Rational expectations equilibria and the ex-post core of an economy with asymmetric information

We study the relationship between the set of rational expectations equilibrium allocations and the ex-post core of exchange economies with asymmetric information.     

Weighted majoritarian rules for the location of multiple public facilities

We consider collective decision problems given by a profile of single-peaked preferences defined over the real line and a set of pure public facilities to be located on the line. In this context, Bochet and Gordon (2012) provide a large class of priority rules based on efficiency, object-population monotonicity and sovereignty. Each such rule is described by a fixed priority ordering among interest groups. We show that any priority rule which treats agents symmetrically — anonymity — respects some form of coherence across collective decision problems — reinforcement — and only depends on peak information — peak-only — is a weighted majoritarian rule. Each such rule defines priorities based on the relative size of the interest groups and specific weights attached to locations. We give an explicit account of the richness of this class of rules.     

Ex-post favoring ranks: a fairness notion for the random assignment problem

We introduce two notions of ex-post fairness, namely ex-post favoring ranks (EFR) and robust ex-post favoring ranks, which consider whether objects are received by those agents who have the highest rank for them. We examine their compatibility with standard properties of random assignments and state some impossibility theorems. We also propose and formalize a revised version of the Boston mechanism and prove that it provides an EFR random assignment.

     

A mechanism design approach to allocating central government funds among regional development agencies

To allocate central government funds among regional development agencies, we look for mechanisms that satisfy three important criteria: efficiency, (individual and coalitional) strategy proofness (a.k.a. dominant strategy incentive compatibility), and fairness. We show that only a uniform mechanism satisfies all three. We also show that all efficient and strategy proof mechanisms must function by assigning budget sets to the agencies and letting them freely choose their optimal bundle. In choosing these budget sets, the agencies’ private information has to be taken into account in a particular way. The only way to additionally satisfy a weak fairness requirement (regions with identical preferences should be treated equally) is to assign all agencies the same budget set, as does the uniform mechanism. Finally and maybe more importantly, we show that the central government should not impose constraints on how much to fund an activity (e.g. by reserving some funds only for a particular activity): otherwise, there are no efficient, strategy proof and fair mechanisms, no matter how small these constraints are.     

Multibidding game under uncertainty

This paper considers situations in which a group of agents has to decide whether to carry out a given public project or its alternative when agents hold private information. I use the budget-balanced multibidding mechanism (Pérez-Castrillo and Wettstein in Am Econ Rev 5:1577–1587, 2002) according to which the game to be played by participants has only one stage and simple rules that can be applied in a wide range of situations. It is shown that the symmetric equilibria of the multibidding game deliver ex-post efficient outcomes if the number of agents is two, for any underlying symmetric distribution characterizing uncertainty, or is very large.     

Pareto-undominated and socially-maximal equilibria in non-atomic games

This paper makes the observation that a finite Bayesian game with diffused and disparate private information can be conceived of as a large game with a non-atomic continuum of players. By using this observation as its methodological point of departure, it shows that (i) a Bayes–Nash equilibrium (BNE) exists in a finite Bayesian game with private information if and only if a Nash equilibrium exists in the induced large game, and (ii) both Pareto-undominated and socially-maximal BNE exist in finite Bayesian games with private information. In particular, it shows these results to be a direct consequence of results for a version of a large game re-modeled for situations where different players may have different action sets.     

Optimal information exchange in contests

We study optimal exchange of private information in a two-player all-pay auction contest with independent private binary values. A benevolent information center who is informed about the players’ values facilitates the exchange of information by disclosing a signal publicly. The informativeness of the signal determines the monotonicity of the unique symmetric equilibrium and the players’ expected payoff. We characterize the upper bound of players’ expected payoff and the corresponding optimal signals utilizing such a relation between the informativeness and the payoff. When the players are ex ante sufficiently heterogeneous, the optimal signals work through an information-rent channel by inducing allocative efficient contests. When the players are ex ante sufficiently homogeneous, the optimal signals work through an unlevel-playing-field channel by inducing asymmetric contests. In order to guarantee efficient allocation, a regulator can punish any exchange of information when the players are sufficiently homogeneous and impose no restrictions when they are sufficiently heterogeneous.     

