Showing papers in "Economic Theory in 2001"

Strategyproof sharing of submodular costs:budget balance versus efficiency

Abstract: A service is produced for a set of agents. The service is binary, each agent either receives service or not, and the total cost of service is a submodular function of the set receiving service. We investigate strategyproof mechanisms that elicit individual willingness to pay, decide who is served, and then share the cost among them. If such a mechanism is budget balanced (covers cost exactly), it cannot be efficient (serve the surplus maximizing set of users) and vice-versa. We characterize the rich family of budget balanced and group strategyproof mechanisms and find that the mechanism associated with the Shapley value cost sharing formula is characterized by the property that its worst welfare loss is minimal. When we require efficiency rather than budget balance – the more common route in the literature – we find that there is a single Clarke-Groves mechanism that satisfies certain reasonable conditions: we call this the marginal cost pricing mechanism. We compare the size of the marginal cost pricing mechanism's worst budget surplus with the worst welfare loss of the Shapley value mechanism.

Evolutionary dynamics on infinite strategy spaces

Abstract: Summary. The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this unsatisfying restriction is unnecessary. We specify a simple condition under which the continuous time replicator dynamics are well defined for the case of infinite strategy spaces. Furthermore, we provide new conditions for the stability of rest points and show that even strict equilibria may be unstable. Finally, we apply this general theory to a number of applications like the Nash demand game, the War of Attrition, linear-quadratic games, the harvest preemption game, and games with mixed strategies.

Coping With Ignorance: Unforeseen Contingencies and Non-Additive Uncertainty

Abstract: In real-life decision problems, decision makers are never provided with the necessary background structure: the set of states of the world, the outcome space, the set of actions. They have to devise all these by themselves. I model the (static) choice problem of a decision maker (DM) who is aware that her perception of the decision problem is too coarse, as for instance when there might be unforeseen contingencies. I make a “bounded rationality'' assumption on the way the DM deals with this difficulty, and then I show that imposing standard subjective expected utility axioms on her preferences only implies that they can be represented by a (generalized) expectation with respect to a non-additive measure, called a belief function. However, the axioms do have strong implications for how the DM copes with the type of ignorance described above. Finally, I show that some decision rules that have been studied in the literature can be obtained as a special case of the model presented here (though they have to be interpreted differently).

Conformism and diversity under social learning

Abstract: Summary When there are competing technologies or products with unknown payoffs an important question is which technology will prevail and whether technologies with different payoffs can coexist in the long run In this paper, we use a social learning model with local interactions to study this question We show that the adoption of technologies as well as the prospects of conformism/diversity depend crucially on the nature of interaction between individuals and the heterogeneity of preferences in a society

Comparing competition and collusion: a numerical approach

Abstract: Collusion is a serious problem in many procurement auctions. In this research, I study a model of first price sealed bid procurement auctions with asymmetric bidders. I demonstrate that the equilibrium to the model is unique and describe three algorithms that can be used to compute the inverse equilibrium bid functions. I then use the computational algorithms to compare competitive and collusive bidding. The algorithms are useful for structural estimation of auction models and for assessing the damages from bid-rigging.

Dividend timing and behavior in laboratory asset markets

Abstract: This paper investigates the effect of dividend timing on price bubbles and endogenous expectations in twenty-six laboratory asset markets. In ten “Al” markets, a single dividend is paid at the end of the trading horizon. In nine “A2” markets, dividends are paid at the end of each trading period. In seven “A3” markets, some of the dividends are paid at the end of the trading horizon, and the rest are paid on a per-period basis. The results indicate that price bubbles are most likely in A2 markets, less likely in A3 markets, and least likely in Al markets. Six distinct hypotheses are considered. The data suggest that the concentration of dividend value at a single point in time helps to create common expectations, and thus significantly reduce the incidence of bubbles. Also, the results underscore the difficulty facing econometric tests on field data where fundamental value has to be approximated.

Asymptotic methods for asset market equilibrium analysis

Abstract: General equilibrium analysis is difficult when asset markets are incomplete. We make the simplifying assumption that uncertainty is small and use bifurcation methods to compute Taylor series approximations for asset demand and asset market equilibrium. A computer must be used to derive these approximations since they involve large amounts of algebraic manipulation. We use this method to analyze the allocative and welfare effects of introducing a new security. We find that adding any nontrivial derivative security will raise the price of the risky security relative to the bond when risks are small.

