nep-mic New Economics Papers
on Microeconomics
Issue of 2018‒07‒23
eighteen papers chosen by
Jing-Yuan Chiou
National Taipei University

  1. Selective Sampling with Information-Storage Constraints By Philippe Jehiel; Jakub Steiner
  2. Information design in multi-stage games By Miltiadis Makris; Ludovic Renou
  3. Endogenous Timing in a Price-Setting Mixed Oligopoly By Haraguchi, Junichi; Hirose, Kosuke
  4. A Not so Myopic Axiomatization of Discounting By Jean-Pierre Drugeon; Thai Ha-Huy
  5. Equilibrium in a dynamic model of congestion with large and small users By Robin Lindsey; André De Palma; Hugo Silva
  6. Minimax theorem and Nash equilibrium of symmetric multi-players zero-sum game with two strategic variables By Masahiko Hattori; Atsuhiro Satoh; Yasuhito Tanaka
  7. On the relation between Sion's minimax theorem and existence of Nash equilibrium in asymmetric multi-players zero-sum game with only one alien By Atsuhiro Satoh; Yasuhito Tanaka
  8. On the Design of Optimal Health Insurance Contracts under Ex Post Moral Hazard By Pierre Martinon; Pierre Picard; Anasuya Raj
  9. On Existence and Properties of Pure-strategy Equilibria under Contests By Sakshi Gupta; Ram Singh
  10. The importance of consumer multi-homing (joint purchases) for market performance: mergers and entry in media markets By Anderson, Simon P; Foros, Øystein; Kind, Hans Jarle
  11. Optimal Dynamic Matching By Baccara, Mariagiovanna; Lee, SangMok; Yariv, Leeat
  12. Random Paths to Popularity in Two-Sided Matching By Aleksei Yu. Kondratev; Alexander S. Nesterov
  13. Voting as a War of Attrition By Kwiek, Maksymilian; Marreiros, Helia; Vlassopoulos, Michael
  14. Using multiple reference levels in Multi-Criteria Decision Aid: the Generalized-Additive Independence model and the Choquet integral approaches By Christophe Labreuche; Michel Grabisch
  15. Portfolio Optimization with Nondominated Priors and Unbounded Parameters By Kerem Ugurlu
  16. Adversarial Persuasion with Cross-Examination By Claude Fluet; Thomas Lanziyz
  17. Transitions and Political Stability in Autocracies. The Role of Public Perception By Mario, Gilli; Yuan, Li;
  18. On Maximin Optimization Problems & the Rate of Discount: a Simple Dynamic Programming Argument By Jean-Pierre Drugeon; Thai Ha-Huy; Thi-Do-Hanh Nguyen

  1. By: Philippe Jehiel; Jakub Steiner
    Abstract: A decision-maker acquires payoff-relevant information until she reaches her storing capacity, at which point she either terminates the decision-making and chooses an action, or discards some information. By conditioning the probability of termination on the information collected, she controls the correlation between the payoff state and her terminal action. We provide an optimality condition for the emerging stochastic choice. The condition highlights the benefits of selective memory applied to the extracted signals. The constrained-optimal choice rule exhibits (i) confirmation bias, (ii) speed-accuracy complementarity, (iii) overweighting of rare events, and (iv) salience effect.
    Keywords: bounded rationality; cognitive constraints; information processing; stochastic choice; confirmation bias; speed-accuracy complementarity; probability weighting; salience;
    JEL: D03 D80 D81 D83 D89 D90
    Date: 2018–07
  2. By: Miltiadis Makris (Department of Economics, University of Southampton); Ludovic Renou (Queen Mary University of London)
    Abstract: We consider multi-stage games, where at each stage, players receive private signals about past and current states, past actions and past signals, and choose actions. We fully characterize the distributions over actions, states, and signals that obtain in any (sequential) communication equilibrium of any expansion of multi-stage games, i.e., when players can receive additional signals about past and current states, past actions, and past and current signals (including the additional past signals). We interpret our results as revelation principles for information design problems. We apply our characterization to bilateral bargaining problems.
