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.     

The efficiency of competitive mechanisms under private information

We consider the efficiency properties of exchange economies where privately informed traders behave strategically. Specifically, a competitive mechanism is any mapping of traders’ reports about their types to an equilibrium price vector and allocation of the reported economy. In our model, some traders may have non-vanishing impact on prices and allocations regardless of the size of the economy. Although truthful reporting by all traders cannot be achieved, we show that, given any desired level of approximation, there is such that any Bayesian-Nash equilibrium of any competitive mechanism of any private information economy with or more traders leads, with high probability, to prices and allocations that are close to a competitive equilibrium of the true economy. In particular, allocations are approximately efficient. A key assumption is that there is small probability that traders behave non-strategically.     

Unmediated communication in games with complete and incomplete information

We study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize S^U(G), the set of outcomes of a game G, that are induced by sequential equilibria of cheap talk extensions. A cheap talk extension of G is an extensive-form game in which players communicate before playing G. A reliable mediator is not available and players exchange private or public messages that do not affect directly their payoffs. We first show that if G is a game of complete information with five or more players and rational parameters, then S^U(G) coincides with the set of correlated equilibria of G. Next, we demonstrate that if G is a game of incomplete information with at least five players, rational parameters and full support (i.e., all profiles of types have positive probability), then S^U(G) is equal to the set of communication equilibria of G.     

Communication, consensus and order. Who wants to speak first?

Parikh and Krasucki [R. Parikh, P. Krasucki, Communication, consensus and knowledge, J. Econ. Theory 52 (1990) 178-189] show that, in a group of rational agents, communication of the value of a function f leads to a consensus on the value of f, provided some conditions on the communication protocol and the function f hold. In this article, we address the issue of the influence of the protocol on the outcome of the communication process, when agents value information positively. We show that, if it is common knowledge in a group of agents that some of them disagree on two protocols, then the consensus value of f must be the same for both protocols.     

On persistent disequilibrium

Consider a standard model of a Walrasian economy where the time derivative of price change is a sign preserving function of excess demand. The only steady states of such a system are the Walrasian equilibria. For if the system is not at a Walrasian equilibrium then there must be excess demands or supplies in some market and thus those prices must be changing. Walras' law implies that all prices cannot change in the same direction, and thus relative prices must change.However, it seems that in real world economies there have been states of persistent disequilibrium. How can this be? How can there be stationary states of an economy that are not Walrasian equilibria?The answer presented in this paper goes something like this: the demands actually presented to the market, i.e., the demands that affect price movements, are not the Walrasian demands. Rather, these demands, the effective demands, are a function of both price and quantity signals. There is no reason why there cannot be equilibria of the effective demand system that are not equilibria of the Walrasian demand system.In this paper, I present a simple abstract model of effective demand systems and given a condition for this system to have non-Walrasian equilibria. I also present a simple example of this phenomena. Finally I discuss the real world implications of this model. Related concepts of effective demand are discussed in [A1H], [2], [3], [L5], and [L6].     

Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers

We consider the efficiency of Cournot and Bertrand equilibria in a duopoly with substitutable goods where firms invest in process R&D that generates input spillovers. Under Cournot competition firms always invest more in R&D than under Bertrand competition. More importantly, Cournot competition yields lower prices than Bertrand competition when the R&D production process is efficient, when spillovers are substantial, and when goods are not too differentiated. The range of cases for which total surplus under Cournot competition exceeds that under Bertrand competition is even larger as competition over quantities always yields the largest producers’ surplus.     

Endogenizing market institutions: An experimental approach

We study experimental two-sided markets in which the information structure is endogenous. When submitting an offer, a trader decides which other traders will be informed about the offer. This setup allows both a decentralized bargaining market (Chamberlin, J. Polit. Econ. 56 (1948) 95), and a double auction market (Smith J. Polit. Econ. 70 (1962) 111) as special cases. The results show that offers are typically directed to all traders of the other side of the market, but to none of the traders of the same side of the market. Even though traders receive much less information, the resulting market institution leads to the same outcomes in terms of prices and efficiency as a double auction market. In two additional treatments we examine the robustness of these results. First, it is found that the market institution adapts predictably, but not necessarily efficiently, to the imposition of transaction costs. Second, we find that the preference of sellers to conceal offers from competitors is strict. At the same time, sellers benefit collectively when they reveal offers to each other.     

