12,976 research outputs found
Comparative Statics with Never Increasing Correspondences
This paper studies models where the correspondences (or functions) under consideration are never increasing (or weakly decreasing) in endogenous variables, and weakly increasing in exogenous parameters. Such models include games of strategic substitutes, and include cases where additionally, some variables may be strategic complements. It is shown that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. For a given parameter value, a pair of distinct equilibria are never comparable. Moreover, generalizing an existing result, it is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. (In particular, in n-player games with real-valued action spaces, symmetric equilibria increase with the parameter.) Furthermore, when functions under consideration are weakly decreasing in endogenous variables, a sufficient condition is presented that guarantees existence of increasing equilibria (symmetric or asymmetric) at a new parameter value. This condition is applied to two classes of examples.Monotone comparative statics, Non-increasing functions, Never increasing correspondences, strategic substitutes
Endogenous Heterogeneity in Strategic Models: Symmetry-breaking via Strategic Substitutes and Nonconcavities
This paper is an attempt to develop a unified approach to endogenous heterogeneity by constructing general class of two-player symmetric games that always possess only asymmetric pure-strategy Nash equilibria. These classes of games are characterized in some abstract sense by two general properties: payo? non-concavities and some form of strategic substitutability. We provide a detailed discussion of the relationship of this work with Matsuyama’s symmetry breaking framework and with business strategy literature. Our framework generalizes a number of models dealing with two-stage games, with long term investment decisions in the first stage and product market competition in the second stage. We present the main examples that motivate this study to illustrate the generality of our approach.firm heterogeneity; submodular games; business strategy; innovation strategies.
Endogenous heterogeneity in strategic models: symmetry-breaking via strategic substitutes and nonconcavities
This paper is an attempt to develop a unified approach to endogenous heterogeneity by constructing general class of two-player symmetric games that always possess only asymmetric pure-strategy Nash equilibria. These classes of games are characterized in some abstract sense by two general properties: payoff non-concavities and some form of strategic substitutability. We provide a detailed discussion of the relationship of this work with Matsuyama’s symmetry breaking framework and with business strategy literature. Our framework generalizes a number of models dealing with two-stage games, with long term investment decisions in the first stage and product market competition in the second stage. We present the main examples that motivate this study to illustrate the generality of our approachinfo:eu-repo/semantics/publishedVersio
Multiple equilibria in Tullock contests
We find the sufficient conditions for the existence of multiple equilibria in Tullock-type contests, and show that asymmetric equilibria arise even under symmetric prize and cost structures. We then present existing contests where multiple equilibria exist under reasonably weak conditions
The Shared Reward Dilemma
One of the most direct human mechanisms of promoting cooperation is rewarding
it. We study the effect of sharing a reward among cooperators in the most
stringent form of social dilemma, namely the Prisoner's Dilemma. Specifically,
for a group of players that collect payoffs by playing a pairwise Prisoner's
Dilemma game with their partners, we consider an external entity that
distributes a fixed reward equally among all cooperators. Thus, individuals
confront a new dilemma: on the one hand, they may be inclined to choose the
shared reward despite the possibility of being exploited by defectors; on the
other hand, if too many players do that, cooperators will obtain a poor reward
and defectors will outperform them. By appropriately tuning the amount to be
shared a vast variety of scenarios arises, including traditional ones in the
study of cooperation as well as more complex situations where unexpected
behavior can occur. We provide a complete classification of the equilibria of
the -player game as well as of its evolutionary dynamics.Comment: Major rewriting, new appendix, new figure
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