Neoclassical life-cycle consumption: a textbook example*

Abstract: We present a simple neoclassical life-cycle model in continuous time, in which the effects of endogenous labor supply, uncertain lifetime, and family composition on consumption and income profiles are jointly analyzed. Due to a parsimonious specification, analytical solutions for consumption growth are available for constant intertemporal elasticity of substitution preferences. Without relying on borrowing constraints, the model can generate a hump in the consumption profile, and a comovement of consumption and income during working life.

Mechanism design in queueing problems

Abstract: A well-known result in incentive theory is that for a very broad class of decision problems, there is no mechanism which achieves truth-telling in dominant strategies, efficiency and budget balancedness (or first best implementability). On the contrary, Mitra and Sen (1998), prove that linear cost queueing problems are first best implementable. This paper is an attempt at identification of cost structures for which queueing problems are first best implementable. The broad conclusion is that, this is a fairly large class. Some of these first best implementable problems can be implemented by mechanisms that satisfy individual rationality.

Competitive and core allocations in large economies with differential information

Abstract: Summary. We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is “irreducible”, then a competitive equilibrium, in the sense of Radner (1968, 1982), exists. Moreover, the set of competitive equilibrium allocations coincides with the “private core” (Yannelis, 1991). We also show that the “weak fine core” of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy.

An experimental study of coordination and learning in iterated two-market entry games

Abstract: Tacit coordination in large groups is studied in an iterated market entry game with complete information and multiple market capacities that are varied randomly from period to period. On each period, each player must decide independently whether to enter any of the markets, and if entering, which of the two markets to enter. Across symmetric and asymmetric markets, we find remarkable coordination on the aggregate level, which is accounted for by the Nash equilibrium, together with considerable individual differences in frequency of entry and decision rules. With experience, the decisions of most players converge to decision rules with cutoff values on the combined market capacity that determine whether or not to enter but not which of the two markets to enter. This latter decision is determined probabilistically by the differential market capacities. The aggregate and individual results are accounted for quite well by a reinforcement-based learning model that combines deterministic and probabilistic elements.

Growth and equilibrium indeterminacy: the role of capital mobility

Abstract: The paper presents a human capital driven endogenous growth model which, in general, permits a multiplicity of equilibrium balanced growth paths. It is shown that allowing for perfect capital mobility across countries increases the range of parameter values for which the model permits equilibrium indeterminacy. As opposed to the closed capital markets case, simple restrictions on preferences are no longer sufficient to eliminate the indeterminacy. Intuitively, under perfect capital mobility agents are able to smooth consumption completely. This induces an economy with open capital markets to behave like a closed economy with linear preferences thereby increasing the possibility of equilibrium indeterminacy.

An experimental comparison of two search models

Abstract: We report an experiment designed to investigate markets with consumer search costs In markets where buyers are matched with one seller at a time, sellers are predicted to sell at prices equal to buyers’ valuations However, we find sellers post prices that offer a more equal division of the surplus, and these prices tend to be accepted, while prices doser to the equilibrium prediction are rejected At the other extreme, sellers are predicted to sell at a price equal to marginal cost when buyers are matched with two sellers at a time Here, we find prices are doser to, but still significantly different from, the equilibrium prediction Thus, our results support theoretical comparative static, but not point, predictions

Utility and entropy

Abstract: In this paper we study an astonishing similarity between the utility representation problem in economics and the entropy representation problem in thermodynamics.

A differentiable homotopy to compute nash equilibria of n-person games

Abstract: The literature on the computation of Nash equilibria in n-person games is dominated by simplicial methods. This paper is the first to introduce a globally convergent algorithm that fully exploits the differentiability present in the problem. It presents an everywhere differentiable homotopy to do the computations. The homotopy path can therefore be followed by several numerical techniques. Moreover, instead of computing some Nash equilibrium, the algorithm is constructed in such a way that it computes the Nash equilibrium selected by the tracing procedure of Harsanyi and Selten. As a by-product of our proofs it follows that for a generic game the tracing procedure defines a unique feasible path. The numerical performance of the algorithm is illustrated by means of several examples.

