Universality of Nash components

We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game—a game where all players have two pure strategies and a common utility function with values either zero or one—whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi-algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets.We discuss implications of our results for the strategic stability of success sets, and use the results to construct a Nash component with index k for any fixed integer k.     

The local best response criterion: An epistemic approach to equilibrium refinement

The standard refinement criteria for extensive form games, including subgame perfect, perfect, perfect Bayesian, sequential, and proper, reject important classes of reasonable Nash equilibria and accept many unreasonable Nash equilibria. This paper develops a new refinement criterion, based on epistemic game theory, that captures the concept of a Nash equilibrium that is plausible when players are rational. I call this the local best response (LBR) criterion. This criterion is conceptually simpler than the standard refinement criteria because it does not depend on out-of-equilibrium, counterfactual, or passage to the limit arguments. The LBR is also informationally richer because it clarifies the epistemic conditions that render a Nash equilibrium reasonable. The LBR criterion appears to render the traditional refinement criteria superfluous.     

Political motivations and electoral competition: Equilibrium analysis and experimental evidence

We study both theoretically and experimentally the set of Nash equilibria of a classical one-dimensional election game with two candidates. These candidates are interested in power and ideology, but their weights on these two motives are not necessarily identical. Apart from obtaining the well known median voter result and the two-sided policy differentiation outcome, the paper uncovers the existence of two new equilibrium configurations, called ‘one-sided’ and ‘probabilistic’ policy differentiation, respectively. Our analysis shows how these equilibrium configurations depend on the relative interests in power (resp., ideology) and the uncertainty about votersʼ preferences. The theoretical predictions are supported by the data collected from a laboratory experiment, as we observe convergence to the Nash equilibrium values at the aggregate as well as at the individual levels in all treatments, and the comparative statics effects across treatments are as predicted by the theory.     

On the convergence to the Nash bargaining solution for action-dependent bargaining protocols

We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player. We consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized. Otherwise, equilibrium proposals of all players converge to a weighted Nash bargaining solution, where the weights are determined by the probability to propose conditional on one's own rejection.     

Price and quantity competition under free entry

This paper complements that of Cellini et al. (Cellini, R., Lambertini, L., Ottaviano, G. I. P., 2004. Welfare in a differentiated oligopoly with free entry: A cautionary note. Research in Economics, 58:125–33.), which shows that Cournot competition may generate higher welfare compared to Bertrand competition in an economy with free entry. Unlike them, we provide a more general proof for this result and show that Cournot competition generates higher welfare compared to Bertrand competition when the products are sufficiently differentiated. If the products are close substitutes, welfare is higher under Bertrand competition. We show that these qualitative results hold whether or not number of varieties increases market size. We also show when the active firms earn higher profits under Bertrand competition compared to Cournot competition.     

Self-Fulfilling Mechanisms in Bayesian Games

Amechanismfor a Bayesian gameGis a mapping μ from the set of states of nature to the set of players' actions. μ isself-fulfillingif players are truthful at the communication stage and, given the information revealed by μ, no player can gain in unilaterally deviating from the action prescribed by the mechanism. We investigate the properties of self-fulfilling mechanisms and we show in particular that they correspond to inert solutions of the infinitely repeated game generated byG. We also discuss applications to market games, regulation, and R&D games.Journal of Economic LiteratureClassification Numbers: D82, C72.     

Competition with Congestible Networks

We analyse competition between two network providers when the quality of each network depends negatively on the number of customers connected to that network. With respect to price competition we provide a sufficient condition for the existence of a unique pure strategy Nash equilibrium. Comparative statics show that as the congestion effect gets stronger quantities will decrease and prices increase, under both Bertrand and Cournot competition. In an example with endogenous capacities it turns out that equilibrium capacities are at first increasing and then decreasing in the strength of congestion. Furthermore, capacities are higher under Cournot competition. Welfare comparisons between Bertrand and Cournot competition are unambiguous for fixed capacities, but may turn around for endogenous capacities.     

On the efficiency of indirect taxes in differentiated oligopolies with asymmetric costs

This paper shows that unit taxation can be welfare superior to ad valorem taxation in asymmetric and differentiated oligopolies if the goods are sufficiently differentiated, the cost variance is sufficiently large and the ad valorem tax rate is sufficiently high. Moreover, this result holds under either Cournot competition or Bertrand competition.      

The strategic Marshallian cross

We prove existence and uniqueness of non-autarkic equilibria in bilateral oligopoly assuming only that preferences are binormal and satisfy a weakened version of gross substitutes. We permit complete heterogeneity of preferences and our analysis exploits the fact that payoffs depend only on own strategy and two universal aggregates. This allows us to define strategic versions of supply and demand curves such that non-autarkic Nash equilibria are in 1–1 correspondence with intersections of these curves. The same approach can be used to establish comparative statics under the assumptions above. As examples, we focus on adding players and changing endowments. This competitive approach also allows us to conclude that much of conventional Marshallian analysis is robust to strategic manipulation.     

Consumer myopia, standardization and aftermarket monopolization

In this paper, I show that the standard Bertrand competition argument does not apply when firms compete for myopic consumers who optimize period-by-period. I develop the model in the context of aftermarket. With overlapping-generations of consumers, simultaneous product offerings in the primary market and aftermarket establishes a price floor for the primary good. This constraint prevents aftermarket rents from being dissipated by the primary market competition. Duopoly firms earn positive profits despite price competition with undifferentiated products. Nonetheless, government interventions to reinforce aftermarket competition such as a standardization requirement may lead to the partial collapse of the primary market.     

Market power of firms and exchange-rate fluctuations

This paper explores the potential of firms to restrict industry outputs (market power) in oligopolistically organized markets where domestic firms compete with foreign ones. Within a stochastic price-setting supergame framework, market power is shown to be lower in general with flexible exchange rates for the following reasons. (i) The conditions that the fully collusive outcome—oligopolists maximizing joint profits — is sustainable in equilibrium become stronger if the exchange rate fluctuates, provided that fluctuations are sufficiently small. (ii) Even if full collusion can be sustained, industry outputs will be higher on the average with flexible than with fixed exchange rates.     

企业最优定价策略与汇率传递效应研究

文章在李嘉图理论模型的框架下讨论了两国企业的最优定价策略,在此基础上分析了汇率传递效应。研究表明,汇率传递效应具有某种突变性,其突变的边界条件依赖于两国市场需求特征、贸易摩擦与两国企业的边际成本。