Technical Note—Characterizing and Computing the Set of Nash Equilibria via Vector Optimization

Published Online:https://doi.org/10.1287/opre.2023.2457

References

  • Anderson RM (1985) Strong core theorems with nonconvex preferences. Econometrica 53(6):1283–1294.CrossrefGoogle Scholar
  • Armand P (1993) Finding all maximal efficient faces in multiobjective linear programming. Math. Programming 61:357–375.CrossrefGoogle Scholar
  • Bade S (2005) Nash equilibrium in games with incomplete preferences. Econom. Theory 26(2):309–332.CrossrefGoogle Scholar
  • Beck M, Stein O (2023) Semi-infinite models for equilibrium selection. Minimax Theory Appl. Forthcoming.Google Scholar
  • Braouezec Y, Kiani K (2023) Economic foundations of generalized games with shared constraint: Do binding agreements lead to less Nash equilibria? Eur. J. Oper. Res. 308(1):467–479.CrossrefGoogle Scholar
  • Corley HW (1985) Games with vector payoffs. J. Optim. Theory Appl. 47:491–498.CrossrefGoogle Scholar
  • De Marco G, Morgan J (2007) A refinement concept for equilibria in multicriteria games via stable scalarizations. Internat. Game Theory Rev. 9(2):169–181.CrossrefGoogle Scholar
  • Evans JP, Steuer RE (1973) A revised simplex method for multiple objective programs. Math. Programming 5(1):54–72.CrossrefGoogle Scholar
  • Facchinei F, Fischer A, Piccialli V (2007) On generalized Nash games and variational inequalities. Oper. Res. Lett. 35(2):159–164.CrossrefGoogle Scholar
  • Feinstein Z, Hey N, Rudloff B (2023) Approximating the set of Nash equilibria for convex games. Working paper, Stevens Institute of Technology.Google Scholar
  • Hamel AH, Löhne A (2018) A set optimization approach to zero-sum matrix games with multi-dimensional payoffs. Math. Methods Oper. Res. 88:369–397.CrossrefGoogle Scholar
  • Hamel AH, Löhne A, Rudloff B (2014) Benson type algorithms for linear vector optimization and applications. J. Global Optim. 59(4):811–836.CrossrefGoogle Scholar
  • Harker PT (1991) Generalized Nash games and quasi-variational inequalities. Eur. J. Oper. Res. 54(1):81–94.CrossrefGoogle Scholar
  • Herings PJJ, Peeters R (2005) A globally convergent algorithm to compute all Nash equilibria for n-person games. Ann. Oper. Res. 137(1):349–368.CrossrefGoogle Scholar
  • Jahn J (2011) Vector Optimization: Theory, Applications, and Extensions, 2nd ed. (Springer, Berlin).CrossrefGoogle Scholar
  • Judd KL, Renner P, Schmedders K (2012) Finding all pure-strategy equilibria in games with continuous strategies. Quant. Econom. 3(2):289–331.CrossrefGoogle Scholar
  • Khan AA, Tammer C, Zălinescu C (2015) Set-Valued Optimization: An Introduction with Applications. Vector Optimization (Springer-Verlag, Berlin).CrossrefGoogle Scholar
  • Löhne A, Weißing B (2017) The vector linear program solver Bensolve—Notes on theoretical background. Eur. J. Oper. Res. 260(3):807–813.CrossrefGoogle Scholar
  • McKelvey RD, McLennan A (1996) Computation of equilibria in finite games. Amman HM, Kendrick DA, Rust J, eds. Handbook of Computational Economics, vol. 1 (Elsevier, Amsterdam), 87–142.Google Scholar
  • Nabetani K, Tseng P, Fukushima M (2011) Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints. Comput. Optim. Appl. 48(3):423–452.CrossrefGoogle Scholar
  • Nash J (1950) Equilibrium points in n-person games. Proc. Natl. Acad. Sci. USA 36(1):48–49.CrossrefGoogle Scholar
  • Nash J (1951) Non-cooperative games. Ann. Math. 54(2):286–295.CrossrefGoogle Scholar
  • Parsopoulos KE, Vrahatis MN (2004) On the computation of all global minimizers through particle swarm optimization. IEEE Trans. Evolutionary Comput. 8(3):211–224.CrossrefGoogle Scholar
  • Rosen JB (1965) Existence and uniqueness of equilibrium points for concave n-person games. Econometrica 33(3):520–534.CrossrefGoogle Scholar
  • Rudloff B, Ulus F, Vanderbei RJ (2017) A parametric simplex algorithm to solve linear vector optimization problems. Math. Programming 163(1):213–242.CrossrefGoogle Scholar
  • Sawaragi Y, Nakayama H, Tanino T (1985) Theory of Multiobjective Optimization. Mathematics in Science and Engineering, vol. 176 (Elsevier, Amsterdam).Google Scholar
  • Shapley LS, Rigby FD (1959) Equilibrium points in games with vector payoffs. Naval Res. Logist. Quart. 6(1):57–61.CrossrefGoogle Scholar
  • Tadelis S (2013) Game Theory: An Introduction (Princeton University Press, Princeton, NJ).Google Scholar
  • Tammer C, Weidner P (2020) Scalarization and Separation by Translation Invariant Functions—With Applications in Optimization, Nonlinear Functional Analysis, and Mathematical Economics (Springer, Cham).CrossrefGoogle Scholar
  • Tohidi G, Hassasi H (2018) Adjacency-based local top-down search method for finding maximal efficient faces in multiple objective linear programming. Naval Res. Logist. 65(3):203–217.CrossrefGoogle Scholar
  • Van Tu T (2017) A new method for determining all maximal efficient faces in multiple objective linear programming. Acta Math. Vietnamica 42:1–25.CrossrefGoogle Scholar
  • von Neumann J (1928) Zur Theorie der Gesellschaftsspiele. Mathematische Annalen 100(1):295–320.CrossrefGoogle Scholar
  • Voorneveld M (1999) Potential games and interactive decisions with multiple criteria. Unpublished doctoral thesis, Center for Economic Research, Tilburg University, Tilburg, Netherlands.Google Scholar
  • Wu Z, Dang C, Hu F, Fu B (2015) A new method to finding all Nash equilibria. He X, Gao X, Zhang Y, Zhou Z-H, Liu Z-Y, Fu B, Hu F, Zhang Z, eds. Internat. Conf. Intelligent Sci. Big Data Engrg. (Springer, Cham, Switzerland), 499–507.Google Scholar
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