nep-mic New Economics Papers
on Microeconomics
Issue of 2013‒06‒16
23 papers chosen by
Jing-Yuan Chiou
IMT Lucca Institute for Advanced Studies

  1. Exit Options and the Allocation of Authority By Bester, Helmut; Krähmer, Daniel
  2. Subjective Evaluation versus Public Information By Bester, Helmut; Münster, Johannes
  3. Information Sharing Networks in Linear Quadratic Games By Sergio Currarini; Francesco Feri
  4. Bayesian Games With a Continuum of States By Ziv Hellman; Yehuda (John) Levy
  5. The bilateral trade model in a discrete setting By Vermeulen A.J.; Schr?der M.J.W.; Flesch J.
  6. Optimal Truncation in Matching Markets By Peter Coles; Ran Shorrer
  7. The Lottery Blotto Game By Osório Costa, Antonio Miguel
  8. Efficient Entry in Competing Auctions By James Albrecht, Pieter Gautier, Susan Vroman
  9. Scoring Rules: A Game-Theoretical Analysis. By Francesco De Sinopoli; Giovanna Iannantuoni; Carlos Pimienta
  10. A Folk Theorem for Repeated Elections with Adverse Selection By John Duggan
  11. Asymmetric Multiple-Object First-Price Auctions By Paul Pezanis-Christou
  12. Cycles and Third-Party Payments in the Partnership Formation Problem By Gudmundsson, Jens
  13. On Aumann and Serrano's Economic Index of Risk By Li, Minqiang
  14. Mathematical Modeling of Consumer's Preferences Using Partial Differential Equations By Jorge Marques
  15. Anonymous Social Influence By Manuel Förster; Michel Grabisch; Agnieszka Rusinowsk
  16. Customer Relationship and Sales By Shouyong Shi
  17. Marriage Formation with Assortative Meeting as a Two-Sided Optimal Stopping Problem By E. M. Parilina; A. Tampieri
  18. Signalling Rivalry and Quality Uncertainty in a Duopoly By Bester, Helmut; Demuth, Juri
  19. Who benefits from resale-below-cost laws? By Noriaki Matsushima; Akira Miyaoka
  20. Updating Beliefs with Ambiguous Evidence: Implications for Polarization By Roland G. Fryer, Jr.; Philipp Harms; Matthew O. Jackson
  21. Peer Discipline and the Strength of Organizations By David K Levine; Salvatore Modica
  22. Window shopping By Oz Shy
  23. Confidence, Optimism and Litigation: A Litigation Model under Ambiguity By Nathalie Chappe; Raphaël Giraud

  1. By: Bester, Helmut; Krähmer, Daniel
    Abstract: We analyze the optimal allocation of authority in an organization whose members have conflicting preferences. One party has decision-relevant private information, and the party who obtains authority decides in a self-interested way. As a novel element in the literature on decision rights, we consider exit option contracts: the party without decision rights is entitled to prematurely terminate the relation after the other party's choice. We show that under such a contract it is always optimal to assign authority to the informed and not to the uninformed party, irrespective of the parties' conflict of interest. Indeed, the first-best efficient solution can be obtained by such a contract.
    Keywords: Authority; decision rights; exit options; incomplete contracts; asymmetric information
    JEL: D23 D82 D86
    Date: 2013–03–13
  2. By: Bester, Helmut; Münster, Johannes
    Abstract: This paper studies a principal-agent relation in which the principal's private information about the agent's effort choice is more accurate than a noisy public performance measure. For some contingencies the optimal contract has to specify ex post inefficiencies in the form of inefficient termination (firing the agent) or third-party payments (money burning). We show that money burning is the less efficient incentive device: it is used at most in addition to firing and only if the loss from termination is small. Under an optimal contract the agent's wage may depend only on the principal's report and not on the public signal. Nonetheless, public information is valuable as it facilitates truthful subjective evaluation by the principal.