    Keywords: multi-stage games, information design, communication equilibrium, sequential communication equilibrium, information structures, Bayes correlated equilibrium, revelation principle
    JEL: C73 D82
    Date: 2018–06–25
  3. By: Haraguchi, Junichi; Hirose, Kosuke
    Abstract: We investigate the endogenous order of moves in a price-setting mixed oligopoly model, comprising two private firms and a public firm. We show that sequential moves emerge as the equilibrium in the observable delay game. Specifically, one of the private firms and the public firm set their prices in period 1, and the other private firm does so in period 2, in equilibrium, if their goods are not significantly differentiated. This is a clear contrast to a mixed duopoly where a simultaneous move game is a unique equilibrium. We also discuss a number of extensions and the robustness of our result.
    Keywords: Mixed Markets; Endogenous Timing; Stackelberg
    JEL: H44 L13
    Date: 2018–06–12
  4. By: Jean-Pierre Drugeon (PSE - Paris School of Economics, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique); Thai Ha-Huy (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne)
    Abstract: This article builds an axiomatization of inter-temporal trade-offs that makes an explicit account of the distant future and therefore encompasses motives related to sustainability, transmission to offsprings and altruism. The focus is on separable representations and the approach is completed following a decision-theory index based approach that is applied to utility streams. This enlightens the limits of the commonly used tail intensity requesites for the evaluation of utility streams: in this article, these are supersed and replaced by an axiomatic approach to optimal myopia degrees that in its turn precedes the determination of optimal discount. The overall approach is anchored in the new and explicit proof of a temporal decomposition of the preference orders between the distant future and the close future itself directly related to the determination of the optimal myopia degrees. The argument is shown to provide a novel understanding of temporal biases with the scope for a distant future bias when the finite dimensional gets influenced by the infinite dimensional. The reference to robust orders and pessimism-like axioms finally allows for determining tractable representations for the indexes.
    Abstract: JEL Codes: D11, D15, D90.
    Keywords: Discount,Temporal Order Decompositions,Infinite Dimensional Topologies,Axiomatization,Myopia
    Date: 2018–04
  5. By: Robin Lindsey (University of Alberta [Edmonton]); André De Palma (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Hugo Silva (Instituto Superior Técnico - Technical University of Lisbon)
    Abstract: Individual users often control a significant share of total traffic flows. Examples include airlines, rail and maritime freight shippers, urban goods delivery companies and passenger transportation network companies. These users have an incentive to internalize the congestion delays their own vehicles impose on each other by adjusting the timing of their trips. We investigate simultaneous trip-timing decisions by large users and small users in a dynamic model of congestion. Unlike previous work, we allow for heterogeneity of trip-timing preferences and for the presence of small users such as individual commuters and fringe airlines. We derive the optimal fleet departure schedule for a large user as a best-response to the aggregate departure rate of other users. We show that when the vehicles in a large user's fleet have a sufficiently dispersed distribution of desired arrival times, there may exist a pure-strategy Nash-equilibrium (PSNE) in which the large user schedules vehicles when there is a queue. This resolves the problem of non-existence of a PSNE identified in Silva et al. (2017) for the case of symmetric large users. We also develop some examples to identify under what conditions a PSNE exists. The examples illustrate how self-internalization of congestion by a large user can affect the nature of equilibrium and the travel costs that it and other users incur.
    Keywords: departure-time decisions,bottleneck model,congestion,schedule delay costs,large users,user heterogeneity,existence of Nash equilibrium $
    Date: 2018–04–06
  6. By: Masahiko Hattori; Atsuhiro Satoh; Yasuhito Tanaka
    Abstract: We consider a symmetric multi-players zero-sum game with two strategic variables. There are $n$ players, $n\geq 3$. Each player is denoted by $i$. Two strategic variables are $t_i$ and $s_i$, $i\in \{1, \dots, n\}$. They are related by invertible functions. Using the minimax theorem by \cite{sion} we will show that Nash equilibria in the following states are equivalent. 1. All players choose $t_i,\ i\in \{1, \dots, n\}$, (as their strategic variables). 2. Some players choose $t_i$'s and the other players choose $s_i$'s. 3. All players choose $s_i,\ i\in \{1, \dots, n\}$.
