There are several solutions to the Nash bargaining problem in the literature. Since various authors have expressed preferences for one solution over another, we find it useful to study preferences over solutions in their own right. We identify a set of appealing axioms on such preferences that lead to unanimity in the choice of solution, which turns out to be the solution of Nash.
We analyze two-candidate elections in which voters are uncertain about the realization of a state variable that affects the utility of all voters. Each voter has noisy private information about the state variable. We show that the fraction of voters whose vote depends on their private information goes to zero as the size of the electorate goes to infinity. Nevertheless, elections fully aggregate information in the sense that the chosen candidate would not change if all private information were common knowledge. Equilibrium voting behavior is to a large extent determined by the electoral rule, i.e., if a candidate is required to get at least x percent of the vote in order to win the election, then in equilibrium this candidate gets very close to x percent of the vote with probability close to one. Finally, if the distribution from which preferences are drawn is uncertain, then elections will generally not satisfy full information equivalence and the fraction of voters who take informative action does not converge to zero.
A number of papers have shown that a strict Nash equilibrium action profile of a game may never be played if there is a small amount of incomplete information. The authors present a general approach to analyzing the robustness of equilibria to a small amount of incomplete information. A Nash equilibrium of a complete information game is said to be robust to incomplete information if every incomplete information game with payoffs almost always given by the complete information game has an equilibrium which generates behavior close to the Nash equilibrium. The authors show that many games with strict equilibria have no robust equilibrium and examine why they get such different results from existing refinements. If a game has a unique correlated equilibrium, it is robust. A natural many-player many-action generalization of risk dominance is a sufficient condition for robustness.
To obtain consistency and asymptotic normality, a generalized method of moments (GMM) estimator typically is defined to be an approximate global minimizer of a GMM criterion function. To compute such an estimator, however, can be problematic because of the difficulty of global optimization. In consequence, practitioners usually ignore the problem and take the GMM estimator to be the result of a local optimization algorithm. This yields an estimator that is not necessarily consistent and asymptotically normal. The use of a local optimization algorithm also can run into the problem of instability due to flats or ridges in the criterion function, which makes it difficult to know when to stop the algorithm. To alleviate these problems of global and local optimization, we propose a stopping-rule (SR) procedure for computing GMM estimators. The SR procedure eliminates the need for global search with high probability. And, it provides an explicit SR for problems of stability that may arise with local optimization problems.
This paper provides an empirical analysis of how the U.S. Social Security and Medicare insurance system affect the labor supply of older males in the presence of incomplete markets for loans, annuities, and insurance. We estimate a detailed dynamic programming (DP) model of the joint labor supply and Social Security acceptance decision, focusing on a sample of males in the low to middle income brackets whose only pension is Social Security. The DP model delivers a rich set of predictions about the dynamics of retirement behavior, and comparisons of actual vs. predicted behavior show that the DP model is able to account for wide variety of phenomena observed in the data, including the pronounced peaks in the distribution of retirement ages at 62 and 65 (the ages of early and normal eligibility for Social Security benefits, respectively). We identify a significant fraction of health insurance constrained individuals who have no form of retiree insurance other than Medicare, and who can only obtain fairly priced private insurance via their employer's group plan. The combination of significant individual risk aversion and a long tailed (Pareto) distribution of care expenditures implies that there is a significant security value for these individuals to remain employed until they are eligible for Medicare coverage at age 65. Overall, our model suggests that a number of heretofore puzzling aspects of retirement behavior can be viewed as artifacts of particular details of the Social Security rules, whose incentive effects are especially strong for lower income individuals and those who do not have access to fairly priced loans, annuities, and insurance.
While optimally weighted generalized method of moments (GAM) estimation has desirable large sample properties, its small sample performance is poor in some applications. The authors propose a computationally simple alternative, for weakly dependent data generating mechanisms, based on minimization of the Kullback-Leibler information criterion. Conditions are derived under which the large sample properties of this estimator are similar to GAM, i.e., the estimator will be consistent and asymptotically normal, with the same asymptotic covariance matrix as GAM. In addition, the authors propose overidentifying and parametric restrictions tests as alternatives to analogous GAM procedures.
The concept of adaptively rational equilibrium (A.R.E.) is introduced. Agents adapt their beliefs over time by choosing from a finite set of different predictor or expectations functions. Each predictor is a function of past observations and has a performance or fitness measure which is publicly available. Agents make a rational choice concerning the predictors based upon their past performance. This results in a dynamics across predictor choice which is coupled to the equilibrium dynamics of the endogenous variables. As a simple, but typical, example we consider a cobweb type demand-supply model where agents can choose between rational and naive expectations. In an unstable market with (small) positive information costs for rational expectations, a high intensity of choice to switch predictors leads to highly irregular equilibrium prices converging to a strange attractor. The irregularity of the equilibrium time paths is explained by the existence of a so-called homoclinic orbit and its associated complicated dynamical phenomena. Thus local instability and global complicated dynamics may be a feature of a fully rational notion of equilibrium.
The standard model of repeated games assumes perfect synchronization in the timing of decisions between the players. In many natural settings, however, choices are made synchronously so that only one player can move at a given time. This paper studies a family of repeated settings in which choices are asynchronous. Initially, we examine, as a canonical model, a simple two person alternating move game of pure coordination. There, it is shown that for sufficient patient players, there is a unique perfect equilibrium payoff which Pareto dominates all other payoffs. The result generalizes to any finite number of players and any game in a class of asynchronously repeated games which includes both stochastic and deterministic repetition. The result complement a recent Folk Theorem by Dutta (1995) for stochastic games which can be applied to asynchronously repeated games if a full dimensionality condition holds. A critical feature of the model is the inertia in decisions. We show how the inertia in asynchronous decisions determines the set of equilibrium payoffs.
ABSTRACT Firm sizes and book‐to‐market ratios are both highly correlated with the average returns of common stocks. Fama and French (1993) argue that the association between these characteristics and returns arise because the characteristics are proxies for nondiversifiable factor risk. In contrast, the evidence in this article indicates that the return premia on small capitalization and high book‐to‐market stocks does not arise because of the comovements of these stocks with pervasive factors. It is the characteristics rather than the covariance structure of returns that appear to explain the cross‐sectional variation in stock returns.
ABSTRACT This article examines the role of corporate headquarters in allocating scarce resources to competing projects in an internal capital market. Unlike a bank, headquarters has control rights that enable it to engage in “winner‐picking”—the practice of actively shifting funds from one project to another. By doing a good job in the winner‐picking dimension, headquarters can create value even when it cannot help at all to relax overall firm‐wide credit constraints. The model implies that internal capital markets may sometimes function more efficiently when headquarters oversees a small and focused set of projects.