Signaling via an agenda in multi-issue bargaining with incomplete information

Summary. While actual bargaining features many issues and decision making on the order in which issues are negotiated and resolved, the typical models of bargaining do not. Instead, they have either a single issue or many issues resolved in some fixed order, typically simultaneously. This paper shows that, when there is incomplete information, such an approach removes an important avenue for information transmission: the bargaining agenda itself. Compared to the standard model, pooling on offers by the informed is reduced and a signaling equilibrium arises when the agenda is determined endogenously. Signaling is carried out by use of an issue-by-issue bargaining agenda. Received: September 3, 1997; revised version: May 11, 1998     

Alternating-offer bargaining over menus under incomplete information

Summary. This paper considers bargaining with one-sided private information and alternating offers where an agreement specifies both a transfer and an additional (sorting) variable. Moreover, both sides can propose menus. We show that for a subset of parameters the alternating-offer game has a unique equilibrium where efficient contracts are implemented in the first period. This stands in sharp contrast to the benchmarks of contract theory, where typically only the uninformed side proposes, and bargaining theory, where typically the agreement only specifies a transfer. Received: September 10, 2001; revised version: March 25, 2002 RID="*" ID="*" I benefitted from discussions with Benny Moldovanu, Holger Müller, and Roland Strausz, and from comments made by an anonymous referee.     

Payoff continuity in incomplete information games: a comment

Kajii and Morris (J. Econ. Theory 82 (1998) 267) provide necessary and sufficient conditions for two priors to be strategically close. The restrictiveness of these conditions establishes that strategic behavior can be highly sensitive to the assumed prior. Their results thus recommend care in the use of priors in economic modelling. Unfortunately, their proof of a central proposition fails for zero probability types. This comment corrects their proof to account for these cases.     

Regulating a risk-averse firm under incomplete information

We examine the optimal regulatory policy for a risk-averse firm when the firm is imperfectly informed about its efficiency parameter for a project at the time of contracting. The firm’s risk aversion shifts the optimal regulatory policy from a fixed-price contract to a cost-plus contract. The optimal regulatory policy entails undereffort by an inefficient firm as in Laffont and Tirole (J Polit Econ 94(3):614–641, 1986) and the effort distortion increases as the firm becomes more risk-averse. Further, the regulator benefits from sequential contracting with the firm where the firm chooses contract terms gradually as it acquires information, albeit the benefit diminishes as the firm becomes more risk-averse.      

Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets

Summary. We prove that locally, Walras' law and homogeneity characterize the structure of market excess demand functions when financial markets are incomplete and assets' returns are nominal. The method of proof is substantially different from all existing arguments as the properties of individual demand are also different. We show that this result has important implications and is part of a more general result that excess demand is an essentially arbitrary function not just of prices, but also of the exogenous parameters of the economy as asset returns, preferences, and endowments. Thus locally the equilibrium manifold, relating equilibrium prices to these parameters has also no structure. Received: September 17, 1996; revised version: November 7, 1997     

Generic inefficiency of equilibria in the general equilibrium model with incomplete asset markets and infinite time

Summary. We consider a Lucas asset-pricing model with heterogeneous agents, exogenous labor income, and a finite number of exogenous shocks. Although agents are infinitely lived, endowments and dividends are time-invariant functions of the exogenous shock alone and are thus restricted to lie in a finite-dimensional space; genericity analysis can be conducted on sets of zero Lebesgue measure. When financial markets are incomplete, that is, there are fewer financial securities than shocks, we show that generically in individual endowments all competitive equilibria are Pareto inefficient. Received: November 22, 1999; revised version: March 4, 2002 RID="*" ID="*" We are grateful to an anonymous referee for very insightful comments on earlier drafts.     

