Solution Principles for Mixtures of Simultaneous and Sequential Games

  • Valeriu UngureanuEmail author
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 89)


This chapter unites mathematical models, solution concepts and principles of both simultaneous and sequential games. The names of Pareto, Nash and Stackelberg, are used to identify simply types of game models. Pareto is associated with multi-criteria decision making (Pareto, Manuel d’economie politique, Giard, Paris, 1904, [1]). Nash is associated with simultaneous games (Nash, Ann Math, 54 (2): 280–295, 1951 [2]). Stackelberg is associated with hierarchical games (Von Stackelberg, Marktform und Gleichgewicht (Market Structure and Equilibrium), Springer, Vienna, 1934. [3]). The names have priorities in accordance with their positions in the game title from left to right. For example, the title Pareto-Nash-Stackelberg game (Ungureanu, ROMAI J, 4 (1): 225–242, 2008, [4]) means that players choose their strategies on the basis of multi-criteria Pareto decision making. They play a simultaneous Nash games. Simultaneous Nash games are played at every stage of a hierarchical Stackelberg game. Nash-Stackelberg games may be called also multi-leader-follower games as they are named in Hu’s survey (Hu, J Oper Res Soc Jpn, 58: 1–23, 2015, [5]). The chapter has general theoretical meaning both for this second part of the monograph and for the next third part. Investigations are provided by means of the concepts of best response mappings, efficient response mappings, mapping graphs, intersection of graphs, and constrained optimization problems.


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceMoldova State UniversityChișinăuMoldova

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