    Keywords: Subjective evaluation; moral hazard; termination clauses; third-party payments
    JEL: D23 D82 D86 J41 M12
    Date: 2013–05–24
  3. By: Sergio Currarini (University of Leicester, Universita' di Venezia, Euro-Mediterranean Center on Climate Change, CIP Division and FEEM); Francesco Feri (Royal Holloway, University of London)
    Abstract: We study the bilateral exchange of information in the context of linear quadratic games. An information structure is here represented by a non directed network, whose nodes are agents and whose links represent sharing agreements. We first study the equilibrium use of information in any given sharing network, finding that the extent to which a piece of information is "public" affects the equilibrium use of it, in line with previous results in the literature. We then study the incentives to share information ex-ante, highlighting the role of the elasticity of payoffs to the equilibrium volatility of one's own strategy and of one's opponents' strategies. For the case of uncorrelated signals we fully characterize pairwise stable networks for the general linear quadratic game. For the case of correlated signals, we study pair-wise stable networks for three specific linear quadratic games - Cournot oligopoly, Keynes’ beauty contest and Public good provision - in which strategies are substitute, complement and orthogonal, respectively. We show that signals’ correlation favors the transmission of information, but may also prevent all information from being transmitted.
    Keywords: Information Sharing, Networks, Bayesian Equilibrium, Beauty Contest, Oligopoly
    JEL: D43 D82 D85 L13
    Date: 2013–05
  4. By: Ziv Hellman; Yehuda (John) Levy
    Abstract: Negative results on the the existence of Bayesian equilibria when state spaces have the cardinality of the continuum have been attained in recent years. This has led to the natural question: are there conditions that characterise when Bayesian games over continuum state spaces have measurable Bayesian equilibria? We answer this in the affirmative. Assuming that each type has finite or countable support, measurable Bayesian equilibria may fail to exist if and only if the underlying common knowledge $\sigma$-algebra is non-separable. Furthermore, anomalous examples with continuum state spaces have been presented in the literature in which common priors exist over entire state spaces but not over common knowledge components. There are also spaces over which players can have no disagreement, but when restricting attention to common knowledge components disagreements can exist. We show that when the common knowledge $\sigma$-algebra is separable all these anomalies disappear.
    Date: 2013–05
  5. By: Vermeulen A.J.; Schr?der M.J.W.; Flesch J. (GSBE)
    Abstract: We consider a bilateral trade model in which both players have a finite number of possible valuations. The sellers valuation and the buyers valuation for the object are private information, but the independent beliefs about these valuations are common knowledge. In this setting, we provide a characterization of the set of interim individually rational-implementable trading rules, analogous to the result of Myerson and Satterthwaite 1983. Thereafter, we derive necessary conditions for incentive compatible and ex post individually rational direct mechanisms. For the special class of corner mechanisms with discrete uniform beliefs, we characterize the set of ex post individually rational-implementable trading rules. In this context it is also shown that ex post efficiency can only be achieved if the number of different valuations is small. The maximal number of different valuations for which efficiency is still possible depends on the prior probability distribution of valuations.
    Date: 2013
  6. By: Peter Coles (Harvard Business School); Ran Shorrer (Harvard University and Harvard Business School)
    Abstract: Since no stable matching mechanism can induce truth-telling as a dominant strategy for all participants, there is often room in matching markets for strategic misrepresentation (Roth [25]). In this paper we study a natural form of strategic misrepresentation: reporting a truncation of one's true preference list. Roth and Rothblum [28] prove an important but abstract result: in certain symmetric, incomplete information settings, agents on one side of the market (“the women”) optimally submit some truncation of their true preference lists. In this paper we put structure on this truncation, both in symmetric and general settings, when agents must submit preference lists to the Men-Proposing Deferred Acceptance Algorithm. We first characterize each woman's truncation payoffs in an incomplete information setting in terms of the distribution of her achievable mates. The optimal degree of truncation can be substantial: we prove that in a uniform setting, the optimal degree of truncation for an individual woman goes to 100% of her list as the market size grows large, when other women are truthful. In this setting, we demonstrate the existence of an equilibrium where all agents use truncation strategies. Compared to truthful reporting, in any equilibrium in truncation strategies, welfare diverges for men and women: women prefer the truncation equilibrium, while men would prefer that participants truthfully report. In a general environment, we show that the less risk averse a player, the greater the degree of her optimal truncation. Finally, when correlation in preferences increases, players should truncate less. While several recent papers have focused on the limits of strategic manipulation, our results serve as a reminder that without the pre-conditions ensuring truthful reporting, even in settings where agents have little information, the potential for manipulation can be significant.
    Keywords: Matching Markets, Truncation
    JEL: C78 C62 D61
    Date: 2013–05
  7. By: Osório Costa, Antonio Miguel
    Abstract: In this paper we relax the Colonel Blotto game assumption that for a given battle the player who allocates the higher measure of resources wins that battle. We assume that for a given battle, the Colonel who allocates the higher measure of resources is more likely to win that battle. We have a simpler model for which we are able to compute all Nash equilibria in pure strategies for any valuations pro le that players might have. Something that is not possible for the original Blotto game. JEL: C72, D74, H56. KEYWORDS: Colonel Blotto game; lottery contest function.
