On equilibrium refinements in supermodular games

Perfect equilibria in games of incomplete information

“…In the special case of complete information games (i.e., when type spaces are singletons), this definition collapses to the notion of perfection considered in Al-Najjar [2], Carbonell-Nicolau [8,9,10,12], Carbonell-Nicolau and McLean [13,14,15], and the strong notion of perfection defined in Simon and Stinchcombe [24].…”

“…In normal-form games with complete information, Selten's [23] perfection refines the Nash equilibrium concept by requiring that equilibrium strategies be immune to slight trembles in the execution of the players' actions. The standard definition of perfect equilibrium for normal-form games with finite action spaces (see, e.g., van Damme [26]) can be extended to normal-form games with infinitely many actions, and these extensions have been studied by several authors (see, e.g., Al-Najjar [2], Simon and Stinchcombe [24], Carbonell-Nicolau [8,9,10,12], Carbonell-Nicolau and McLean [13,14,15], and Bajoori et al [4]).…”

Organizational refinements of Nash equilibrium

“…Games with strategic complemetarities are commonly utilized in the literature both for the existence of Nash equilibrium (seeZhou, 1994;Echenique, 2005;Calciano, 2007; Keskin et al, 2014, among others) and for the existence of some of the refinements of Nash equilibrium; such as minimally altruistic Nash equilibrium (seeKaragozoglu et al, 2013), perfect equilibrium (seeCarbonell-Nicolau and McLean, 2014), and strong Berge equilibrium (see.10 Note that a complete lattice X is compact in its interval topology which is the topology generated by taking the closed intervals, [y, z] = {x ∈ X : y ≤ x ≤ z} with y, z ∈ X as a subbasis of closed sets (seeBirkhoff (1967)). 11 A strategy profile is said to be serially undominated if it survives the iterated elimination of strictly dominated strategies.…”