Knowledge that Transforms

THE CENTRAL PURPOSE OF THIS PAPER is to develop a model of insider trading (i.e., trading based on private information) in the context of an imperfectly competitive multi-security market with risk-neutral agents. Imperfect competition allows us to consider strategic behavior, and a multi-security market lets us study the effect of a correlated environment on equilibrium. We employ the informational assumption that market makers can observe all order flows, and so portfolio diversification arises in this model for strategic reasons. Given correlated fundamentals, market makers can potentially learn about every security from each order flow. This causes even a risk neutral trader who does not face short-selling restrictions to refrain from determining the demand for each security independently. This contrasts with traditional multi-asset models, which focus on the incentive to reduce portfolio variance, or the effect of short-selling restrictions or budget constraints. Under imperfect competition, correlation has two effects. One, ceteris paribus, it allows the uninformed to learn from additional variables since each order flow could potentially have information about all payoffs. On the other hand, it creates an incentive for informed traders to restrict what others can learn from public information. Thus, our analysis can be viewed as an application to the multi-security, heterogeneous-information model in Admati (1985) of the imperfectly competitive equilibrium concept which Kyle (1985) first applied to the single-security, homogeneous-information model of Grossman and Stiglitz (1980). Our principal results include an explicit characterization of a linear equilibrium as a function of three general covariance matrices associated with payoffs, noise trading, and errors in private signals. Under general covariance structures, we show that there always exists an equilibrium in which the relationship between the vector of prices and the vector of order flows is governed by a symmetric positive definite matrix. The plan of the paper is as follows. In Section 2, we introduce our model. We derive the equilibrium in Section 3, and Section 4 comments on the properties of the equilibrium. The proofs of the results are in the Appendix.

This paper presents conditions under which a person's beliefs about the occurrence of uncertain events are quantified by a capacity measure, i.e., a nonadditive probability. Additivity of probability is violated in a large number of applications where probabilities are vague or ambiguous due to lack of information.The key feature of the theory presented in this paper is a separation of the derivation of capacities for events from a specific choice model. This is akin to eliciting a probability distribution for a random variable without committing to a specific decision model. Conditions are given under which Choquet expected utility, the Machina-Schmeidler probabilistically sophisticated model, and subjective expected utility can be derived as special cases of our general model.

IT IS OFrEN THE CASE that an individual's decision is at least partly based on information received from another. And when the agents' payoffs depend on both the former's decision and on the latter's information, there is an incentive for the individual to attempt to bias the decision maker's decision in his or her favor by strategically manipulating the information transmitted. In a seminal paper, Crawford and Sobel (1982) (hereafter, C/S) study such strategic information transmission in the context of an abstract sender/receiver game. Variants of the Crawford and Sobel model have been applied widely, and as the application varies so often does the interpretation of type. In some cases, type refers to a preference parameter given by Nature-as, for example, in bargaining theory (e.g., Farrell and Gibbons (1989), Matthews (1989)), whereas in other settings-for instance, legislative decision making or expert testimony -type refers to more or less technical information concerning how decisions map into final consequences and, as such, is acquired information (e.g., Gilligan and Krehbiel (1987), Milgrom and Roberts (1986)). When the information has to be acquired, it is natural to suppose the acquisition is costly; for otherwise, there is no reason why such information is asymmetrically distributed. So long as the receiver can observe surely-or, at least, accurately infer-whether the sender is informed, and so long as messages are cheap-talk, there is no issue here for strategic information transmission (save whether to become at all). However, there are many circumstances when it is inappropri- ate to assume the receiver has such knowledge. One possibility is that a receiver may know that a sender has some relevant informa- tion, but be uncertain of the quality of this information. A second, perhaps more important, possibility is that a receiver is unable to tell whether a (potential) sender is uninformed. Inter alia, this problem constitutes the rationale for of the law being inadmissible as a legal defense (were it admissible, then informed miscreants would mimic uninformed transgressors); leads voters to be skeptical of politicians claiming ignorance of illegal arms deals; and makes the SEC sensitive to problems in distinguishing insider trading from legitimate good judgement. So there is an intrinsic asymmetry in that it is generally possible for, say, senders to verify possession of at least some information, but it is typically prohibitively difficult to verify any lack of knowledge

General equilibrium model, Incomplete markets, Speculative bubbles, Short-lived numeraire assets, Pseudoequilibrium, Financial markets

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.

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.

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.