Numerical solution of dynamic oligopoly games with capital investment

Abstract: This paper discusses how numerical techniques may be used to solve the simultaneous functional equations that arise in general dynamic stochastic games. Unlike the conventional linear-quadratic approach, our methods may be used to address general model specifications that may include non-quadratic objective functions, non-linear equations of motion, and constraints on decision variables. As an illustration, we apply our methods to a dynamic duopoly game in which competing firms play short-run quantity game subject to production cost that can be lowered through investment in capital stock in the long run.

Profitability of price and quantity strategies in a duopoly with vertical product differentiation

Abstract: Using a model according to Mussa and Rosen (1978) and Bonanno and Haworth (1998) we consider a sub-game perfect equilibrium of a two-stage game in a duopolistic industry in which the products of the firms are vertically differentiated. In the industry, there are a high quality firm and a low quality firm. In the first stage of the game, the firms choose their strategic variables, price or quantity. In the second stage, they determine the levels of their strategic variables. We will show that, under an assumption about distribution of consumers' preference, we obtain the result that is similar to Singh and Vives (1984)' proposition (their Proposition 3) in the case of substitutes with nonlinear demand functions. That is, in the first stage of the game, a quantity strategy dominates a price strategy for both firms.

Real-time decentralized information processing and returns to scale

Abstract: We use a model of real-time decentralized information processing to understand how constraints on human information processing affect the returns to scale of organizations We identify three informational (dis)economies of scale: diversification of heterogeneous risks (positive), sharing of information and of costs (positive), and crowding out of recent information due to information processing delay (negative) Because decision rules are endogenous, delay does not inexorably lead to decreasing returns to scale However, returns are more likely to be decreasing when computation constraints, rather than sampling costs, limit the information upon which decisions are conditioned The results illustrate how information processing constraints together with the requirement of informational integration cause a breakdown of the replication arguments that have been used to establish nondecreasing technological returns to scale

Secret information acquisition in Cournot markets

Abstract: Two-stage game models of information acquisition in stochastic oligopolies require the assumption that firms observe the precision of information chosen by their competitors before determining quantities. This paper analyzes secret information acquisition as a one-stage game. Relative to the two-stage game firms are shown to acquire less information. Policy implications based on the two-stage game yield, therefore, too high taxes or too low subsidies for research activities. For the case of heterogeneous duopoly we briefly discuss comparative statics results.

Differential information economies: Introduction

Abstract: Since the Cournot-Nash and Arrow-Debreu-McKenzie contributions to equilibrium theory with complete information, two main advances in equilibrium theory with differential information appeared. The first one is by Harsanyi (1967), who introduces differential information into the Cournot-Nash model, and the second one is by Radner (1968), who introduces differential information into the Arrow-Debreu-McKenzie model. Those two papers generated a literature on Bayesian Cournot-Nash equilibrium and on Walrasian expectations equilibrium respectively. In the seventies and eighties there was a growing literature on Rational Expectations Equilibrium (REE), which is a natural extension of the Arrow-DebreuMcKenzie deterministic model of Walrasian equilibrium to a differential information framework. This literature on REE (a non-cooperative equilibrium concept) didn’t provide an adequate explanation as to how prices reveal the same information to agents who are differentially informed, or to put it differently, how agents who have different information obtain the same information from the equilibrium prices. In other words, prices don’t reflect the informational asymmetries of agents and this can be a major criticism of the REE concept under full revelation. A new literature emerges from two early seminal works on cooperative equilibrium concepts with differential information. The first one was by Wilson (1979), who considers the core of an economy with differential information,

Stochastically independent randomization and uncertainty aversion

Abstract: This paper proposes a preference-based condition for stochastic independence of a randomizing device in a product state space. This condition is applied to investigate some classes of preferences that allow for both independent randomization and uncertainty or ambiguity aversion (a la Ellsberg). For example, when imposed on Choquet Expected Utility (CEU) preferences in a Savage framework displaying uncertainty aversion in the spirit of Schmeidler [27], it results in a collapse to Expected Utility (EU). This shows that CEU preferences that are uncertainty averse in the sense of Schmeidler should not be used in settings where independent randomization is to be allowed. In contrast, Maxmin EU with multiple priors preferences continue to allow for a very wide variety of uncertainty averse preferences when stochastic independence is imposed. Additionally, these points are used to reexamine some recent arguments against preference for randomization with uncertainty averse preferences. In particular, these arguments are shown to rely on preferences that do not treat randomization as a stochastically independent event.

