In recent decades, the concept of subjective probability has been increasingly applied to an adversary s choices in strategic games. A careful examination reveals that the standard construction of subjective probabilities does not apply in this context. We show how the difficulty may be overcome by means of a different construction.

Let A be a finite set of m ¥ 3 alternatives, let N be a finite set of n ¥ 3 players and let Rn be a profile of linear preference orderings on A of the players. Throughout most of the paper the considered voting system is the majority rule. Let uN be a profile of utility functions for RN. Using $\pm$-effectiveness we define the NTU game VuN and investigate its Aumann-Davis-Maschler and Mas-Colell bargaining sets. The first bargaining set is nonempty for m = 3 and it may be empty for m¥ 4. Moreover, in a simple probabilistic model, for fixed m, the probability that the Aumann-Davis-Maschler bargaining set is nonempty tends to one if n tends to infinity. The Mas-Colell bargaining set is nonempty for m 5 and it may be empty for m ¥ 6. Moreover, we prove the following startling result: The Mas-Colell bargaining set of anysimple majority voting game derived from the k-th replication of RN is nonempty, provided that k ¥ n + 2.We also compute the NTU games which are derived from choice by plurality voting and approval voting, and we analyze some interesting examples.

A social choice rule is a collection of social choice correspondences, one for each agenda. An effectivity rule is a collection of effectivity functions, one for each agenda. We prove that every monotonic and superadditive effectivity rule is the effectivity rule of some social choice rule. A social choice rule is binary if it is rationalized by an acyclic binary relation. The foregoing result motivates our definition of a binary effectivity rule as the effectivity rule of some binary social choice rule. A binary social choice rule is regular if it satisfies unanimity, monotonicity, and independence of infeasible alternatives. A binary effectivity rule is regular if it is the effectivity rule of some regular binary social choice rule. We characterize completely the family of regular binary effectivity rules. Quite surprisingly, intrinsically defined von Neumann-Morgenstern solutions play an important role in this characterization.

Why do brokers charge per-share commissions to institutional traders? What determines the commission charge? We examine commissions and order flow for a sample of institutional orders and find that most per-share commissions are concentrated at only a few price points, primarily 5 and 6 cents per share. Further, we find that the prior-period commission, rather than execution costs, is the strongest determinant of next period's commission. These results are inconsistent with negotiation of commissions on an order-by-order basis or with the impression of a continuous transaction cost that is deduced from the distribution of percentage commissions, suggesting that commissions are not a marginal cost of execution. We also find that institutional clients concentrate their order flow with a small set of brokers, and that small institutions concentrate more than large institutions. Collectively, our results suggest that brokers and their institutional clients enter into long-term agreements where the per-share commission is constant, and the order flow routed to a particular broker is used to maintain the required payment for an institution's desired level of service. Commissions, therefore, constitute a convenient way of charging a predetermined fixed fee for broker services.

The extended Chinese postman (CP) enterprize is induced by a connected and undirected graph G. A server is located at some fixed vertex of G, to be referred to as the post office. Each player resides in a single edge, and each edge contains at most one player. Thus, some of the edges can be public . Each edge has a cost and a prize attached to it. The players need some service, e.g., mail delivery, which requires the server to travel from the post office and visit all edges wherein players reside, before returning to the post office. The server collects the prize attached to an edge upon the first traversal of this edge, but the cost of an edge is incurred every time it is traversed. The cost of a cheapest tour for each coalition defines a CP cost game. The issue is how to allocate, among the players, the cost that the server incurs. We study the class of extended CP enterprizes which are induced by Eulerian graphs satisfying two properties: The 4-cut property (Definition 4.4) and completeness (Definition 4.8). For this class we prove that the core, resp., the nucleolus when the core is not empty, are Cartesian products of the cores, resp., nucleoli of CP enterprizes whose graphs are simple cycles generated from G by identifying therein the end points of each elementary path (Definition 4.3). Finally, for the class of extended complete Eulerian graphs having the 4-cut property, we are able to test core membership in O(n) time, and when the core is not empty, we show how to calculate the nucleolus in O(n^2) time, n being the number of players.

We report an intriguing empirical observation. The relationship between corruption and output depends on the economy's degree of openness: in open economies, corruption and GNP per capita are strongly negatively correlated; but in closed economies, there is no relationship at all. This stylized fact is robust to a variety of different empirical specifications. In particular, the same basic pattern persists if we use alternative measures of openness, if we focus on different time periods, if we restrict the sample to include only highly corrupt countries, if we restrict attention to specific geographic areas or to poor countries, and if we allow for the possible endogeneity of both the corruption and openness measures. We find that the extent to which corruption affects output is determined primarily by the degree of financial openness. The difference between closed and open economies is mainly due to the different effect of corruption on capital accumulation. We present a model, consistent with these findings, in which the main channel through which corruption affects output is capital drain.

Adaptive decision-making requires that environmental contingencies between decision options and their relative advantages and disadvantages be assessed accurately and quickly. The research presented in this article addresses the challenging notion that contingencies may be more visible from small than large samples of observations. An algorithmic account for such a ""less-is-more"" effect is offered within a threshold-based decision framework. Accordingly, a choice between a pair of options is only made when the contingency in the sample that describes the relative utility of the two options exceeds a critical threshold. Small samples - due to their instability and the high dispersion of their sampling distribution - facilitate the generation of above-threshold contingencies. Across a broad range of parameter values, the resulting small-sample advantage in terms of hits is stronger than their disadvantage in terms of false alarms. Computer simulations and experimental findings support the predictions derived from the threshold model. In general, the relative advantage of small samples is most apparent when information loss is low, when decision thresholds are high, and when ecological contingencies are weak to moderate.