    Keywords: Jocs no-cooperatius (Matemàtica), Gestió de conflictes, Seguretat nacional, 33 - Economia,
    Date: 2013
  8. By: James Albrecht, Pieter Gautier, Susan Vroman (Department of Economics, Georgetown University)
    Abstract: In this paper, we demonstrate the e¢ ciency of seller entry in a model of competing auctions. We generalize the competitive search literature by simultaneously allowing for nonrival (many on one) meetings and private information. We consider both the case in which buyers learn their valuations before visiting a seller and the case in which they learn their valuations after visiting the seller. We also allow for seller heterogeneity with respect to reservation values.
    Keywords: JEL Codes:
    Date: 2013–01–05
  9. By: Francesco De Sinopoli (University of Verona); Giovanna Iannantuoni (University of Milano-Bicocca); Carlos Pimienta (University of New South Wales)
    Abstract: We prove two results on the generic determinacy of Nash equilibrium in voting games. The first one is for negative plurality games. The second one is for approval games under the condition that the number of candidates is equal to three. These results are combined with the analogous one obtained in De Sinopoli (2001) for plurality rule to show that, for generic utilities, three of the most well-known scoring rules, plurality, negative plurality and approval, induce finite sets of equilibrium outcomes in their corresponding derived games—at least when the number of candidates is equal to three. This is a necessary requirement for the development of a systematic comparison amongst these three voting rules and a useful aid to compute the stable sets of equilibria (Mertens, 1989) of the induced voting games. To conclude, we provide some examples of voting environments with three candidates where we carry out this this comparison.
    Keywords: Approval voting, Plurality voting, Negative plurality, Sophisticated voting, Mertens Stability
    JEL: C72 D72
    Date: 2012–09
  10. By: John Duggan (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158)
    Abstract: I establish a folk theorem for a model of repeated elections with adverse selection: when citizens are sufficiently patient, arbitrary policy paths through arbitrarily large regions of the policy space can be supported by a refinement of perfect Bayesian equilibrium. Politicians are policy-motivated (so office benefits cannot be used to incentivize policy choices), the policy space is one-dimensional (limiting the dimensionality of the set of utility imputations), and politicians’ preferences are private information (so punishments cannot be targeted to a specific type). The equilibrium construction relies critically on differentiability and strict concavity of citizens’ utility functions. An extension of the arguments allows policy paths to depend on the office holder’s type, subject to incentive compatibility constraints.
    Date: 2013–05
  11. By: Paul Pezanis-Christou (School of Economics, University of Adelaide)
    Abstract: The paper reports on the effects of one-sided imperfect information on bidding behaviour in simultaneous and sequential first-price auctions of non-identical objects when bidders have multi-unit demands. The analysis provides the following four main results. First, when different objects are to be sold in sequence, the seller maximises her expected revenues by selling the most valuable object first. Second, the more the objects are different and the more the sequential format favours the informed bidder. Third, by switching the order of sales, the seller may want to change her initial preference for a simultaneous format (in which bidders submit object-specific bids) to one for a sequential format. Fourth, sequential auctions are mostly preferred by the seller when the objects are likely to be of low value and the precision of the informed bidder's signal is low.
    Keywords: multiple-object auctions, sequential and simultaneous procedures, first-price auctions, asymmetric bidders, multi-unit demands, common value, price trends, order of sales.
    JEL: C7 D4 D44 D8
    Date: 2013–05
  12. By: Gudmundsson, Jens (Department of Economics, Lund University)
    Abstract: We characterize the core of the partnership formation problem (Talman and Yang, Journal of Mathematical Economics 47, 2011) using cycles in the solution of a linear programming problem. The cycles also lead us to a new and intuitive sufficient condition for the existence of equilibrium, generalizing known results. We then introduce the partnership-stable equilibrium, a weakened solution concept in the sense that each equilibrium is also a partnership-stable equilibrium, and find sufficient and necessary conditions for its existence. Finally, we conduct a simulation study to see how often existence is an issue and which factors affect the rate at which problems have solutions.
