Abstract
Since most real life decisions are multiobjective, multicriteria games offer a more realistic modeling of real-life interactions. Although several equilibrium concepts have been proposed for solving multicriteria games, equilibria detection has not received much attention. Generative relations are proposed to characterize multicriteria equilibria. An evolutionary method based on generative relations is proposed for detecting various multicriteria equilibria: Nash-Pareto, Ideal Nash and Pareto equilibria. Numerical experiments on discrete and continuous games indicate the potential of the proposed approach.
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References
Bade, S., Haeringer, G., Renou, L.: More strategies, more nash equilibria. J. Econ. Theory 135(1), 551–557 (2009)
Borm, P.E.M., Tijs, S.H., van den Aarssen, J.C.M.: Pareto equilibria in multiobjective games. In: Technical report, Tilburg University (1988)
Borm, P., van Megen, F., Tijs, S.: A perfectness concept for multicriteria games. Math. Methods Oper. Res. 49, 401–412 (1999)
Christos, H.: Papadimitriou: on the complexity of the parity argument and other inefficient proofs of existence. J. Comput. Syst. Sci. 48(3), 498–532 (1994)
Dumitrescu, D., Lung, R.I., Mihoc, T.D.: Evolutionary equilibria detection in non-cooperative games. Applications of Evolutionary Computing, pp. 253–262. Springer, Heidelberg (2009)
Lung, R.I., Dumitrescu, D.: Computing nash equilibria by means of evolutionary computation. Int. J. Comput. Commun. Control 6, 364–368 (2008)
McKelvey, R.D., McLennan, A.: Computation of equilibria in finite games. Handbook of Computational Economics, pp. 87–142. Elsevier, Amsterdam (1996)
Nash, J.: Non-cooperative games. Ann. Math. 54(2), 286–295 (1951)
Osborne, M.J.: An introduction to game theory. In: Oxford University Press (2004)
Radjef, M.S., Fahem, K.: A note on ideal nash equilibrium in multicriteria games. Appl. Math. Lett. 21, 1105–1111 (2008)
Shapley, L.S., Rigby, F.D.: Equilibrium points in games with vector payoffs. Nav. Res. Logist. Q. 6(1), 57–61 (1959)
Storn, R., Price, K.: Differential evolution a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)
Thomsen, R.: Multimodal optimization using crowding-based differential evolution. In: IEEE Proceedings of the Congress on Evolutionary Computation, CEC’04, pp. 1382–1389 (2004)
Voorneveld, M., Grahn, S., Dufwenberg, M.: Ideal equilibria in non-coperative multicriteria games. In: Uppsala - Working Paper Series, 1999:19 (1999)
Wang, S.Y.: Existence of a pareto equilibrium. J. Optim. Theory Appl. 79, 373–384 (1993)
Zhao, J.: The equilibria of a multiple objective game. Int. J. Game Theory 20, 171–182 (1991)
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Nagy, R., Dumitrescu, D. (2017). Evolutionary Equilibrium Detection in Multicriteria Games. In: Emmerich, M., Deutz, A., Schütze, O., Legrand, P., Tantar, E., Tantar, AA. (eds) EVOLVE – A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation VII. Studies in Computational Intelligence, vol 662. Springer, Cham. https://doi.org/10.1007/978-3-319-49325-1_4
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DOI: https://doi.org/10.1007/978-3-319-49325-1_4
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