Strict Monotonicity in Comparative Statics

Edlin, Aaron S.; Shannon, Chris

doi:10.1006/jeth.1998.2405

Cited by 216 publications

(108 citation statements)

References 9 publications

Supporting

Mentioning

106

Contrasting

Order By: Relevance

“…Additional classes of examples are provided by Cournot oligopolies, bargaining games (Nash demand game), and as described in Dubey et al (2006), games of team projects with complementary or substitutable tasks, and tournaments. 2 Some of this work can be seen in Topkis (1979), Lippman et al (1987), Sobel (1988), Vives (1990), Milgrom and Roberts (1990), Zhou (1994), Milgrom and Shannon (1994), Milgrom and Roberts (1994), Shannon (1995), Villas-Boas (1997), Edlin and Shannon (1998), Echenique (2002Echenique ( , 2003a, and Echenique and Sabarwal (2003), among others. Extensive bibliographies are available in Topkis (1998) and in Vives (1999).…”

Section: Introductionmentioning

confidence: 99%

On the (non-)lattice structure of the equilibrium set in games with strategic substitutes

Roy

Sabarwal

2007

Econ Theory

View full text Add to dashboard Cite

This paper studies models where the optimal response functions under consideration are not increasing in endogenous variables, and weakly increasing in exogenous parameters. Such models include games with strategic substitutes, and include cases where additionally, some variables may be strategic complements. The main result here is that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. Indeed, for a given parameter value, a pair of distinct equilibria are never comparable. Therefore, with multiple equilibria, some of the established techniques for exhibiting increasing equilibria or computing equilibria that use the largest or smallest equilibrium, or that use the lattice structure of the equilibrium set do not apply to such models. Moreover, there are no ranked equilibria in such models. Additionally, the analysis here implies a new proof and a slight generalization of some existing results. It is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. (In particular, in n-player games of strategic substitutes with real-valued action spaces, symmetric equilibria increase with the parameter.)

show abstract

Section: Introductionmentioning

confidence: 99%

On the (non-)lattice structure of the equilibrium set in games with strategic substitutes

Roy

Sabarwal

2007

Econ Theory

View full text Add to dashboard Cite

show abstract

“…By the strengthening of Topkis's Theorem given in Amir (1996b) or Edlin and Shannon (1998), a sufficient condition for every selection of r 0 (.) to be strictly increasing (strictly decreasing) whenever it is interior is for ∂W f (q 0 ,q 1 ) ∂q 0 to be strictly increasing (decreasing) in q 1 .…”

Section: Proof Of Lemmamentioning

confidence: 99%

Endougenous Timing in a Mixed Duopoly

Amir

Feo

2012

SSRN Journal

View full text Add to dashboard Cite

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may May 2011Abstract This paper applies the framework of endogenous timing in games to mixed quantity duopoly, wherein a private -domestic or foreign -firm competes with a public, welfaremaximizing firm. We show that simultaneous play never emerges as a subgame-perfect equilibrium of the extended game, in sharp contrast to private duopoly games. We provide sufficient conditions for the emergence of public and/or private leadership equilibrium. In all cases, private profits and social welfare are higher than under the corresponding Cournot equilibrium. From a methodological viewpoint we make extensive use of the basic results from the theory of supermodular games in order to avoid common extraneous assumptions such as concavity, existence and uniqueness of the different equilibria, whenever possible. Some policy implications are drawn, in particular those relating to the merits of privatization.

show abstract

“…What is needed is: (i) That agent i's best-replies are always in the interior of S i , (ii) That strategy sets are locally convex, and (iii) That D x −i π i (s i , x −i ) exists and is strictly decreasing in s i (if D 2 x −i s i π i (s i , x −i ) 0 this will be the case). See also Edlin and Shannon (1998) who present an alternative (and weaker) set of conditions.…”

Section: Assumption 1 Each Of the Correspondencesmentioning

confidence: 99%

Aggregative games and best-reply potentials

2008

View full text Add to dashboard Cite

This paper introduces quasi-aggregative games and establishes conditions under which such games admit a best-reply potential. This implies existence of a pure strategy Nash equilibrium without any convexity or quasi-concavity assumptions. It also implies convergence of best-reply dynamics under some additional assumptions. Most of the existing literature's aggregation concepts are special cases of quasi-aggregative games, and many new situations are allowed for. An example is payoff functions that depend on own strategies as well as a linear combination of the mean and the variance of players' strategies.

show abstract

Strict Monotonicity in Comparative Statics

Cited by 216 publications

References 9 publications

On the (non-)lattice structure of the equilibrium set in games with strategic substitutes

On the (non-)lattice structure of the equilibrium set in games with strategic substitutes

Endougenous Timing in a Mixed Duopoly

Aggregative games and best-reply potentials

Contact Info

Product

Resources

About