Rationing rule, imperfect information and equilibrium

Summary. The impact of imperfect information on the price setting behaviour of firms is analysed. Specifically, consumers support an information cost to become informed about prices. Firms are endowed with U-shaped average cost curves. If a firm does not supply more than its competitive supply as determined by its marginal cost schedule, then we show that the existence of a pure strategy equilibrium is conditional on the rationing rule employed. If uninformed consumers are served first then the monopoly price is the sole equilibrium whenever consumers' information costs are high enough. Otherwise, a pure strategy equilibrium fails to exist contrary to the results of Salop and Stiglitz (1977) or Braverman (1980) who implicitly suppose that firms supply all the demand at a given price. Received: May 17, 1999; revised version: September 15, 2000     

Complete and incomplete markets with short-sale constraints

Summary. This paper argues that the introduction of a short-sale constraint in the Arrow-Radner framework invalidates standard definitions of complete and incomplete markets. Two threshold values with familiar properties arise in this constrained set-up. If short sales are not allowed on some security, then financial markets will be incomplete in the standard sense. Beyond a particular level of the short-sale bound, financial markets are “complete”, since the short-sale constraint is not effective. For intermediate bounds the distinction between complete and incomplete financial markets is blurred. Although some technical definitions hold, agents can not fully transfer wealth among states. These intermediate cases, called “technically incomplete markets”, exhibit interesting welfare properties. For instance, the resulting equilibrium allocations may not be Pareto-dominated by those of the non-restricted complete markets equilibrium. Received: November 28, 2000; / revised version: November 9, 2001     

Incentive compatible contractible information

Summary. The paper seeks to characterize what information is always available for contracting, independent of the form of the contract and the probabilities of different states of nature. The paper denotes such information as contractible. It is established that it is possible to speak uniquely of maximal contractible information. Several characterizations are exhibited. In particular, it is shown that if either (a) punishments are bounded everywhere, or (b) deviations from truth-telling are either always or never detected, then maximum contractible information coincides with where is the information partition of agent j. An argument is given for why (b) may be expected to hold. Received: August 7, 2000; revised version: December 21, 2001 RID="*" ID="*" I thank Michael Chwe, Douglas Diamond, Lars Stole, Robert Townsend, Nicholas Yannelis and an anonymous referee for helpful comments.     

Core concepts in economies where information is almost complete

Summary. The paper analyzes the properties of cores with differential information, as economies converge to complete information. Two core concepts are investigated: the private core, in which agents' net trades are measurable with respect to agents' private information, and the incentive compatible core, in which coalitions of agents are restricted to incentive compatible allocations. Received: March 15, 2000; revised version: August 24, 2000     

Non-myopic learning in differential information economies: the core

Summary. We study the process of learning in a differential information economy, with a continuum of states of nature that follow a Markov process. The economy extends over an infinite number of periods and we assume that the agents behave non-myopically, i.e., they discount the future. We adopt a new equilibrium concept, the non-myopic core. A realized agreement in each period generates information that changes the underlying structure in the economy. The results we obtain serve as an extension to the results in Koutsougeras and Yannelis (1999) in a setting where agents behave non-myopically. In particular, we examine the following two questions: 1) If we have a sequence of allocations that are in an approximate non-myopic core (we allow for bounded rationality), is it possible to find a subsequence that converges to a non-myopic core allocation in a limit full information economy? 2) Given a non-myopic core allocation in a limit full information economy can we find a sequence of approximate non-myopic core allocations that converges to that allocation? Received: May 25, 1999; revised version: August 9, 1999     

The set of sunspot equilibria in economies with incomplete financial markets: variable asset prices

Summary. I consider the set of equilibria of two-period economies with S extrinsic states of nature in the second period and I assets with linearly independent nominal payoffs. Asset prices are variable. If the number of agents is greater than (S-I), the payoff matrix is in general position and S 2I, the set of equilibrium allocations generically (in utility function space) contains a smooth manifold of dimension (S-1). Moreover, the map from states o f nature to equilibrium allocations (restricted to this manifold) is one-to-one at each equilibrium. Received: February 23, 1998; revised version: June 1, 2000     

Recursive structure and equilibria in games with private monitoring

Summary. In each stage of a repeated game with private monitoring, the players receive payoffs and privately observe signals which depend on the players' actions and the state of world. I show that, contrary to a widely held belief, such games admit a recursive structure. More precisely, I construct a representation of the original sequential problem as a sequence of static games with incomplete information. This establishes the ground for a characterization of strategies and, hence, of behavior in interactive-decision settings where private information is present. Finally, the representation is used to give a recursive characterization of the equilibrium payoff set, by means of a multi-player generalization of dynamic programming. Received: February 11, 2002; revised version: July 22, 2002 RID="*" ID="*" I am very grateful to In-Koo Cho, Larry Epstein, Denis Gromb, Stephen Morris, Paolo Siconolfi, Lones Smith and Max Stinchcombe for several insights and suggestions. A referee's comments helped improving the exposition. Finally, I wish to thank the participants to the seminars at MEDS, NYU, Columbia University, Caltech, UCLA, University of Rochester, University of Texas-Austin, Northwestern Summer Microeconomics Conference 98, Summer in Tel Aviv 98, and NASM98.     