In 1996, a committee was formed to examine the results that had been reported by H.J. Gans regarding the existence of "encoded" text in the bible foretelling events that took place many years after the Bible was written. The committee performed two additional tests in the spirit of the Gans experiments. Both tests failed to confirmed the existence of the putative code.

The inequality conjectured by van den Berg and Kesten in [9], and proved by Reimerin [6], states that for A and B events on S, a product of finitely many finite sets, and P any product measure on S, P(A¿B) P(A)P(B), where A¿B are the elementary events which lie in both A and B for `disjoint reasons.' This inequality on events is the special case, for indicator functions, of the inequalityhaving the following formulation. Let X be a random vector with n independent components, each in some space Si (such as„d), and set S = ˆni=1Si. Say that the function f : S †’„depends on K Š‚ 1,...,n if f(x) = f(y) whenever xi = yi for all i ˆˆ K. Then for any given finite or countable collections of non-negative real valued functions f$\pm$$\pm$ˆˆA, g²²ˆˆB on S which depend on K$\pm$ and L² respectively,EsupK$\pm$ˆ\copyrightL²=ˆłdots} f$\pm$(X) g²(X) Esup f$\pm$(X) Esup g²(X). Related formulations, and functional versions of the dual inequality on events by Kahn,Saks, and Smyth [4], are also considered. Applications include order statistics, assignment problems, and paths in random graphs.

We consider a simple dynamic "collective reputation" model of a market for an experience good into''  which we introduce imperfect quality inspections. In each period two markets operate: a prime market''  for sellers with a good reputation, and a regular market for all other sellers. In every period, the quality of produced goods is inspected, and producers who have been found to produce low quality goods are barred from selling in the prime market in the next period. We demonstrate that the average quality of the good in both markets may decrease as inspection technology improves. A few applications of the model are discussed.

It has been noted and demonstrated that people are reluctant to make changes in their current state (called the status quo bias, Samuelson & Zeckhauser, 1988), and to trade objects they own (called the endowment effect, Thaler, 1980). This reluctance has been explained by a combination of loss aversion and reference dependence which causes the status quo to appear better than its alternative, ceteris paribus. In the present study, respondents were asked to rate the attractiveness of various policies, and to list their pros and cons. We find that just labeling some state of affairs status quo enhances its rating (which we call the status quo label bias); namely, a policy seemed more attractive to respondents who thought it is the status quo than to those who did not. An analysis of the listed pros and cons provides evidence that a model of the balance of a policy's pros and cons is a good predictor of that policy's attractiveness. Rendering the pros and cons in terms of losses and gains provides evidence that losses do, indeed, loom larger than gains. When put together, our results provide an empirical grounding for the loss aversion explanation of the status quo bias.

Let Xn, ¦,X1 be i.i.d. random variables with distribution function F and finite expectation. A statistician, knowing F, observes the X values sequentially and is given two chances to choose X's using stopping rules. The statistician's goal is to select a value of X as large as possible. Let Vn2 equal the expectation of the larger of the two values chosen by the statistician when proceeding optimally. We obtain the asymptotic behavior of the sequence Vn2 for a large class of F's belonging to the domain of attraction (for the maximum) D(GII''$\pm$), where GII''$\pm$ (x) = exp(-x-''$\pm$)''(x > 0) with$\pm$ > 1. The results are compared with those for the asymptotic behavior of the classical one choice value sequence Vn1, as well as with the ""prophet value"" sequence E(maxXn, ¦,X1), and indicate that substantial improvement is obtained when given two chances to stop, rather than one.

The paper reports a perceptual asymmetry for the two diagonals that is related to gender such that females prefer the diagonal spanning from top-right to bottom left (/) while males the opposite one (''). This relationship is observed in a variety of tasks: Aesthetic judgment of paintings, spotting differences between two paintings, and visual search for a tilted line among similarly tilted distractors. The paper does not provide an explanation of the relationship between this asymmetry and gender but rules out several potential mediating factors, such as eye dominance, head tilt, handedness, and hemispheric differences. At the same time, the paper does outline the scope of the phenomenon: The asymmetry is found both for meaningful and for meaningless stimuli and both at brief and at extended presentation. Moreover, the asymmetry is found related to the tilt of the visual elements that require processing not to their location in the visual field.

A number of studies, most notably Cr×mer and McLean (1985, 1988), have shown that in Harsanyi type spaces of a fixed finite size, it is generically possible to design mechanisms that extract all the surplus  from players, and as a consequence, implement any outcome as if the players' private information  were commonly known. In contrast, we show that within the set of common priors on the universal type  space, the subset of priors that permit the extraction of the players' full surplus is shy. Shyness is a  notion of smallness for convex subsets of infinite-dimensional topological vector spaces (in our case,  the set of common priors), which generalizes the usual notion of zero Lebesgue measure in  finite-dimensional spaces.

We introduce an extension of the Mas-Colell bargaining set and construct, by an elabo- ration on a voting paradox, a superadditive four-person nontransferable utility game whose extended bargaining set is empty. It is shown that this extension constitutes an upper hemi- continuous correspondence. We conclude that the Mas-Colell bargaining set of a non-levelled superadditive NTU game may be empty.

Asymptotic results for the problem of optimal two choice stopping on an n elementlong i.i.d. sequence Xn, . . . ,X1 have previously been obtained for two of the threedomains of attraction. An asymptotic result is proved for the exponential distribution,a representative from the remaining, Type I domain, and it is conjectured that thesame behavior obtains for all Type I distributions.

We study a repeated game with asymmetric information about a dynamic state of nature. In the course of the game, the better informed player can communicate some or all of his information with the other. Our model covers costly and/or bounded communication. We characterize the set of equilibrium payoffs, and contrast these with the communication equilibrium payoffs, which by definition entail no communication costs.