    Date: 2018–06
  7. By: Atsuhiro Satoh; Yasuhito Tanaka
    Abstract: We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in an asymmetric multi-players zero-sum game in which only one player is different from other players, and the game is symmetric for the other players. Then, 1. The existence of a Nash equilibrium, which is symmetric for players other than one player, implies Sion's minimax theorem for pairs of this player and one of other players with symmetry for the other players. 2. Sion's minimax theorem for pairs of one player and one of other players with symmetry for the other players implies the existence of a Nash equilibrium which is symmetric for the other players. Thus, they are equivalent.
    Date: 2018–06
  8. By: Pierre Martinon (Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems - CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique - UMA - Unité de Mathématiques Appliquées - Univ. Paris-Saclay, ENSTA ParisTech - École Nationale Supérieure de Techniques Avancées - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique); Pierre Picard (Département d'Économie de l'École Polytechnique - X - École polytechnique); Anasuya Raj (Département d'Économie de l'École Polytechnique - X - École polytechnique)
    Abstract: We analyze the design of optimal medical insurance under ex post moral haz- ard, i.e., when illness severity cannot be observed by insurers and policyholders decide for themselves on their health expenditures. The trade-o¤ between ex ante risk sharing and ex post incentive compatibility is analyzed in an optimal revelation mechanism under hidden information and risk aversion. The optimal contract provides partial insurance at the margin, with a deductible when in- surers' rates are affected by a positive loading, and it may also include an upper limit on coverage. The potential to audit the health state leads to an upper limit on out-of-pocket expenses.
    Keywords: optimal control,health insurance, ex post moral hazard, audit, background risk
    Date: 2018
  9. By: Sakshi Gupta (Department of Economics, Columbia University, New York); Ram Singh (Department of Economics, Delhi School of Economics)
    Abstract: The use of ‘ratio form’ probability of success function dominates the existing literature on contests. Very few works have focused on the ’difference form’functions, notwithstanding their robust theoretical foundations and intuitive appeal in several contexts. Assuming the cost of efforts to be linear, Hirshleifer (1989) and Baik (1998) have argued that under the difference form contests, there is no interior pure strategy Nash equilibrium. In contrast, existence of interior pure strategy Nash equilibrium is well known for the ratio form contest functions. In this paper we use strictly convex cost functions and demonstrate existence of pure strategy Nash equilibrium for the difference form. Moreover, we show that several properties of equilibria and the comparative statics for the difference form closely resemble those for the ratio form. However, unlike the ratio form, under a difference form contest the existence of pure strategy Nash equilibrium is sensitive to the value of the prize.
    Date: 2018–05
  10. By: Anderson, Simon P; Foros, Øystein; Kind, Hans Jarle
    Abstract: Consumer "multi-homing" (watching two TV channels, or buying two news magazines) has surprisingly important effects on market equilibrium and performance in (two-sided) media markets. We show this by introducing consumer multi-homing and advertising-finance into the classic circle model of product differentiation. When consumers multi-home (attend more than one platform), media platforms can charge only incremental-value prices to advertisers. Entry or merger leaves consumer prices unchanged under consumer multi-homing, but leaves advertiser prices unchanged under single-homing: multi-homing flips the side of the market on which platforms compete. In contrast to standard circle results, equilibrium product variety can be insufficient under multi-homing.