Efficiency and surplus bounds in Cournot competition

We derive bounds on the ratios of deadweight loss and consumer surplus to producer surplus under Cournot competition. To do so, we introduce a parameterization of the degree of curvature of market demand using the parallel concepts of ρ-concavity and ρ-convexity. The “more concave” is demand, the larger the share of producer surplus in overall surplus, the smaller is consumer surplus relative to producer surplus, and the lower the ratio of deadweight loss to producer surplus. Deadweight loss over total potential surplus is at first increasing with demand concavity, then eventually decreasing.     

An efficiency theorem for incompletely known preferences

There are n agents who have von Neumann-Morgenstern utility functions on a finite set of alternatives A. Each agent i's utility function is known to lie in the nonempty, convex, relatively open set Ui. Suppose L is a lottery on A that is undominated, meaning that there is no other lottery that is guaranteed to Pareto dominate L no matter what the true utility functions are. Then, there exist utility functions ui∈Ui for which L is Pareto efficient. This result includes the ordinal efficiency welfare theorem as a special case.     

Buyer search and price dispersion: a laboratory study

We study markets with costly buyer search in which sellers simultaneously post prices. Buyers costlessly observe one or (with probability 1−q) two of the posted prices, and can accept one or pay to search again. The experiment varies q, the search cost, and the number of buyers. Equilibrium theory predicts a unified very low (high) price for q=0 (q=1) and predicts specific distributions of dispersed prices for q=1/3 and 2/3. Actual prices conform closely to the predictions in some treatments. Buyers’ reservation prices are biased away from the extremes, however, and sellers’ prices have positive autocorrelation and cross-sectional correlation.     

The genericity of beliefs-determine-preferences models revisited

Barelli [P. Barelli, On the genericity of full surplus extraction in mechanism design, J. Econ. Theory 144 (2009) 1320-1332] defines beliefs-determine-preferences (BDP) models and argues that BDP models are nongeneric in a topological sense. In this note, we point out some difficulties in Barelli?s approach. Furthermore, we follow the idea of Heifetz and Neeman [A. Heifetz, Z. Neeman, On the generic (im)possibility of full surplus extraction, Econometrica 74 (2006) 213-233] to propose a more relevant notion of BDP^? model. We prove that BDP^? models are generic, which is opposite to Barelli?s conclusion.     

Hiding an inconvenient truth: Lies and vagueness

When truth conflicts with efficiency, can verbal communication destroy efficiency? Or are lies or vagueness used to hide inconvenient truths? We consider a sequential 2-player public good game in which the leader has private information about the value of the public good. This value can be low, high, or intermediate, the latter case giving rise to a prisoners? dilemma. Without verbal communication, efficiency is achieved, with contributions for high or intermediate values. When verbal communication is added, the leader has an incentive to hide the precise truth when the value is intermediate. We show experimentally that, when communication must be precise, the leader frequently lies, preserving efficiency by exaggerating. When communication can be vague, the leader turns to vague messages when the value is intermediate. Thus, she implicitly reveals all values. Interestingly, efficiency is preserved, since the follower does not seem to realize that vague messages hide inconvenient truths.     

An ordinal Shapley value for economic environments

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for transferable utility (TU) games. We show a solution exists, and call it the ordinal Shapley value (OSV). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous.     

COMPETITIVE PRICING AND EFFICIENCY IN SEARCH EQUILIBRIUM*

We consolidate and generalize some results on price determination and efficiency in search equilibrium. Extending models by Rubinstein and Wolinsky and by Gale, heterogeneous buyers and sellers meet according to a general matching technology and prices are determined by a general bargaining condition. When the discount rate r and search costs converge to 0, we show that prices in all exchanges are the same and equal the competitive, market clearing, price. Given positive search costs, efficiency obtains iff bargaining satisfies Hosios' condition and r=0. When prices are set by third‐party market makers, however, we show that search equilibrium is necessarily efficient.     