Technology transfer with commitment

Abstract: This paper considers technology transfer in a duopoly where the firms have two types of commitment strategies: incentive delegation and capacity installation. It turns out that the possibility of technology transfer significantly differs under these two types of commitment as well as depending on whether one or both firms commit. Under strategic incentive delegation, the possibility of technology transfer is minimal when both firms use the incentive delegation strategy and the costs of incentive delegation are negligible. If both firms choose the incentive delegation strategy and the costs of incentive delegation are significant then the possibility of technology transfer rises compared to a situation with no pre-commitment. In case of commitment to a capacity level before production, the possibility of technology transfer does not change when both firms simultaneously commit to their capacity levels. Different sets of results arise when only one firm can pre-commit.

Some factors affecting demand withholding in posted-offer markets

Abstract: Both oligopoly theory and experiments are concerned almost uniquely with sellers’ behavior. Buyers’ ability to exhibit non-trivial behavior in different market institutions remains unaddressed. This paper investigates the impact of three variables (number of buyers, surplus division at the market-clearing price and information revelation) on strategie and fairness-motivated demand withholding. Demand withholding and its ability to force lower prices increase as the number of buyers or theshare of surplus earned by the buyers decreases. However, increasing the information revealed to subjects about the surplus inequality favoring seHers mildly facilitates coHusion among sellers rather than provoking demand withholding as conjectured.

Scoring run-off paradoxes for variable electorates

Abstract: Summary. A no-show paradox occurs each time a single voter or a group of voters can manipulate the outcome by not participating to the election process. Among other voting procedures, the scoring run-off methods, which eliminate progressively the alternatives on the basis of scoring rules, suffer from this flaw. We here estimate how frequent this paradox is for three candidate elections under the classical Impartial Culture and Impartial Anonymous Culture assumptions, for different population sizes. The conditions under which this paradox occurs are also described, as well as the relationships with manipulations for a fixed number of voters.

Theoretically robust but empirically invalid? An experimental investigation into tax equivalence

Abstract: The idea that the final distribution of the tax burden (economic incidence) does not depend on the initial distribution of tax liabilities (statutory incidence) is referred to as the Liability Side Equivalence principle. This paper tests this principle in the laboratory and findsthat subjects who actually have to pay the tax carry a higher tax burden. It is argued that this violation of Liability Side Equivalence is due to the fact that a change in the distribution of tax liabilities induces a shift in behaviorally relevant social norms. This shift, in turn, affects the impact of the tax. Our results explain some striking empirical observations and have important theoretical and practical implications.

An extensive form interpretation of the private core

Abstract: The private core of an economy with differential information, (Yannelis (1991)), is the set of all state-wise feasible and private information measurable allocations which cannot be dominated, in terms of ex ante expected utility functions, by state-wise feasible and private information measurable net trades of any coalition It is coalitionally Bayesian incentive compatible and also takes into account the information superiority of an individual We provide a noncooperative extensive form interpretation of the private core for three person games We construct game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs In the spirit of the Nash programme, the private core is thus shown to be supported by the perfect Bayesian equilibrium of a noncooperative game The discussion contributes not only to the development of ideas but also to the understanding of the dynamics of how coalitionally incentive compatible contracts can be realized

Ranking of information systems in agency models: an integral condition

Abstract: 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.

Incentive compatible core and competitive equilibria in differential information economies

Abstract: If the allocations of a differential information economy are defined as incentive compatible state-contingent lotteries over consumption goods, competitive equilibrium allocations exist and belong to the (ex ante incentive) core Furthermore, any competitive equilibrium allocation can be viewed as an element of the core of the n-fold replicated economy, for every n The converse holds under the further assumption of independent private values but not in general, as shown by a counter-example

The analytics of search with posted prices

Abstract: This paper investigates the characteristics of the optimal posted price in the standard sequential search paradigm. Much of the intuition gleaned from the extensive sequential search literature in which the seller adopts a reservation price does not carry over to the posted price setting. For example, an increase in buyer valuations can lead to a reduction in the optimal posted price. We do, however, provide sufficient conditions on the hazard rate function h which ensure that an increase in demand induces an increase in the optimal posted price. As exhibited herein, the analysis of the posted price model depends critically upon analytical properties of h. Amongst the issues treated are the elasticity of demand, finite horizon, sale of multiple units, and competitive equilibrium.

Risk aversion and incentive compatibility with ex post information asymmetry

Abstract: 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.