    Keywords: Partnership; equilibrium; linear programming; cycles; third-party payments
    JEL: C62 D02 D60
    Date: 2013–05–30
  13. By: Li, Minqiang
    Abstract: We study the risk index of an additive gamble proposed in Aumann and Serrano (2008).We establish a generalized duality result for this index and use it to prove Yaari's (1969) alternative characterization of DARA utilities. A new characterization result for the risk index is obtained through essentially monotonic risk aversion utilities. We also extend the domain of gambles by introducing a price for gambles. We then develop a theory on the risk index for multiplicative gambles. Relative risk aversion functions for multiplicative gambles play the same role as absolute risk aversion functions for additive gambles.
    Keywords: Risk index Attractiveness index Duality Additive gambles Multiplicative gambles
    JEL: C00 D80 D81
    Date: 2013
  14. By: Jorge Marques (Faculty of Economics, University of Coimbra, Portugal)
    Abstract: The aim of this paper is to define consumer's preferences from the differentiable viewpoint in the sense of Debreu. In this framework given the marginal rates of substitution we can consider a vector field to represent consumer's preferences in the microeconomic theory. By definition the marginal rates of substitution satisfy a system of first order partial differential equations. For a continuously differentiable vector field that holds the integrability conditions we provide a general method to solve the system. In the special case of integrable preferences these conditions impose symmetry properties in the underlying preferences. Our results allow to characterize consumer's preferences in terms of the indifference map for the following classes: linear, quasi-linear, separable, homothetic, homothetic and separable. We show that this alternative approach is connected with the traditional formulation concerning the representability of preferences by utility functions. Moreover, we deduce even the general expression of utility functions that satisfy the integrability conditions in the context of ordinal utility.
    Keywords: smooth preferences, marginal rates of substitution, indifference map, ordinal utility, integrability conditions, differential equations.
    JEL: C60 C62 D01
    Date: 2013–05
  15. By: Manuel Förster (Université Paris 1 Panthéon-Sorbonne, France, Université catholique de Louvain – CORE, Belgium); Michel Grabisch (Paris School of Economics – Université Paris 1 Panthéon-Sorbonne, France); Agnieszka Rusinowsk (Paris School of Economics – CNRS Centre d’Économie de la Sorbonne, France)
    Abstract: We study a stochastic model of influence where agents have “yes” or “no” inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ordered weighted averaging operators, which are anonymous: they only depend on how many agents share an opinion. For instance, this allows to study situations where the influence process is based on majorities, which are not covered by the classical approach of weighted averaging aggregation. We find a necessary and sufficient condition for convergence to consensus and characterize outcomes where the society ends up polarized. Our results can also be used to understand more general situations, where ordered weighted averaging operators are only used to some extent. We provide an analysis of the speed of convergence and the possible outcomes of the process. Furthermore, we apply our results to fuzzy linguistic quantifiers, i.e., expressions like “most” or “at least a few”.
    Keywords: Influence, Anonymity, Ordered Weighted Averaging Operator, Convergence, Consensus, Speed Of Convergence, Fuzzy Linguistic Quantifier
    JEL: C7 D7 D85
    Date: 2013–05
  16. By: Shouyong Shi
    Abstract: I analyze a search equilibrium in a large market where customer relationship based on past trade arises endogenously together with service priority and sales. Specifically, there exists a unique equilibrium where it is optimal for a buyer to make repeat purchases from the related seller and optimal for a seller to give service priority to the related buyer. Customer relationship always improves welfare by reducing search frictions, but the equilibrium is socially efficient only when the buyer/seller ratio in the market is below a critical level. When the buyer/seller ratio exceeds this critical level, the equilibrium is inefficient because it fails to induce the coexistence of trading priority for related buyers and partial mixing of buyers for related sellers. Customer relationship induces price variations for individual sellers over time even when market conditions do not change. A seller posts a (high) regular price to sell to the related buyer and, once the seller loses the relationship, the seller posts a (low) sale price to sell to unrelated buyers until he gains a relationship. I also examine how market conditions affect the aggregate stock of relationships, markups, the size and the duration of a sale.
    Keywords: Customer relationship; Sales; Directed search
    JEL: D83 D40
    Date: 2013–06–03
  17. By: E. M. Parilina; A. Tampieri
    Abstract: In this paper we study marriage formation through a two-sided secretary problem approach. We consider individuals with nontransferable utility and two different dimensions of heterogeneity, a characteristic evaluated according to the idiosyncratic preferences of potential partners, and an universally-rankable characteristic. There are two possible states of the world, one in which people meet their partner randomly, and one in which the meeting occurs between individuals with similar characteristics. We show that individuals with higher universal characteristic tend to be more picky in their marriage hunting. This does not necessarily mean that they marry later than other individuals, since the higher expected quality of their potential partners in the assortative meeting state can make them marry earlier than individuals with a lower universal characteristic.
