nep-mic New Economics Papers
on Microeconomics
Issue of 2019‒10‒21
23 papers chosen by
Jing-Yuan Chiou
National Taipei University

  1. Rational Buyers Search When Prices Increase By Cabral, Luís M B; Gilbukh, Sonia
  2. Individually-Consistent Sequential Equilibrium. By Gisčle Umbhauer; Arnaud Wolff
  3. UNDISCOUNTED BANDIT GAMES By Godfrey Keller; Sven Rady
  4. Sequential Majoritarian Blotto Games By Tilman Klumpp; Kai A. Konrad
  5. Platform Competition with Multihoming on Both Sides: Subsidize or Not? By Yannis Bakos; Hanna Halaburda
  6. Complete Information Pivotal-Voter Model with Asymmetric Group Size By Christos Mavridis; Marco Serena
  7. All-pay competition with captive consumers By Renaud Foucart; Jana Friedrichsen
  8. Mission Drift in Microcredit: A Contract Theory Approach By Sara Biancini; David Ettinger; Baptiste Venet
  9. Games of Incomplete Information Played By Statisticians By Annie Liang
  10. Debunking Rumors in Networks By Luca Paolo Merlino; Nicole Tabasso
  11. Optimal mechanism for the sale of a durable good By Doval, Laura; Skreta, Vasiliki
  12. Biasing Unbiased Dynamic Contests By Stefano Barbieri; Marco Serena
  13. Pure rank preferences and variation in risk-taking behavior By Stark, Oded; Budzinski, Wiktor; Jakubek, Marcin
  14. Sorting in the Presence of Misperceptions By Lisa Windsteiger
  15. Rules versus Discretion in Bank Resolution By Walther, Ansgar; White, Lucy
  16. A Theory of Simplicity in Games and Mechanism Design By Pycia, Marek; Troyan, Peter
  17. Sequential Learning By Antler, Yair; Bird, Daniel; Oliveros, Santiago
  18. How do trade and communication costs shape the spatial organization of firms? By Gokan, Toshitaka; Kichko, Sergey; Thisse, Jacques-François
  19. Incentives to Discover Talent By Bruenner, Tobias; Friebel, Guido; Holden, Richard; Prasad, Suraj
  20. Rational hyperbolic discounting By Jos\'e Cl\'audio do Nascimento
  21. Bitcoin: An Impossibility Theorem for Proof-of-Work based Protocols By Jacob Leshno; Philipp Strack
  22. Dynamically Aggregating Diverse Information By Annie Liang; Xiaosheng Mu; Vasilis Syrgkanis
  23. Higher orders of rationality and the structure of games By Francesco Cerigioni; Fabrizio Germano; Pedro Rey-Biel; Peio Zuazo-Garin

  1. By: Cabral, Luís M B; Gilbukh, Sonia
    Abstract: We develop a dynamic pricing model motivated by observed patterns in business-to-business (and some business-to-customer) transactions. Seller costs are perfectly correlated and evolve according to a Markov process. In every period, each buyer observes (for free) the price set by their current supplier, but not the other sellers' prices or the sellers' (common) cost level. By paying a cost s the buyer becomes "active" and benefits from (Bertrand) competition among sellers. We show that there exists a semi-separating equilibrium whereby sellers increase price immediately when costs increase and otherwise decrease price gradually. Moreover, buyers become active when prices increase but not otherwise. In sum, we deliver a theory whereby buyers become active ("search") if and only if their supplier increases price.
    JEL: D83
    Date: 2019–08
  2. By: Gisčle Umbhauer; Arnaud Wolff
    Abstract: We introduce a new equilibrium concept, called the individually-consistent sequential equilibrium (ICSE). This concept is more permissive than the sequential equilibrium (Kreps, Wilson (1982)) but more demanding than the self-confirming one (Fudenberg, Levine (1993)). We require that players share common beliefs on the actions planned to be played at all the information sets, but not on the potential deviations. Therefore, in contrast to Kreps, Wilson (1982), we allow different players to have in mind different perturbation systems, or alternative hypotheses. This is motivated by the fact that beliefs about unobserved events are by essence not verifiable.
    Keywords: Sequential Equilibrium, Consistency, Perturbations, Beliefs.
