Imperfect competition and capital accumulation: the role of price normalization

We consider a capital-accumulation model with infinitely lived households and two production sectors. The intermediate-good sector is characterized by perfect competition, a constant-returns-to-scale technology, and production externalities. The final-good sector is a monopoly operating under constant returns to scale. We analyze the general equilibrium in the sense of Gabszewicz and Vial [Journal of Economic Theory (1972) 4: 381–400] for this economy and different price-normalization rules. It is shown that the qualitative behavior of the equilibrium paths depends crucially on the chosen normalization rule. In particular, whether equilibria are monotonic or oscillating and whether indeterminacy occurs or not may depend on the choice of the numeraire.     

The (sub-)optimality of the majority rule

We consider collective choice from two alternatives. Ex-ante, each agent is uncertain about which alternative she prefers, and may be uncertain about the intensity of her preferences. An environment is given by a probability distribution over utility vectors that is symmetric across agents and neutral across alternatives. In many environments, the majority voting rule maximizes agents? ex-ante expected utilities among all anonymous and dominant-strategy implementable choice rules. But in some environments where the agents? utilities are stochastically correlated, other dominant-strategy choice rules are better for all agents. If utilities are stochastically independent across agents, majority voting is ex-ante optimal among all anonymous and incentive-compatible rules. We also compare rules from an interim-viewpoint.     

Pigouvian pricing and stochastic evolutionary implementation

We study the implementation of efficient behavior in settings with externalities. A planner would like to ensure that a group of agents make socially optimal choices, but he only has limited information about the agents’ preferences, and can only distinguish individual agents through the actions they choose. We describe the agents’ behavior using a stochastic evolutionary model, assuming that their choice probabilities are given by the logit choice rule. We prove that there is a simple price scheme with the following property: regardless of the realization of preferences, a group of agents subjected to the price scheme will spend the vast majority of time in the long run behaving efficiently. The price scheme defines a game that may possess multiple equilibria, but we are able to obtain a unique and efficient selection from this set because of the stochastic nature of the agents’ choice rule. We conclude by comparing the performance of our price scheme with that of VCG mechanisms.     

Expectations and the Stability Problem for Optimal Monetary Policies

A fundamentals based monetary policy rule, which would be the optimal monetary policy without commitment when private agents have perfectly rational expectations, is unstable if in fact these agents follow standard adaptive learning rules. This problem can be overcome if private expectations are observed and suitably incorporated into the policy maker's optimal rule. These strong results extend to the case in which there is simultaneous learning by the policy maker and the private agents. Our findings show the importance of conditioning policy appropriately, not just on fundamentals, but also directly on observed household and firm expectations.     

The communication requirements of social choice rules and supporting budget sets

The paper examines the communication requirements of social choice rules when the (sincere) agents privately know their preferences. It shows that for a large class of choice rules, any minimally informative way to verify that a given alternative is in the choice rule is by verifying a “budget equilibrium”, i.e., that the alternative is optimal to each agent within a “budget set” given to him. Therefore, any communication mechanism realizing the choice rule must find a supporting budget equilibrium. We characterize the class of choice rules that have this property. Furthermore, for any rule from the class, we characterize the minimally informative messages (budget equilibria) verifying it. This characterization is used to identify the amount of communication needed to realize a choice rule, measured with the number of transmitted bits or real variables. Applications include efficiency in convex economies, exact or approximate surplus maximization in combinatorial auctions, the core in indivisible-good economies, and stable many-to-one matchings.     

Mechanism Design under Alternative Information Structures and Constrained Capacity

In applied models, the choice of a particular incomplete information structure appears to have been motivated primarily by technical convenience. The information structures used can be classified as either probabilistic or partitional. Information is probabilistic if no agent can rule out any type profile of the remaining agents and, for at least one type of one agent, the conditional and marginal probability distributions over the remaining agents' types are not equal. Information is partitional if the only information the agents have is that one or more agents (individually) can rule out type profiles of the remaining agents and, for at least one type of one agent, that agent has information about the remaining agents. Partitional information includes complete information as a special case. Existing results on complete information environments suggest that partitional information might simplify implementation problems. Within the context of an applied agency model in which capacity is constrained, we provide results that seem to challenge this intuition.Journal of Economic LiteratureClassification Numbers: C72, D82.     

Exchange Rules and the Incentive Compatibility of Choice Experiments

The incentive properties of stated-preference surveys continue to be a central debate in the valuation of public goods. The majority of empirical studies have focused on incentive properties of contingent valuation questions in relation to situations where answers have monetary consequences. This research explores the incentive properties of repeated, attribute-based choice questions when subjects are provided with an explicit connection between choices and outcomes. Two market/provision-rules are investigated: a posted-price market and a plurality-rule vote. These two provision rules are contrasted to treatments in which no provision rule is discussed—subjects are simply asked to choose their preferred alternative. These three hypothetical choice treatments are compared with a binding choice treatment. While none of the public good treatments are theoretically incentive compatible, we include a comparison of hypothetical and binding choices for a private-good that is incentive compatible. The private good experiments indicate that marginal willingness to pay (WTP) estimates from the hypothetical treatment are larger, but not statistically different than corresponding estimates in the binding choice treatment. Results for the public good experiments indicate that marginal WTP estimates from the hypothetical treatments are much larger, and statistically different than corresponding estimates in the binding choice treatment. The bias is largest when no provision rule is discussed. The bias is reduced with the inclusion of a provision rule, but surprisingly, there was no difference across provision rule treatments. Overall, our results indicate that choice experiments involving a public good should include a provision rule to reduce bias, but the resulting marginal WTP estimates may still be more biased, on average, than those arising from contingent valuation survey formats.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

