Barton L. Lipman

Representing Preferences with a Unique Subjective State Space

Ž. We extend Kreps’ 1979 analysis of preference for flexibility, reinterpreted by Kreps Ž. 1992 as a model of unforeseen contingencies. We enrich the choice set, consequently obtaining uniqueness results that were not possible in Kreps’ model. We consider several representations and allow the agent to prefer commitment in some contingencies. In the representations, the agent acts as if she had coherent beliefs about a set of possible future Ž. ex post preferences, each of which is an expected-utility preference. We show that this set of ex post preferences, called the subjectie state space, is essentially unique given the restriction that all ex post preferences are expected-utility preferences and is minimal even without this restriction. Because the subjective state space is identified, the way ex post utilities are aggregated into an ex ante ranking is also essentially unique. Hence when a representation that is additive across states exists, the additivity is meaningful in the sense that all representations are intrinsically additive. Uniqueness enables us to show that the size of the subjective state space provides a measure of the agent’s uncertainty about future contingencies and that the way the states are aggregated indicates whether these contingencies lead to a desire for flexibility or commitment.

Standard State-Space Models Preclude Unawareness

We show that a very broad class of models, including possibility correspondences, necessarily fail to capture very simple and intuitive implications of unawareness. We explain why standard state–space formulations suffer from this problem, illustrating the point with an example of a nonstandard state–space model which avoids the difficulty.

Information Processing and Bounded Rationality: A Survey

This paper surveys some recent attempts to formulate a plausible and tractable model of bounded rationality. I focus in particular on models which view bounded rationality as stemming from limited information processing. I discuss computability, partitional models (such as automata, perceptrons, and optimal networks), nonpartitional models, and axiomatic approaches

Stock Price Manipulation Through Takeover Bids

The announcement of a takeover bid causes significant increases in the targets stock price, but the possibility that a bid is motivated to cause this increase so that the bidder can sell his holdings has not been studied. We show that stock price manipulation lowers the prebid stock price. Furthermore, if there is little takeover activity, manipulation increases takeover bids and prevents some efficient takeovers. In this case, stockholders prefer to ban it. However, if there is a high level of takeover activity, serious bidders are better off and social surplus is increased by the possibility of manipulation. In this case, stockholders may oppose a ban.

Recent developments in modeling unforeseen contingencies

We survey recent models of unforeseen contingencies, discussing both epistemic and decision-theoretic approaches. We also briefly comment on the hurdles which remain for applying these models to contract theory

Decision Theory without Logical Omniscience: Toward an Axiomatic Framework for Bounded Rationality

I propose modelling boundedly rational agents as agents who are not logically omniscient—that is, who do not know all logical or mathematical implications of what they know. I show how a subjective state space can be derived as part of a subjective expected utility representation of the agents preferences. The representation exists under very weak conditions. The representation uses the familiar language of probability, utility, and states of the world in the hope that this makes this model of bounded rationality easier to use in applications.

Private Provision of Public Goods Can Be Efficient

Economists have long believed that private provision of public goods will be inefficient, though recently some have argued that altruism may mitigate the inefficiencies. Without altruism, agents contribute to the point where marginal cost equals their private marginal benefits. With altruism, they contribute more and hence are closer to the point where marginal cost and total marginal benefits are equated. In an earlier paper (Bagnoli and Lipman, 1989), we showed that private provision need not be inefficient. In a very natural model of private provision without altruism, we showed that the set of (undominated perfect) equilibrium outcomes is identical to the core. Here we consider the effect of altruism on private provision. Altruism essentially creates more public goods because the well-being of others becomes a public good. We show that our model of private provision still has efficient equilibria under a wide variety of circumstances. Interestingly, the equilibria may be inefficient when agents are concerned about the effect of private provision on the distribution of wealth. Intuitively, the game we consider is a very powerful instrument for efficient private provision, but must be supported by other instruments if the set of public goods is expanded too far.

Finite Order Implications of Common Priors

I characterize the implications of the common prior assumption for finite orders of beliefs about beliefs at a state and show that the only such implications are those stemming from the weaker assumption of a common support. More precisely, given any model where priors have the same support and any finite

Implementation with Partial Provability

N

Ex ante versus interim rationality and the existence of bubbles

, there is another model with common priors which has the same