    JEL: C72
    Date: 2019
  3. By: Godfrey Keller; Sven Rady
    Abstract: We analyze undiscounted continuous-time games of strategic experimentation with two-armed bandits. The risky arm generates payoffs according to a Le´vy process with an unknown average payoff per unit of time which nature draws from an arbitrary finite set. Observing all actions and realized payoffs, players use Markov strategies with the common posterior belief about the unknown parameter as the state variable. We show that the unique symmetric Markov perfect equilibrium can be computed in a simple closed form involving only the payoff of the safe arm, the expected current payoff of the risky arm, and the expected full-information payoff, given the current belief. In particular, the equilibrium does not depend on the precise specification of the payoff-generating processes.
    Keywords: Strategic Experimentation, Two-Armed Bandit, Strong Long-Run Av¬erage Criterion, Markov Perfect Equilibrium, HJB Equation, Viscosity Solution
    JEL: C73 D83
    Date: 2019–10–10
  4. By: Tilman Klumpp; Kai A. Konrad
    Abstract: We study Colonel Blotto games with sequential battles and a majoritarian objective. For a large class of contest success functions, the equilibrium is unique and characterized by an even split: Each battle that is reached before one of the players wins a majority of battles is allocated the same amount of resources from the player’s overall budget. As a consequence, a player’s chance of winning any particular battle is independent of the battleï¬ eld and of the number of victories and losses the player accumulated in prior battles. This result is in stark contrast to equilibrium behavior in sequential contests that do not involve either ï¬ xed budgets or a majoritarian objective. We also consider the equilibrium choice of an overall budget. For many contest success functions, if the sequence of battles is long enough the payoff structure in this extended games resembles an all-pay auction without noise.
    Keywords: Blotto games, dynamic battles, multi-battle contest, all-pay auctions, sequential elections
    JEL: D72 D74
    Date: 2018–06
  5. By: Yannis Bakos (Stern School of Business, New York University); Hanna Halaburda (Stern School of Business, New York University)
    Abstract: As the costs of joining platforms decrease, we often see participants in both sides of two-sided platforms to multihome, a case mostly ignored in the literature on competition between two-sided platforms. We help to fill this gap by developing a model for platform competition in a differentiated setting (a Hoteling line), which is similar to other models in the literature but focuses on the case where at least some agents on each side multihome. We show that in that case the strategic interdependence between the two sides of the same platform may be of lesser importance, or even not be present at all, compared to models that assume single-homing on at least one side of the market. The implication is that when multihoming may be present on both sides of the market, the benefit of subsidizing one side (typically the one with higher price elasticity) is diminished or may not be present at all. This outcome differs from most of the two-sided platform literature, where interdependence between the two sides served by the same platform is a major result leading to the policy implication that a platform will often maximize its total profits by subsidizing one side, typically the one with more elastic demand. Our analysis shows that the common strategic advice to subsidize one side in order to maximize total profits may be limited or even incorrect when both sides multihome, which can be significant given the increasing prevalence of multihoming.
    Keywords: multihoming, platforms, two-sided platforms, network effects, platform subsidies
    JEL: L10 L81 L82 L86 O33
    Date: 2019–09
  6. By: Christos Mavridis; Marco Serena
    Abstract: In this note, we characterize the equilibria of the standard pivotal-voter participation game between two groups of voters of asymmetric sizes, as originally proposed by Palfrey and Rosenthal [1983. A strategic calculus of voting. Public Choice. 41, 7-53].
    Keywords: Costly voting, pivotal voter model, complete information
    Date: 2018–11
  7. By: Renaud Foucart; Jana Friedrichsen
    Abstract: We study a game in which two firms compete in quality to serve a market consisting of consumers with different initial consideration sets. If both firms invest below a certain quality threshold, they only compete for those consumers already aware of their existence. Above this threshold, a firm is visible to all and the highest quality attracts all consumers. In equilibrium, firms do not choose their investment deterministically but randomize over two disconnected intervals. On the one hand, the existence of initially captive consumers introduces an anti-competitive element: holding fixed the behavior of the rival firm, a firm with a larger captive segment enjoys a higher payoff from not investing at all. On the other hand, the fact that a firm’s initially captive consumers can still be attracted by very high quality introduces a pro-competitive element: high quality investments becomes more profitable for the underdog when the captive segment of the dominant firm increases. The share of initially captive consumers therefore has a non-monotonic effect on the investment levels of both firms.