On fixed point theorems and social choice paradoxes

This note explores the relationship of social choice paradoxes to fixed point theorems. A special case of the paradox proven in Chichilnsky (forthcoming), the non-existence of a continuous anonymous rule that respects anonymity with two voters and two dimensional choice spaces, is proven here to be equivalent to a fixed point problem. We indicate also how the results can be extended to higher dimensional choice spaces and any finite number of agents.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

Making Good Decisions with Minimal Information: Simultaneous and Sequential Choice

The adaptive pressures facing humans and other animals to make decisions quickly can be met both by increasing internal information-processing speed and by minimizing the amount of information to be used. Here we focus on the latter effect and ask how, and how well, agents can make good decisions with a minimal amount of information, using two specific tasks as examples. When a choice must be made between simultaneously-available options, minimal information in the form of binary recognition (whether or not each item is recognized) can be used in the recognition heuristic to choose effectively. When options are encountered sequentially one at a time, minimal information as to whether or not each option is the best encountered so far is sufficient to guide agents using a simple search-cutoff rule to high performance along several choice criteria. Both of these examples have important economic as well as biological applications, and show the power of simple fast and frugal heuristics to produce good decisions with little information. This revised version was published online in August 2006 with corrections to the Cover Date.     

Solidarity and Probabilistic Target Rules

We consider a probabilistic approach to collective choice problems where a group of agents with single-peaked preferences have to decide on the level or location of a public good. We show that every probabilistic rule that satisfies Pareto efficiency and "solidarity" (population-monotonicity or replacement-domination) must equal a so-called target rule.     

The strategy-proof provision of public goods under congestion and crowding preferences

We examine the strategy-proof provision of excludable public goods when agents care about the number of other consumers. We show that strategy-proof and efficient social choice functions satisfying an outsider independence condition must always assign a fixed number of consumers, regardless of individual desires to participate. A hierarchical rule selects participants and a generalized median rule selects the level of the public good. Under heterogeneity in agents’ views on the optimal number of consumers, strategy-proof, efficient, and outsider independent social choice functions are much more limited and in an important case must be dictatorial.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

Coalition Stability in Public Goods Provision: Testing an Optimal Allocation Rule

We test the canonical model of international environmental agreements (IEAs) in a laboratory setting with asymmetric agents. IEA participation represents coalition formation and public good provision where there are gains to cooperation, but an incentive to free-ride. We test four competing methods of dividing the coalition’s worth: a recently proposed optimal rule which accounts for subjects’ payoffs as a single free-rider, the Shapley value, the Nash bargaining solution, and an equal split. Each treatment generates the theoretically predicted coalition size more often than not. The shares of the potential gains to cooperation achieved by each rule are: 51, 36, 40 and 13%, respectively. These results highlight the importance of using an optimal rule to improve IEAs, and more broadly for voluntary public good provision.     

Proposal power and majority rule in multilateral bargaining with costly recognition

This paper studies a sequential bargaining model in which agents expend efforts to be the proposer. In equilibrium, agents’ effort choices are influenced by the prize and cost effects. The (endogenous) prize is the difference between the residual surplus an agent obtains when he is the proposer and the payment he expects to receive when he is not. Main results include: (1) under the unanimity voting rule, two agents with equal marginal costs propose with equal probabilities, regardless of their time preferences; (2) under a nonunanimity rule, however, the more patient agent proposes with a greater probability; (3) while, under the unanimity rule, the social cost decreases in group heterogeneity, it can increase under a nonunanimity rule; and (4) when agents are identical, the unanimity rule is socially optimal.     

Credibility costs in the monetary integration game*

Euro candidates are expected to maintain the value of their currency within the fluctuation band of the new exchange rate mechanism for at least two years. This paper highlights some unpleasant macroeconomic effects that could occur during this interval. The problem is cast as a two‐stage sequential game between private agents and the government of the applicant country. The policy‐maker decides whether to devaluate the domestic currency or not at two distinct dates; it makes a last choice just before accession to the monetary union. Under an assumption of incomplete information of private agents about the government's priorities on inflation and economic activity, the game presents a hybrid perfect Bayesian equilibrium. In the pooling configuration, an initial policy of zero devaluation does not signal the final devaluation decision. As private agents cannot completely rule out the risk of a ‘last devaluation’, a premium adds to interest rates and entails a systematic output loss.     

Public decisions: Solidarity and the status quo

A public decision model specifies a set of alternatives, a variable population, and a common set of admissible preferences. We study the implications of the principle of solidarity, for social choice functions in all such models. The principle says that when the environment changes, all agents not responsible for the change should either all weakly win, or all weakly lose. Under weak additional requirements, but regardless the domain of preferences, each of two formulations of this principle, population-monotonicity and replacement-domination, imply coalition-strategy-proofness; that the choice only depends on the set of preferences that are present in the society, but not on the number, nor on the labels of agents having particular preferences; and that there exists an alternative always weakly Pareto-dominated by the alternative selected by the rule. Replacement-domination is generally at least as strong as population-monotonicity.     

Portfolio choice and pricing in illiquid markets

This paper studies portfolio choice and pricing in markets in which immediate trading may be impossible. It departs from the literature by removing restrictions on asset holdings, and finds that optimal positions depend significantly and naturally on liquidity: When expected future liquidity is high, agents take more extreme positions, given that they do not have to hold those positions for long when they become undesirable. Consequently, larger trades should be observed in markets with more frequent trading. Liquidity need not affect the price significantly, however, because liquidity has offsetting impacts on different agents' demands. This result highlights the importance of unrestricted portfolio choice. The paper draws parallels with the transaction-cost literature and clarifies the relationship between the price level and the realized trading frequency in this literature.