A theoretical relationship between the rank-size rule and Clark's law of urban population distribution: Duality in the rank-size rule

This paper theoretically shows the necessary and sufficient conditions for the robust rank-size rule: the rank-size rule that robustly holds for any choice of threshold urban population density by which populations of cities are determined. First, it is shown that when urban population distribution follows Clark's law, the robust rank-size rule holds if and only if the gradient parameter of the negative exponential distribution of the ith ranked city as √i times as large as that of the first ranked city and the population density at the center is the same for all cities. Second, when urban population distribution follows a certain general class of urban population distribution functions, the robust rank-size rule (of population) holds if and only if the boundary condition is satisfied and the rank-size rule holds with respect to urban areas. These two rank-size rules, the rank-size rule of population and the rank-size rule of urban areas, form the primal-dual relation. Third, if the robust rank-size rule holds, then the constant density rule holds, that is, the average population density of a city over its urban area is the same for all cities.     

Optimal speculative trade among large traders

A collection of large traders holds heterogeneous prior beliefs regarding market fundamentals. This gives them a motive to engage in speculative trade with respect to market prices. Rather than assuming a particular institution or market for speculative trade, we take a mechanism-design approach by attempting to characterize the mechanism that maximizes the traders’ gains from speculative trade, subject to the incentive constraints that result from the traders’ ability to manipulate market prices. Within a stylized market model, we show that this mechanism affects price volatility without destroying ex-post efficient allocations. We also characterize the implementability of optimal speculative trade when the traders’ prior beliefs are private information. Financial support from the US-Israel Binational Science Foundation, Grant No. 2002298 is gratefully acknowledged.     

Some new characterization of rational expectation equilibria in economies with asymmetric information

We compare the family of rational expectation equilibria with the ex-post Aubin core allocations in the framework of an economy with uncertainty and asymmetric information. We do it in a very general setting: an arbitrary space of agents and an infinite dimensional commodity space. We also present a characterization of the ex–post Aubin core by allocations belonging to the core of the associated complete information economies, and we use a suitable definition of Edgeworth equilibria to characterize the family of rational expectation equilibria. Moreover, we study some generalizations of the ex-post Aubin core obtained by making some restriction on the families of blocking coalitions.     

Quasi ex-ante inflation forecast uncertainty

We propose a measure of the effects of monetary policy based on an analysis of the distribution of the ex-post inflation forecast uncertainty. We argue that the difference between the distributions of the ex-ante and ex-post uncertainties reflects the impact of monetary policy decisions. Using the theoretical background of the New Keynesian model with imperfect information and a monetary policy rule, we derive a proxy for ex-ante inflation uncertainty called quasi ex-ante forecast uncertainty, which is free to a certain extent of the effects of monetary policy decisions. Furthermore, we introduce the compound strength measure of monetary policy, as well as the uncertainty ratio, which approximates the impact of monetary policy on the reduction of the inflation forecast uncertainty. Our empirical results show that the greatest policy effect in reducing the inflation forecast uncertainty occurs for countries which conduct either a well-established or a relatively pure inflation targeting policy.     

An optimistic search equilibrium

We study a market search equilibrium with aggregate uncertainty, private information and heterogeneous beliefs that are initially optimistic. Despite these biased beliefs, it is shown that all optimistic equilibria converge to perfect competition in the limit as the time between matches tends to 0.     

Swap-flexibility in the assignment of houses

A house allocation rule should be flexible in its response to changes in agents’ preferences. We propose a specific notion of this flexibility. An agent is said to be swap-sovereign over a pair of houses at a profile of preferences if the rule assigns her one of the houses at that profile and assigns her the other house when she instead reports preferences that simply swap the positions of the two houses. A pair of agents is said to be mutually swap-sovereign over their assignments at a profile if the rule exchanges their assignments when they together report such ‘swap preferences’. An allocation rule is individually swap-flexible if any pair of houses has a swap-sovereign agent, and is mutually swap-flexible if any pair of houses has either a swap-sovereign agent or mutually swap-sovereign agents. We show for housing markets that the top-trading-cycles rule is the unique strategy-proof, individually rational and mutually swap-flexible rule. In house allocation problems, we show that queue-based priority rules are uniquely strategy-proof, individually swap-flexible and envy non-bossy. Varying the strength of non-bossiness, we characterise the important subclasses of sequential priority rules (additionally non-bossy) and serial priority rules (additionally pair-non-bossy and pair-sovereign).     