    Keywords: quality competition, all-pay auction, endogenous prize, consideration sets
    JEL: D21 D44 M13
    Date: 2019
  8. By: Sara Biancini (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - UNIV-RENNES - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique); David Ettinger (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique, LEDa - Laboratoire d'Economie de Dauphine - Université Paris-Dauphine); Baptiste Venet (LEDa - Laboratoire d'Economie de Dauphine - Université Paris-Dauphine, DIAL - Développement, institutions et analyses de long terme, Institut de Recherche pour le Développement (IRD))
    Abstract: We analyze the relationship between Microfinance Institutions (MFIs) and external funding institutions, with the aim of contributing to the debate on "mission drift" (the tendencyfor MFIs to lend money to wealthier borrower rather than to the very poor). We suggestthat funding institutions build incentives for MFIs to choose the adequate share of poorerborrowers and to exert effort to increase the quality of the funded projects. We show thatasymmetric information on both the effort level and its cost may increase the share of richerborrowers. However the unobservability of the cost of effort has an ambiguous effect. Itpushes efficient MFIs to serve a higher share of poorer borrowers, while less efficient onesdecrease their poor outreach.
    Keywords: Microfinance,Funding Institutions,Mission Drift,Contract Theory
    Date: 2019–10–03
  9. By: Annie Liang
    Abstract: This paper proposes a foundation for heterogeneous beliefs in games, in which disagreement arises not because players observe different information, but because they learn from common information in different ways. Players may be misspecified, and may moreover be misspecified about how others learn. The key assumption is that players nevertheless have some common understanding of how to interpret the data; formally, players have common certainty in the predictions of a class of learning rules. The common prior assumption is nested as the special case in which this class is a singleton. The main results characterize which rationalizable actions and Nash equilibria can be predicted when agents observe a finite quantity of data, and how much data is needed to predict various solutions. This number of observations needed depends on the degree of strictness of the solution and speed of common learning.
    Date: 2019–10
  10. By: Luca Paolo Merlino (Department of Economics University of Antwerp, Antwerp, Belgium; Université Paris 1-Panthéon Sorbonne); Nicole Tabasso (Department of Economics Ca' Foscari University of Venice; School of Economics, University of Surrey)
    Abstract: We study the diffusion of a true and a false opinion (the rumor) in a social network. Upon hearing an opinion, individuals may believe it, disbelieve it, or debunk it through costly verification. Whenever the truth survives in steady state, so does the rumor. Online social communication exacerbates relative rumor prevalence as long as it increases homophily or verification costs. Our model highlights that successful policies in the fight against rumors increase individuals’ incentives to verify.
    Keywords: Social Networks, Rumors, Verification
    JEL: D83 D85
    Date: 2019
  11. By: Doval, Laura; Skreta, Vasiliki
    Abstract: We show that posted prices are the optimal mechanism to sell a durable good to a privately informed buyer when the seller has limited commitment in an infinite horizon setting. We provide a methodology for mechanism design with limited commitment and transferable utility. Whereas in the case of commitment, subject to the buyer's truthtelling and participation constraints, the seller's problem is a decision problem, in the case of limited commitment, the seller's problem corresponds to an intrapersonal game, where different "incarnations" of the seller represent the different beliefs he may have about the buyer's valuation.
    Keywords: information design; intrapersonal equilibrium; Limited Commitment; mechanism design; posted price; self-generation
    JEL: D84 D86
    Date: 2019–08
  12. By: Stefano Barbieri; Marco Serena
    Abstract: We consider a best-of-three Tullock contest between two ex-ante identical players. An effortmaximizing designer commits to a vector of player-specific biases (advantages or disadvantages). In our benchmark model the designer chooses victory-dependent biases (i.e., the biases depend on the record of matches won by players); the effort-mazimizing biases eliminate the discouragement effect, leaving players equally likely to win each match and the overall contest. We contrast our benchmark model with one where the designer chooses victory-independent biases; the effort-maximizing biases leave players unequally likely to win each match and the overall contest. This result holds in Tullock contests and all-pay auctions, as well as under maximization of total effort and winner's effort. The appeal of our result comes from the players being ex-ante identical; thus, it challenges the conventional wisdom of optimality of unbiased contests. Our result has also an applied interest, as it shows that alternating biases, as when teams alternate home and away games, may increase total effort as opposed to an unbiased contest.
    Date: 2018–05
  13. By: Stark, Oded; Budzinski, Wiktor; Jakubek, Marcin
    Abstract: Assuming that an individual's rank in the wealth distribution is the only factor determining the individual's wellbeing, we analyze the individual's risk preferences in relation to gaining or losing rank, rather than the individual's risk preferences towards gaining or losing absolute wealth. We show that in this characterization of preferences, a high-ranked individual is more willing than a low-ranked individual to take risks that can provide him with a rise in rank: relative risk aversion with respect to rank in the wealth distribution is a decreasing function of rank. This result is robust to incorporating (the level of) absolute wealth in the individual's utility function.