A dynamic approach to PES pricing and finance for interlinked ecosystem services: Watershed conservation and groundwater management

A theory of payment for ecosystem services (PES) pricing consistent with dynamic efficiency and sustainable income requires optimized shadow prices. Since ecosystem services are generally interdependent, this requires joint optimization across multiple resource stocks. We develop such a theory in the context of watershed conservation and groundwater extraction. The optimal program can be implemented with a decentralized system of ecosystem payments to private watershed landowners, financed by efficiency prices of groundwater set by a public utility. The theory is extended to cases where land is publicly owned, conservation instruments exhibit non-convexities on private land, or the size of a conservation project is exogenous. In these cases, conservation investment can be financed from benefit taxation of groundwater consumers. While volumetric conservation surcharges induce inefficient water use, a dynamic lump-sum tax finances investment without distorting incentives. Since the optimal level of conservation is generated as long as payments are correct at the margin, any surplus can be returned to consumers through appropriate block pricing. The present value gain in consumer surplus generated by the conservation-induced reduction in groundwater scarcity serves as a lower bound to the benefits of conservation without explicit measurement of other benefits such as recreation, biodiversity, and cultural values.     

How Communication Improves Efficiency in Bargaining Games

We study a double auction with two-sided private information and preplay communication, for which Myerson and Satterthwaite (1983, J. Econ. Theory28, 265–281) showed that all equilibria are inefficient and the Chatterjee–Samuleson linear equilibrium is most efficient. Like several others, we find that players use communication to surpass equilibrium levels of efficiency, especially when the communication is face-to-face. Our main contribution is an analysis of how communication helps the parties achieve such high levels of efficiency. We find that when preplay communication is allowed, efficiency above equilibrium levels is a result of what we call “dyadic” strategies that allow the parties to coordinate on a single price that reflects both parties' valuations. Journal of Economic Literature Classification Numbers: C78, D82.     

The informational effects of competition and collusion in legislative politics

We use a mechanism design approach to study the organization of interest groups in an informational model of lobbying. Interest groups influence the legislature only by communicating private information on their preferences and not by means of monetary transfers. Interest groups have private information on their ideal points in a one-dimensional policy space and may either compete or adopt more collusive behaviors. Optimal policies result from a trade-off between imposing rules which are non-responsive to the groups' preferences and flexibility that pleases groups better. Within a strong coalition, interest groups credibly share information which facilitates communication of their joint interests, helps screening by the legislature and induces flexible policies responsive to the groups' joint interests (an informativeness effect). Competing interest groups better transmit information on their individual preferences (a screening effect). The socially and privately optimal organization of lobbying favors competition between groups only when their preferences are not too congruent with those of the legislature. With more congruence, a strong coalition is preferred. Finally, within a weak coalition, interest groups must design incentive compatible collusive mechanisms to share information. Such weak coalitions are always inefficient.     

Non-marketed options, non-existence of equilibria, and non-linear prices

This paper presents a surprising example that shows that the lattice theoretic properties in Mas-Colell's (1986) seminal work are relevant to the existence of equilibrium even when the commodity space is finite dimensional.The example is a two-period securities model with a three-dimensional portfolio space and two traders. The paper identifies a non-marketed call option that fails to have a minimum cost super-replicating portfolio. Using this option, we construct an economy that satisfies all of Mas-Colell's assumptions, except that the three-dimensional commodity space is not a vector lattice. In this economy, there is no Walrasian equilibrium and the second theorem of welfare economics fails.Our example has important finite- as well as infinite-dimensional implications. It is also an example of a “well behaved” economy in which optimal allocations that are not supported by linear Walrasian prices are decentralized by the non-linear prices studied in Aliprantis-Tourky-Yannelis (2001).     

Innovation,licensing, and price vs. quantity competition

In this paper, we develop a differentiated duopoly model with endogenous cost-reducing R&D and review the argument on welfare effect of price and quantity competition in the presence of technology licensing. We show that, with licensing, the standard conclusion on duopoly (Singh and Vives, 1984) is completely reversed. Cournot competition induces lower R&D investment than Bertrand competition does. Moreover, Cournot competition leads to lower prices, lower industry profit, higher consumer surplus and higher social welfare than Bertrand competition.     

Giving gifts to groups: How altruism depends on the number of recipients

When a single gift goes to a group of recipients, how does giving depend on the size of the group? This question is important for understanding charitable giving and fund-raising, public goods provision, family altruism, and more. If we think of the gift as giving up a dollar to create a social surplus, then we want to know how the number of recipients of that surplus affects its value to the giver. In other words, how congestible is altruism? This paper builds a theoretical framework for this question and begins to answer it with a controlled experiment. The finding is that for most subjects altruism is congestible. For the average subject, a gift that results in one person receiving x is equivalent to one in which n people receive x / n^0.68 each.