    Keywords: circle model; equilibrium product variety; media platforms; multi-homing; two-sided markets; media platforms; incremental-value prices; merger; single-homing
    Date: 2018–06
  11. By: Baccara, Mariagiovanna; Lee, SangMok; Yariv, Leeat
    Abstract: We study a dynamic matching environment where individuals arrive sequentially. There is a tradeoff between waiting for a thicker market, allowing for higher quality matches, and minimizing agents' waiting costs. The optimal mechanism cumulates a stock of incongruent pairs up to a threshold and matches all others in an assortative fashion instantaneously. In discretionary settings, a similar protocol ensues in equilibrium, but expected queues are inefficiently long. We quantify the welfare gain from centralization, which can be substantial, even for low waiting costs. We also evaluate welfare improvements generated by transfer schemes, and alternative priority protocols.
    Keywords: Dynamic Matching; market design; mechanism design; Organ Donation
    Date: 2018–06
  12. By: Aleksei Yu. Kondratev (National Research University Higher School of Economics); Alexander S. Nesterov (National Research University Higher School of Economics)
    Abstract: We study practically relevant aspects of popularity in two-sided matching where only one side has preferences. A matching is called popular if there does not exist another matching that is preferred by a simple majority. We show that for a matching to be popular it is necessary and sucient that no coalition of size up to 3 decides to exchange their houses by simple majority.We then constructively show that a market where such coalitions meet at random converges to a popular matching whenever it exists.
    Keywords: two-sided matching, popular matching, random paths, house allocation, assignment problem
    JEL: Z
    Date: 2018
  13. By: Kwiek, Maksymilian (University of Southampton); Marreiros, Helia (Universidade Catolica Portuguesa, Porto); Vlassopoulos, Michael (University of Southampton)
    Abstract: We study communication in committees selecting one of two alternatives when consensus is required and agents have private information about their preferences. Delaying the decision is costly, so a form of multiplayer war of attrition emerges. Waiting allows voters to express the intensity of their preferences and may help to select the alternative correctly more often than simple majority. In a series of laboratory experiments, we investigate how various rules affect the outcome reached. We vary the amount of feedback and the communication protocol available to voters: complete secrecy about the pattern of support; feedback about this support; public communication; and within-group communication. The feedback no-communication mechanism is worse than no feedback benchmark in all measures of welfare - the efficient alternative is chosen less often, waiting cost is higher, and thus net welfare is lower. Our headline result is that adding communication restores net efficiency, but in different ways. Public communication does poorly in terms of selecting the correct alternative, but limits the cost of delay, while group communication improves allocative efficiency, but has at best a moderate effect on delay.
    Keywords: voting, intensity of preferences, supermajority, conclave, war of attrition, communication
    JEL: C78 C92 D72 D74
    Date: 2018–06
  14. By: Christophe Labreuche (Thales Research and Technology [Palaiseau] - THALES); Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)
    Abstract: In many Multi-Criteria Decision problems, one can construct with the decision maker several reference levels on the attributes such that some decision strategies are conditional on the comparison with these reference levels. The classical models (such as the Choquet integral) cannot represent these preferences. We are then interested in two models. The first one is the Choquet with respect to a p-ary capacity combined with utility functions, where the p-ary capacity is obtained from the reference levels. The second one is a specialization of the Generalized-Additive Independence (GAI) model, which is discretized to fit with the presence of reference levels. These two models share common properties (monotonicity, continuity, properly weighted, …), but differ on the interpolation means (Lovász extension for the Choquet integral, and multi-linear extension for the GAI model). A drawback of the use of the Choquet integral with respect to a p-ary capacity is that it cannot satisfy decision strategies in each domain bounded by two successive reference levels that are completely independent of one another. We show that this is not the case with the GAI model.