Incomplete markets: transverse financial structures

Summary. In a multiperiod economy with incomplete markets and assets with payoff depending on the price history (e.g., asset and derivatives), we show that in order to get endowment generic existence of an equilibrium it is not needed to alter settlement features such as when payments are made and when the asset is traded. This is non-trivial as each such characteristic introduces a non-generic subclass of financial instruments. We show essentially that expiry date payments are the only payments that one needs perturbing (if at all). For previous periods - the P&L discovery map - is the one relevant for wealth transfers. This map transfers wealth between one period and the next by associating to each portfolio next period potential profit and losses as a function of the revealed information at the node. All present values involved can in general - because of backward induction pricing structure - be appropriately controlled via expiry payoffs only. This enables us to extend two-period work and introduce Transverse Financial Structures for multiperiod economies, where one cannot identify the payoffs of financial instruments to the P&L discovery map (in other words we introduce some financial ingeneering for Transverse Financial Structures). We capitalize on that difference using unexploited “maturity payout degrees of freedom” and rolling back the uncertainty tree. As an application of this approach we prove a conjecture by Magill and Quinzii that commodity forward contracts lead to endowment generic existence of an equilibrium in a multiperiod set-up. Received: June 25, 1999; revised version: April 4, 2001     

Common knowledge and quantification

Summary. The paper consists of two parts. The first one is a concise introduction to epistemic (both propositional and predicate) logic with common knowledge operator. As the full predicate logics of common knowledge are not even recursively enumerable, in the second part we introduce and investigate the monodic fragment of these logics which allows applications of the epistemic operators to formulas with at most one free variable. We provide the monodic fragments of the most important common knowledge predicate logics with finite Hilbert-style axiomatizations, prove their completeness, and single out a number of decidable subfragments. On the other hand, we show that the addition of equality to the monodic fragment makes it not recursively enumerable. Received: March 7, 2001; revised version: April 4, 2001     

Bancruptcy in a model of unsecured claims

Summary. We study a two periods model of incomplete markets with nominal assets unsecured by collateral, where agents can go bankrupt but there are no bankruptcy penalties entering directly in the utility function. We address two cases: first, a proportional reimbursement rule under bounded short sales and limited liability and, secondly, a nonproportional reimbursement rule, favoring smaller claims, without bounds on short-sales, but assuming that liability approaches total garnishment as debt goes to infinity. Received: September 10, 1998; revised version: August 6, 2001     

Ranking of information systems in agency models: an integral condition

Summary. We provide a condition for ranking of information systems in agency problems. The condition has a straightforward economic interpretation in terms of the sensitivity of a cumulative distribution with respect to the agent's effort. The criterion is shown to be equivalent to the mean preserving spread condition on the likelihood ratio distributions. Received: November 10, 1999; revised version: February 17, 2000     

Risk aversion and incentive compatibility with ex post information asymmetry

Summary. The paper extends Diamond's (1984) analysis of financial contracting with information asymmetry ex post and endogenous “bankruptcy penalties” to allow for risk aversion of the borrower. The optimality of debt contracts, which Diamond obtained for the case of risk neutrality, is shown to be nonrobust to the introduction of risk aversion. This contrasts with the costly state verification literature, in which debt contracts are optimal for risk averse as well as risk neutral borrowers. Received: December 7, 1998; revised version: June 9, 1999     

Bank's capital structure under non-diversifiable risk

Summary. The aim of this paper is to study the design of optimal capital structure of a “large” intermediary when the intermediary faces a non-diversifiable risk, within the standard costly-state-verification (CSV) model. I demonstrate that, under weaker conditions, a “large” intermediary realizes more efficient allocation by issuing both debt and equity than by issuing only debt. Unlike Diamond (1984) and Williamson (1986), the set of optimal contracts involves ex ante monitoring made by shareholders of the intermediary. Changes in parameters, such as the variance of the aggregate risk or the cost of monitoring, affect bankruptcy costs and the capital structure. Received: October 12, 1998; revised version: March 20, 2001