Game Theory

Siegfried Carl () and Seppo Heikkilä ()
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Siegfried Carl: Martin-Luther-Universität Halle-Wittenberg, Institut für Mathematik
Seppo Heikkilä: University of Oulu, Department of Mathematical Sciences

Chapter 8 in Fixed Point Theory in Ordered Sets and Applications, 2011, pp 317-399 from Springer

Abstract: Abstract The main goal of this chapter is to study the existence of extremal Nash equilibria for normal-form games. Our interest is focused on games with strategic complementarities, which means roughly speaking that the best responses of players are increasing in actions of the other players. Properties, known as ‘increasing differences,’ ‘(quasi)supermodular,’ and ‘single crossing property,’ are used to formalize, or even to define strategic complementarities, cf. [9, 12, 74, 75, 146, 179, 218]. In the last section of this chapter we consider the existence of winning strategies in a pursuit and evasion game. In addition we obtain new fixed point results for set-valued and single-valued mappings.

Keywords: Nash Equilibrium; Pure Strategy; Order Limit; Winning Strategy; Strategy Space (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4419-7585-0_8

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