On the Relation Among Some Definitions of Strategic Stability

Hillas, John; Jansen, M.J.M.; Potters, J.A.M.; Vermeulen, Dries

doi:10.1287/moor.26.3.611.10585

Cited by 18 publications

(28 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…But quasistable set may not be stable to perturbations of strategy sets, as the perturbation of best reply correspondence does not need to be sufficiently small, even the perturbation of strategy sets is small enough. Thus, some concepts of stable set, such as homotopy-stable set (see, Mertens [14]), essential set (see, McLennan [13]), CKM-set, and CT -set (see, Hillas et al [6]), were presented, where a perturbation of strategy sets was defined with some additional conditions. Mclennan [13] introduced a related type of stable set called essential sets.…”

Section: Introductionmentioning

confidence: 99%

Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria

Xiang¹,

Xia²,

Yang³

et al. 2017

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

In this paper, we mainly focus on the stability of Nash equilibria to any perturbation of strategy sets. A larger perturbation, strong δ-perturbation, will be proposed for set-valued mapping. The class of perturbed games considered in the definition of strong δ-perturbation is richer than those considered in many other definitions of stability of Nash equilibria. The strong δ-perturbation of the best reply correspondence will be used to define an appropriate stable set for Nash equilibria, called SBR-stable set. As an SBR-stable set is stable to any strong δ-perturbation and, various perturbations of strategy sets are not beyond the range of strong δ-perturbation, it has the stability that various stable sets possess, such as fully stable set, stable set, quasistable set, and essential set. An SBR-stable set is stable to any perturbation of strategy sets, so it will provide convenience for study in strategic stability, which is even used to study any noncooperative game.

show abstract

Section: Introductionmentioning

confidence: 99%

Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria

Xiang¹,

Xia²,

Yang³

et al. 2017

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

show abstract

“…4 Since Mertens stable sets are known to contain Hillas stable sets see e.g. Hillas et al 1999 , the same negative result holds for Hillas stable sets.…”

Section: Introductionmentioning

confidence: 83%

On Forward Induction and Evolutionary and Strategic Stability

Hauk

Hurkens

2000

SSRN Journal

View full text Add to dashboard Cite

We analyze which normal form solution concepts capture the notion of forward induction, as de ned by v an Damme JET, 1989 in the class of generic two player normal form games preceded by an outside option. We nd that none of the known strategic stability concepts including Mertens stable sets and hyperstable sets captures this form of forward induction. On the other hand, we show that the evolutionary concept of EES set Swinkels, JET, 1992 is always consistent with forward induction.

show abstract

“…We do not define most of these notions, because we rely on the results of D&R and Hillas et al [12] for most of our conclusions. We explicitly use the definitions of essentiality and strong stability though, and for that reason we state here their formal definitions.…”

Section: Strategic Stabilitymentioning

confidence: 99%

“…We then take a look at the above choice problem from the perspective of strategic stability. For the more demanding notions of strategic stabilityessentiality as defined by Wu Wen-Tsün and Jiang Jia-He ( [16], [30]), best response stability as defined by Hillas ([11], [12]), and strategic stability in the sense of Mertens ([21], [22])-it turns out that the total number of passengers starts to matter. Surprisingly, the question is not whether the number of passengers is large or small, but whether it is even or odd.…”

mentioning

confidence: 99%

Where Strategic and Evolutionary Stability Depart - A Study of Minimal Diversity Games

2010

Self Cite

View full text Add to dashboard Cite

A minimal diversity game is an n player strategic form game in which each player has m pure strategies at his disposal. The payoff to each player is always 1, unless all players select the same pure strategy, in which case all players receive zero payoff. Such a game has a unique isolated completely mixed Nash equilibrium in which each player plays each strategy with equal probability, and a connected component of Nash equilibria consisting of those strategy profiles in which each player receives payoff 1. The Pareto superior component is shown to be asymptotically stable under a wide class of evolutionary dynamics, while the isolated equilibrium is not. On the other hand, the isolated equilibrium is strategically stable, while the strategic stability of the Pareto efficient component depends on the dimension of the component, and hence on the number of players, and the number of pure strategies.JEL Codes. C72, D44.

show abstract

On the Relation Among Some Definitions of Strategic Stability

Cited by 18 publications

References 17 publications

Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria

Stability of fixed points of set-valued mappings and strategic stability of Nash equilibria

On Forward Induction and Evolutionary and Strategic Stability

Where Strategic and Evolutionary Stability Depart - A Study of Minimal Diversity Games

Contact Info

Product

Resources

About