    JEL: C73 C78
    Date: 2013–06
  18. By: Bester, Helmut; Demuth, Juri
    Abstract: This paper considers price competition in a duopoly with quality uncertainty. The established firm (the `incumbent') offers a quality that is publicly known; the other firm (the `entrant') offers a new good whose quality is not known by some consumers. The incumbent is fully informed about the entrant's quality. This leads to price signalling rivalry because the incumbent gains and the entrant loses if observed prices make the uninformed consumers more pessimistic about the entrant's quality. When the uninformed consumers' beliefs satisfy the `intuitive criterion' and the `unprejudiced belief refinement', prices signal the entrant's quality only in a two-sided separating equilibrium and are identical to the full information outcome.
    Keywords: Quality uncertainty; Signalling; Oligopoly; Price competition
    JEL: D43 D82 L15
    Date: 2013–05
  19. By: Noriaki Matsushima; Akira Miyaoka
    Abstract: We investigate the effect of banning resale-below-cost offers. There are two retailers with heterogeneous bargaining positions in relation to a monopolistic manufacturer. Each retailer sells two goods: one procured from the monopolistic manufacturer and the other, from a competitive fringe. In equilibrium, banning resale-below-cost offers can decrease the retailers' prices. The ban can benefit the weak retailer in terms of bargaining position and increase the total consumer surplus, although it harms the dominant retailer and the monopolistic manufacturer. Contrary to the basic scenario, when the weak retailer is horizontally separated, the ban benefits the monopolistic manufacturer.
    Date: 2013–06
  20. By: Roland G. Fryer, Jr.; Philipp Harms; Matthew O. Jackson
    Abstract: We introduce and analyze a model in which agents observe sequences of signals about the state of the world, some of which are ambiguous and open to interpretation. Instead of using Bayes' rule on the whole sequence, our decision makers use Bayes' rule in an iterative way: first to interpret each signal and then to form a posterior on the whole sequence of interpreted signals. This technique is computationally efficient, but loses some information since only the interpretation of the signals is retained and not the full signal. We show that such rules are optimal if agents sufficiently discount the future; while if they are very patient then a time-varying random interpretation rule becomes optimal. One of our main contributions is showing that the model provides a formal foundation for why agents who observe exactly the same stream of information can end up becoming increasingly polarized in their posteriors.
    JEL: D03 J01
    Date: 2013–06
  21. By: David K Levine; Salvatore Modica
    Date: 2013–06–03
  22. By: Oz Shy
    Abstract: The terms "window shopping" and "showrooming" refer to the activity in which potential buyers visit a brick-and-mortar store to examine a product but end up either not buying it or buying the product from an online retailer. This paper analyzes potential buyers who differ in their preference for after-sale service that is not offered by online retailers. For some buyers, making a trip to the brick-and-mortar store is costly; however, going to the store to examine the product has the advantage of mitigating the uncertainty as to whether the product will suit the buyer's needs. The model shows that the number of buyers engaged in window shopping behavior exceeds the optimal number, both under duopoly and under joint ownership of the online and walk-in store outlets.
    Keywords: Consumer behavior
    Date: 2013
  23. By: Nathalie Chappe (CRESE, Université de Franche-comté); Raphaël Giraud (LED, University Paris 8)
    Abstract: This paper introduces ambiguity into an otherwise standard litigation model. The aim is to take into account optimism and confidence on the plaintiff side. We examine the following questions : 1) How optimism and confidence affect the outcomes of the settlement stage? 2) How optimism and confidence affect the level of care? 3) As a result what are the public policy implications in terms of monitoring the level of confidence? We show that the equilibrium probability of settlement is increasing in the degree of optimism for every plaintiffs and increasing in the level of confidence for pessimistic plaintiffs, provided the sensitivity of plaintiffs to a rise in the settlement offer is high, and that the same holds for the level of care independently of the sensitivity of plaintiffs to rises in the settlement offer. Finally, assuming the objective of the government is to minimize the probability of litigation and assuming that it can only manipulate the level of confidence, we find that a clear recommendation is possible only in the case of a high sensitivity of plaintiffs to rises in the settlement offer: government intervention to raise public confidence in the judicial system is recommended only when plaintiffs are pessimistic about their chances of winning and in that case, as much as possible should be spent.
    Keywords: confidence, ambiguity, litigation, behavioral law and economics.
    JEL: K41 D81
    Date: 2013–05

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