The author proves an equivalence between large games with effective small groups of players and games generated by markets. Small groups are effective if all or almost all gains to collective activities can be achieved by groups bounded in size of membership. A market is an exchange economy where all participants have concave, quasi-linear payoff functions. The market approximating a game is socially homogeneous--all participants have the same monotonic nondecreasing, and 1-homogeneous payoff function. The author's results imply that any market (more generally, any economy with effective small groups) can be approximated by a socially homogeneous market. Copyright 1994 by The Econometric Society.
This paper introduces and characterizes a new class of solutions to cooperative bargaining problems that can be rationalized by generalized Gini orderings defined on the agents' utility gains. Generalized Ginis are orderings that can be represented by quasi-concave, nondecreasing functions that are linear in rank-ordered subspaces of Euclidean space. In the case of three or more agents, the authors' characterization of (multivalued) generalized Gini bargaining solutions uses a linear invariance requirement in addition to some standard conditions. In the two-person case, the generalized Gini bargaining solutions can be characterized with a weakening of linear invariance. Copyright 1994 by The Econometric Society.
The distinction between nonatomicity and thick markets as the source of perfect competition is examined. The authors construct a model of an imperfectly competitive economy with a nonatomic continuum of traders and a continuum of differentiated commodities for which Walrasian equilibria exist. The failure of perfect competition is identified in two ways: individuals can affect prices and the core is strictly larger than the set of Walrasian allocations. By contrast, it is shown that, when markets are physically or economically thick (or both), then individuals cannot typically affect prices and the core always coincides with the set of Walrasian allocations. Copyright 1994 by The Econometric Society.
WE ARE CONCERNED here with perfect for infinitely repeated games with complete information. Folk theorems assert that any feasible and individually rational payoff vector of the stage game is a (subgame perfect) equilibrium payoff in the associated infinitely repeated game with little or no discounting (where payoff streams are evaluated as average discounted or average values respectively). It is obvious that feasibility and individual rationality are necessary conditions for a payoff vector to be an equilibrium payoff. The surprising content of the folk theorems is that these conditions are also (almost) sufficient. Perhaps the first folk theorem type result is due to Friedman (1971) who showed that any feasible payoff which Pareto dominates a equilibrium payoff of the stage game will be an equilibrium payoff in the associated repeated game with sufficiently patient players. This kind of result is sometimes termed a Nash threats folk theorem, a reference to its method of proof. For the more permissive kinds of folk theorems considered here, the seminal results are those of Aumann and Shapley (1976) and Rubinstein (1977, 1979). These authors assume that payoff streams are undiscounted.2 Fudenberg and Maskin (1986) establish an analogous result for discounted repeated games as the discount factor goes to 1. Their result uses techniques of proof rather different from those used by Aumann-Shapley and Rubinstein, respectively. See their paper for an insightful discussion of this point, and quite generally for more by way of background. It is a key reference for subsequent work in this area, including our own. For the two-player case, the result of Fudenberg and Maskin (1986) is a complete if and only if characterization (modulo the requirement of strict rather than weak individual rationality, which we retain in this note) and does not employ additional conditions. For three or more players Fudenberg and Maskin introduced a full dimensionality condition: The convex hull F, of the set of feasible payoff vectors of the stage game must have dimension n (where n is the number of players), or equivalently a nonempty interior. This condition has been widely adopted in proving folk theorems for related environments such as finitely repeated games (Benoit and Krishna (1985)), and overlapping generations games (Kandori (1992), Smith (1992)). Full dimensionality is a sufficient condition. Fudenberg and Maskin present an example of a three-player stage game in which the conclusion of the folk theorem is false. In this example all players receive the same payoffs in all contingencies; the (convex hull of the) set of feasible payoffs is one-dimensional. This example violates full dimensionality in a rather extreme way. Less extreme violations may also lead to
A recently developed quantile regression technique, which parsimoniously describes the entire conditional distribution, is applied to every March Current Population Survey since 1964. The study examines changes in the returns to schooling and experience at different points of the wage distribution and changes in within-group wage inequality. The results from the one-group and sixteen-group linear models show that the returns to schooling and experience differ across quantiles of the wage distribution but that their patterns of change are similar. Significant differences in wage inequality are also found across the various skill groups. Copyright 1994 by The Econometric Society.
[We analyze the Shapley value allocation of an economy with differential information. Since the intent of the Shapley value is to measure the sum of the expected marginal contributions made by an agent to any coalition to which he/she belongs, the value allocation of an economy with differential information provides an interesting way to measure the information advantage of an agent. This feature of the Shapley value allocation is not necessarily shared by the rational expectation equilibrium. Thus, we analyze the informational structure of an economy with differential information from a different and new viewpoint. In particular we address the following questions: How do coalitions of agents share their private information? How can one measure the information advantage or superiority of an agent? Is each agent's private information verifiable by other members of a coalition? Do coalitions of agents pool their private information? Do agents have an incentive to report their true private information? What is the correct concept of a value allocation in an economy with differential information? Do value allocations exist in an economy with differential information? We provide answers to each of these questions.]
We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.
Abstract This article develops a new method for inferring risk‐neutral probabilities (or state‐contingent prices) from the simultaneously observed prices of European options. These probabilities are then used to infer a unique fully specified recombining binomial tree that is consistent with these probabilities (and, hence, consistent with all the observed option prices). A simple backwards recursive procedure solves for the entire tree. From the standpoint of the standard binomial option pricing model, which implies a limiting risk‐neutral lognormal distribution for the underlying asset, the approach here provides the natural (and probably the simplest) way to generalize to arbitrary ending risk‐neutral probability distributions.