[This paper presents a Bayesian analysis of a single equation from a simultaneous equations system. The analysis is carried out under "limited information" because no prior information (other than a list of endogenous and exogenous variables) is introduced on the parameters of the remaining equations in the in the system. These parameters are integrated out analytically. The equation of interest may or may not be identified by means of exact a priori information; probabilistic prior information is equally acceptable. The prior density is either of the non-informative or the natural conjugate type. The kernel of the posterior density for the regression coefficients is a ratio of t kernels. The existence of posterior moments is ascertained. This approach is applied for illustrative purposes to Tintner's model of the meat market.]

The notion of stability in the sense of Lyapunov is applied to economic dynamic processes of the Champsaur-Dreze-Henry type. Our purpose in this note is to fill a small gap in the literature concerning dynamic processes in economic theory, of the type presented by Champsaur, Dreze, and Henry [3]. Indeed, these authors do not discuss stability in the sense of Lyapunov [7]. However, a recent result of Maschler and Peleg [9] on this kind of stability (presented in a discrete model) can easily be applied to both continuous and discrete processes used in economics. We shall present this result for a very general class of such processes and conclude with references to a few economic applications. For our purpose a (set valued) dynamic system is simply a pair 〈X,φ〉, where X is a compact subset of R and φ a correspondence from X to its nonempty subsets. Let T be a subset of [0,∞) containing 0 and x0 an element of X. Then a φ-process starting at x0 is a pair of functions: x(·) : T → X, ẋ(·) : T → R, such that: x(0) = x0 and, ∀ t ∈ T , ẋ(t) ∈ φ(x(t)). If T = {0, 1, 2, · · · , } and ẋ(t) = x(t + 1) then the process 〈x(·), ẋ)(·)〉 is called discrete. If T = [0,∞), if x(·) is absolutely continuous on any interval [0, τ ] in T , and ẋ(t) = dx(t)/dt for almost every t in T , then the process 〈x(·), ẋ(·)〉 is called continuous. In the first case the Econometrica, 47(3), 733-737, 1979. As pointed out by Negishi [10], this is the same as Samuelson’s stability of the second kind [11]. The term “stability in the sense of Lyapunov” is used by Arrow and Hahn [1]. Heal [5] and Hori [6] also use this concept of stability. See Champsaur, Dreze, and Henry [3, Section 5].

In an earlier paper on "Interdependence as a Specification Error," Strotz has considered a recursive model with endogenous variables lagged by θ; letting θ go to 0, he argued that the likelihood function of the limit form of the model differed from the limit form of the likelihood function of the model. We show here that the two limits are obtained under different underlying assumptions; these alternative assumptions are brought out explicitly; under fixed assumptions, the two methods are shown to yield identical results.

[In markets with satiation, competitive equilibria may fail to exist, because no matter what the prices are, the satiation points of some traders may be in the interiors of their budget sets. Thus some traders will be using less than the maximum budget available to them, creating a total budget excess. This suggests a revision of the equilibrium concept that allows the budget excess to be divided among all the traders, as dividends. Each trader's budget is then the sum of his dividend and the market value of his endowment. A given system of dividends and prices defines a dividend equilibrium if it generates equal supply and demand. This in itself is not satisfactory because it is too broad: Every Pareto optimal allocation is sustained by some system of dividends and prices. However, the Shapely value yields much more specific information. We prove that, when there are many individually insignificant agents, every Shapely value allocation is generated by a system of dividends and prices in which all dividends are nonnegative and depend only on the net trade sets of the agents, not on their utilities. Moreover, the dependence is monotonic; the larger the net trade set, the higher the dividend. The same result holds for markets with fixed prices, which can be analyzed formally as a special case of markets with satiation. On a more technical level, our analysis has some unusual features. We use a finite-type asymptotic model, rather than a nonatomic continuum. Surprisingly, the results are qualitatively different. (The continuum is too rough a tool for our problem, and leads to inconclusive results.) Also, small coalitions play a critical role in our analysis. (We are led to equations in which the first-order terms cancel; the second-order terms, which take events of small probability into account, become decisive.)]

A player i's actions in a game are determined by her beliefs about other players; these depend on the game's real-life context, not only its formal description. Define a game situation as a game together with such beliefs; call the beliefs—and i's resulting expectation—rational if there is common knowledge of rationality and a common prior. In two-person zero-sum games, i's only rational expectation is the game's value. In an arbitrary game G, we characterize i's rational expectations in terms of the correlated equilibria of the doubled game 2G in which each of i's strategies in G appears twice.