Abstract
In this chapter, the notion of Pareto–Nash equilibrium is investigated as a continuation of the precedent chapter as well as a continuation of prior works (Sagaidac and Ungureanu, Operational research, CEP USM, Chişinău, 296 pp, 2004 (in Romanian), [1]; Ungureanu, Comp Sci J Moldova, 14(3(42)):345–365, 2006, [2]; Ungureanu, ROMAI J, 4(1):225–242, 2008, [3]). First, problems and needed basic theoretical results are exposed. The method of intersection of graphs of best response mappings presented above and initiated in Ungureanu (Comp Sci J Moldova, 14(3(42)):345–365, 2006, [2]) is applied to solve dyadic two-criterion mixed-strategy games. To avoid misunderstanding, some previous results, which are applied in this chapter, are briefly exposed, too.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Sagaidac, M., and V. Ungureanu. 2004. Operational Research. Chişinău: CEP USM, 296 pp. (in Romanian).
Ungureanu, V. 2006. Nash equilibrium set computing in finite extended games. Computer Science Journal of Moldova 14 (3(42)): 345–365.
Ungureanu, V. 2008. Solution principles for simultaneous and sequential games mixture. ROMAI Journal 4 (1): 225–242.
Selten, R. 1975. Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory 4 (1): 22–55.
Borm, P., F. Van Megen, and S. Tijs. 1999. A perfectness concept for multicriteria games. Mathematical Methods of Operations Research 49 (3): 401–412.
Yu, H. 2003. Weak Pareto equilibria for multiobjective constrained games. Applied Mathematics Letters 16: 773–776.
Podinovskii, V.V., and V.D. Nogin. 1982. Pareto-optimal solutions of the multi-criteria problems. Moscow: Nauka, 255 pp. (in Russian).
Jahn, J. 2004. Vector Optimization: Theory, Applications and Extensions, Series Operations Research. Berlin: Springer, XV+481 pp.
Lozan, V., and V. Ungureanu. 2009. Principles of Pareto-Nash equilibrium. Studia Universitatis 7: 52–56.
Lozan, V., and V. Ungureanu. 2011. Pareto–Nash equilibria in bicriterial dyadic games with mixed strategies, Wolfram Demonstrations Project. http://demonstrations.wolfram.com/ParetoNashEquilibriaInBicriterialDyadicGamesWithMixedStrateg/. Accessed 13 Oct 2011.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Ungureanu, V. (2018). Sets of Pareto–Nash Equilibria in Dyadic Two-Criterion Mixed-Strategy Games. In: Pareto-Nash-Stackelberg Game and Control Theory. Smart Innovation, Systems and Technologies, vol 89. Springer, Cham. https://doi.org/10.1007/978-3-319-75151-1_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-75151-1_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-75150-4
Online ISBN: 978-3-319-75151-1
eBook Packages: EngineeringEngineering (R0)