    Abstract: Dans beaucoup de problème de décision multicritère, on peut construire avec le décideur plusieurs niveaux de référence sur les attributs de telle sorte que des stratégies de décision soient conditionnelles sur la comparaison avec les niveaux de référence. Les modèles classiques (Choquet) ne peuvent représenter ces préférences. Nous nous intéressons à deux modèles, le premier étant Choquet vs. une p-capacité qui est obtenue à partir des niveaux de référence. Le second est une spécialisation du modèle GAI (Generalized-Additive Independence). Ces deux modèles ont en commun des propriétés (monotonie, continuité), mais diffèrent sur le type d'interpolation (Lovász, multilinéaire). Un défaut de l'intégrale de Choquet est qu'elle ne satisfait pas les stratégies de décision dans chaque domaine borné par deux niveaux de références indépendants l'un de l'autre. Nous montrons que cela ne peut arriver avec le modèle GAI.
    Keywords: multiple criteria analysis,Generalized Additive Independence,Choquet integral,reference levels,intégrale de Choquet,niveau de références,interpolation,GAI,analyse multicritère
    Date: 2018–03
  15. By: Kerem Ugurlu
    Abstract: We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular, both mean and volatility are unbounded. We assume that there is Knightian uncertainty on the parameters of both mean and volatility. We take that the investor has logarithmic utility function, and solve the corresponding utility maximization problem explicitly. To the best of our knowledge, this is the first work on utility maximization with unbounded mean and volatility in Knightian uncertainty under nondominated priors.
    Date: 2018–07
  16. By: Claude Fluet; Thomas Lanziyz
    Abstract: Two parties with opposed interests invest in acquiring evidence which they may only partially disclose. The decision maker then adjudicates. This set-up is compared with one permitting cross-examination of the other party?s report. Now the decision maker can better assess whether a report was deceitful through withholding of evidence. Nevertheless, decision-making need not be improved. The parties invest less in gathering evidence because they are less able to successfully manipulate information and because cross-examination is a substitute in potentially countering the other party. From the decision maker's standpoint, there is too much cross-examination at the expense of too little direct evidence.
    Keywords: disclosure, persuasion, evidence, adversarial, cross-examination, judicial procedures.
    JEL: D82 K41
    Date: 2018
  17. By: Mario, Gilli; Yuan, Li;
    Abstract: The literature on the functioning of autocracies has not analyzed the consequences of the fact that policies have multiple dimensions and that these dimensions are perceived with di¤erent bias by people. This fact is obviously more striking in autocracies where the public perception of policies' effects might be partially manipulated. We try to fill the gap. This paper makes three contributions to the literature on the functioning of autocratic regimes. First, we show that, may be counter-intuitively, both the probability of full e¢ cient and full inefficient policies decrease as opacity increases, while the probability of partially efficient policies has the opposite behavior. This implies that the probability of efficient policies on different policy dimensions diverges as opacity increases, and this provides an explanation for the observed heterogeneity of policies within an autocracy. Second, the expected probability of a coup has a non monotone behavior w.r.t. opacity, so that at intermediate level an increment in opacity might actually increase the likelihood of a selectorate coup. Finally, also the expected probability of a citizens' revolt might have a non monotone behavior w.r.t. opacity, so that the likelihood of a revolt might actually increase as opacity increases. We conclude that the e¤ect of bias in public perception of some policy dimension is non monotone on authoritarian regime stability. These results provide a reason to explain why transition periods are dangerous for a dictator.
    Keywords: Multidimensional policies, public perception, political stability.
    JEL: D02 H11 D74
    Date: 2018–07–13
  18. By: Jean-Pierre Drugeon (PSE - Paris School of Economics, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique); Thai Ha-Huy (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne); Thi-Do-Hanh Nguyen (Vietnam Maritime University)
    Abstract: This article establishes a dynamic programming argument for a maximin optimization problem where the agent completes a minimization over a set of discount rates. Even though the consideration of a maximin criterion results in a program that is not convex and not stationary over time, it is proved that a careful reference to extended dynamic programming principles and a maxmin functional equation however allows for circumventing these difficulties and recovering an optimal sequence that is time consistent. This in its turn brings about a stationary dynamic programming argument.
    Keywords: maximin principle,non-convexities,value fun-ion,policy fun-ion,supermodularity
    Date: 2018–04

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