Inter-temporal preference for flexibility and risky choice

We derive an inter-temporal theory of choice, in the spirit of Kreps and Porteus [Kreps, D.M., Porteus, E.L., 1978. Temporal resolution of uncertainty and dynamic choice theory. Econometrica 46, 185–200], where decision makers have incomplete preferences. This can be used to model indecisiveness as well as unforeseen contingencies. The key to our approach is a time consistency condition and therefore the normative connection between ex-ante and ex-post choice. The time consistency condition enables a representation that is a straight forward extension of recursive utility with the exception that it features an inter-temporal ‘utility for flexibility’.     

Population monotonic and strategy-proof mechanisms respecting welfare lower bounds

The significance of population monotonicity and welfare bounds is well-recognized in the fair division literature. We consider the welfare bounds that are central to the fair allocation literature, namely, the identical-preferences lower-bound, individual rationality, the stand-alone lower-bound,   and k$k$-fairness. We characterize population monotonic and incentive compatible mechanisms which allocate an object efficiently and respect a welfare lower bound chosen in the fair allocation problem of allocating a collectively owned indivisible good or bad when monetary transfers are possible and preferences are private information.     

Multiperiod security markets with differential information: Martingales and resolution times

We model multiperiod securities markets with differential information. A price system that admits no free lunches is related to martingales when agents have rational expectations. We introduce the concept of resolution time, and show that a better informed agent and a less informed agent must agree on the resolution times of commonly marketed events if they have rational expectations and if there are no free lunches. It then follows that if all elementary events are marketed for a less informed agent then any price system that admits no free lunches to a better informed agent must eliminate any private information asymmetry between the two. We provide an example of a dynamically fully revealing price system that is arbitrage free and yields elementarily complete markets.     

A policy-based rationalization of collective rules: Dimensionality,specialized houses,and decentralized authority

We offer a policy-basis for interpreting, justifying, and designing (3, 3)-political rules, a large class of collective rules analogous to those governing the selection of papers in peer-reviewed journals, where each referee chooses to accept, reject, or invite a resubmission of a paper, and an editor aggregates his own and referees’ opinions into one of these three recommendations. We prove that any such rule is a weighted multicameral rule: a policy is collectively approved at a given level if and only if it is approved by a minimal number of chambers — the dimension of the rule — where each chamber evaluates a different aspect of the policy using a weighted rule, with each evaluator’s weight or authority possibly varying across chambers depending on his area(s) of expertise. These results imply that a given rule is only suitable for evaluating finite-dimensional policies whose dimension corresponds to that of the rule, and they provide a rationale for using different rules to pass different policies even within the same organization. We further introduce the concept of compatibility with a rule and exploit its topological properties to propose a method to construct integer weights corresponding to evaluators’ possible judgments under a given rule, which are more intuitive and easier to interpret for policymakers. Our findings shed light on multicameralism in political institutions and multi-criteria group decision-making in the firm. We provide applications to peer review politics, rating systems, and real-world organizations.     

Welfare Effects of Endogenous Information Acquisition and Disclosure in Duopoly Markets

Abstract

This paper investigates the interaction between firms' information acquisition decisions and disclosure of internally acquired information in a Cournot duopoly market under demand uncertainty. The main results are as follows. When the correlation between firms' demands is positive and sufficiently high, disclosure of information on demand uncertainty can enhance social welfare, given that the quality of firms' private information is constant. However, in the setting where firms' private information is endogenously determined, mandatory disclosure is not always desirable. This is because, when disclosure is mandated, firms acquire less precise information compared with the case where the acquired information is not disclosed; hence, their internal information environments are deteriorated. This can lead to unintended consequences such that disclosure regulation decreases social welfare.