Knowledge that Transforms

Egalement paru dans : Document de travail ; 91-09 WP, INRA-ESR Toulouse

This paper elucidates the logic behind recent papers which show that a unique equilibrium is selected in the presence of higher order uncertainty, i.e., when players lack common knowledge.We introduce two new concepts: belief potential of the information system and p-dominance of Nash-equilibria of the game, and show that a Nash-equilibrium is uniquely selected whenever its p-dominance is below the belief potential.This criterion applies to many-action games, not merely 2 x 2 games.It also applies to games without dominant strategies, where the set of equilibria is shown to be smaller and simpler than might be initially conjectured.Finally, the new concepts help understand the circumstances under which the set of equilibria varies with the amount of common knowledge among players.

In a recent paper Rubinstein, Safra, and Thomson (RST) have provided an interesting re-examination of the widely applied Nash solution for a two-person bargaining problem. They recast the usual Nash bargaining problem into a more natural setting of feasible alternatives with a disagreement outcome. The two players are then described by their risk preferences defined on the set of lotteries over the alternatives and the disagreement outcome. This enables them to define an ordinal Nash solution in terms of the agents' risk preferences. Essentially, their ordinal solution is an outcome that is immune against possible objections. Freeing the definition of the Nash solution from utility naturally led RST to extending its scope to Non-Expected Utility (NEU) preferences. We contend, however, that the family of NEU preferences considered by RST is unduly restrictive. The assumptions imposed on the risk preferences by RST essentially exclude any members of the Rank Dependent Expected Utility (RDEU) and betweenness families that can accommodate the very choice paradoxes that stimulated the development of NEU theory. As these are two of the most extensively analyzed and widely applied NEU models in the literature, this seems to cast doubt on how broad an extension to NEU preferences the RST approach affords. We demonstrate, however, that RST's analysis can be modified so that their conclusion is valid in a wider class of preferences that can include examples of RDEU preferences. This class consists of preferences that admit what we term a disagreement linear representation.

MUCH RESEARCH INTO THE PERFORMANCE of econometric estimators utilizes Monte Carlo experiments, either as a primary tool or as a check on the accuracy of first or higher order asymptotic approximations. It is important to design efficient experiments and to extract all the information they provide. But it is also important to avoid constructing experiments which give an overly optimistic view of the performance of an estimator or test. This note gives a theorem concerning choice of covariate distribution which is relevant to both these considerations. It is shown that, when a subset of covariates, X, has a symmetric conditional distribution given the remaining covariates, Z, a mirror image invariance applies to M-estimators (Huber (1977)) of the coefficients that measure the impact of X on the conditional distribution of the response variates, namely that reversal of the signs of the coefficients causes the marginal2 sampling distributions of their M-estimators to be reflected around the origin while the marginal sampling distributions of estimators of other parameters are unaffected. It follows that, when covariate distributions are symmetric, results for one half of the parameter space can be deduced from results for the other half. For example, if bias(b)( 3) and MSE b)(P) are respectively the bias and mean squared error (assumed for the moment to exist) of an estimator ,3 when the true value of ,3 is b, then bias(b)(13)= -bias(b)(!3) and MSE(b(3) =MSE( b(P). It follows that bias(O)(13)=0 and, more generally, the result implies that sampling distributions are symmetric when coefficients associated with symmetrically distributed covariates are zero. This typically removes the (n- 1/2) term from the Edgeworth expansion of the estimator and associated t statistics. Therefore choosing a symmetric covariate distribution in a Monte Carlo experiment may lead to a false view of the accuracy of first order approximations to distributions of certain estimators and test statistics. The theorem highlights the potential sensitivity of the results of Monte Carlo experiments to the choice of covariate distribution. The mirror image result and the associated symmetry result are unusual because they do not require strong assumptions about the distribution of the response variate, in contrast to the symmetry results described by Andrews (1986) and the mirror image invariance given by Cryer, Nankervis, and Savin (1989). Apart from the symmetry of the conditional distribution of a subset of covariates, the main requirements are that the coefficients of interest, /3, satisfy two related single index restrictions, namely that they

This paper examines the effect on health outcomes of moving from cost-based to prospective reimbursement of hospitals. The paper reaches two conclusions. First, hospitals that experienced average price declines had a greater share of deaths occur in the hospital or shortly after discharge. By one year postdischarge, however, this increased mortality was eliminated. Second, there was an increase in readmission rates as hospitals were no longer reimbursed for marginal units of care they provided. This increased readmission appears to be due to accounting changes on the part of hospitals rather than changes in patient morbidity. Copyright 1995 by The Econometric Society.

This paper proposes two consistent one-sided specification tests for parametric regression models, one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values; the other based on the difference in sums of squared residuals between the parametric and nonparametric models. We estimate the nonparametric model by series regression

A common interest game is a game in which there exists a unique pair of payoffs which strictly Pareto-dominates all other payoffs. We consider the undiscounted repeated game obtained by the infinite repetition of such a two-player stage game. We show that if supergame strategies are restricted to be computable within Church's thesis, the only pair of payoffs which survives any computable tremble with sufficiently large support is the Pareto-efficient pair. The result is driven by the ability of the players to use the early stages of the game to communicate their intention to play cooperatively in the future.

We study the strategic equilibria of a negotiation game where potential buyers are affected by identity-dependent, negative externalities. The unique equilibrium of long, finitely repeated generic games can either display delay--where a transaction can take place only in several stages before the deadline--or, in spite of the random element in the game, a well-defined buyer exists that obtains the object with probability close to one.

Core allocations may be defined for infinite horizon capital accumulation models. If agents cannot trust each other in the sense of Gale, then agents may renege on their commitments; their decisions appear time inconsistent. A core allocation is a recursive core allocation provided no coalition can improve upon its consumption stream at any time given its accumulation of assets up to that period. We show for every allocation of consumption in the initial core, one can find a distribution of capital stocks among the agents where no coalition of agents will break the initial core contract at any date. It follows that if the proper distribution of the streams of capital is achieved, then the allocation in the core is also in the recursive core. The latter therefore forges a link between the distribution of wealth (capital), the problem of trust, and time consistent intertemporal contracts