1), 57–61 (1959)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ghose, D., Prasad, U.R.: Multicriterion differential games with applications to combat problems. Comput. Math Appl. 18(1–3), 117–126 (1989)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Ghose, D., Prasad, U.R.: Solution concepts in two-person multicriteria games. J. Optim. Theory Appl. 63(2), 167–189 (1989)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Tel-Aviv UniversityTel-AvivIsrael
  2. 2.ORT Braude College of EngineeringKarmielIsrael

Personalised recommendations