    Keywords: Rank in the wealth distribution,Rank-based utility,Variation in risk-takingbehavior,Relative risk aversion
    JEL: D01 D31 D81 G32
    Date: 2019
  14. By: Lisa Windsteiger
    Abstract: In this paper I develop a general model of how social segregation and beliefs interact. Sorting decisions will be affected by beliefs about society, but these beliefs about society are in turn influenced by social interactions. In my model, people sort into social groups according to income, but become biased about the income distribution once they interact only with their own social circle. I define "biased sorting equilibria", which are stable partitions in which people want to stay in their chosen group, despite their acquired misperceptions about the other groups. I introduce a refinement criterion - the consistency requirement - and find necessary and su¢ cient conditions for existence and uniqueness of biased sorting equilibria.
    Keywords: Stratification, Assortative Matching, Group Formation, Beliefs
    JEL: D83 D85 Z13
    Date: 2018–10
  15. By: Walther, Ansgar; White, Lucy
    Abstract: Recent reforms give regulators broad powers to "bail-in" bank creditors during financial crises. We analyze efficient bail-ins and their implementation. To preserve liquidity, regulators must avoid signalling negative private information to creditors. Therefore, optimal bail-ins in bad times depend only on public information. As a result, the optimal policy cannot be implemented if regulators have wide discretion, due to an informational time-inconsistency problem. Rules mandating tough bail-ins after bad public signals, or contingent convertible (co-co) bonds, improve welfare. We further show that bail-in and bailout policies are complementary: if bailouts are possible, then discretionary bail-ins are more effective.
    Keywords: bail-in; bail-out; bank resolution; bank runs; financial crises
    JEL: G01 G18 G21
    Date: 2019–10
  16. By: Pycia, Marek; Troyan, Peter
    Abstract: We introduce a general class of simplicity standards that vary the foresight abilities required of agents in extensive-form games. Rather than planning for the entire future of a game, agents are presumed to be able to plan only for those histories they view as simple from their current perspective. Agents may update their so-called strategic plan as the game progresses, and, at any point, for the called-for action to be simply dominant, it must lead to unambiguously better outcomes, no matter what occurs at non-simple histories. We use our approach to simplicity to provide characterizations of simple mechanisms in general social choice environments both with and without transfers, including canonical mechanisms such as ascending auctions, posted prices, and serial dictatorship-style mechanisms. As a final application, we explain the widespread popularity of the well-known Random Priority mechanism by characterizing it as the unique mechanism that is efficient, fair, and simple to play.
    JEL: C72 C78 D44 D82
    Date: 2019–10
  17. By: Antler, Yair; Bird, Daniel; Oliveros, Santiago
    Abstract: Two players sequentially and privately examine a project of unknown quality. Launching the project requires mutual consent and the first player values the project more than the second player does. The combination of the conflict of interest and private learning leads to moral hazard. We show that an efficient equilibrium must take one of two forms as a function of the prior: either one player relinquishes control of the project, thereby rendering the collaboration moot, or the first player occasionally makes false claims about achieving positive findings. In the latter case, the players' relevant beliefs diverge as time progresses. In addition, we show that projects for which an initial examination failed to generate positive findings may be launched, and that projects known to be good by the first player may be delayed or even aborted.
    Date: 2019–08
  18. By: Gokan, Toshitaka; Kichko, Sergey; Thisse, Jacques-François
    Abstract: We consider an economic geography setting in which firms are free to choose one of the following organizational types: (i) integrated firms, which perform all their activities at the same location, (ii) horizontal firms, which operate several plants producing the same good at different locations, and (iii) vertical firms, which perform distinct activities at separated locations. We show that there exists a unique organizational equilibrium, which typically involves the coexistence of various organizational forms. We also give necessary and sufficient conditions for the three types of firms to coexist within the same region and show that transportation and communication costs have opposite effects on firms' organizational choices. This suggests that, depending on its nature, the supply of a new transportation infrastructure may lead to contrasted locational patterns.
    Keywords: Communication costs; horizontal firm; Region; Transportation Costs; vertical firm
    JEL: F12 F21 R12
    Date: 2019–10
  19. By: Bruenner, Tobias; Friebel, Guido; Holden, Richard; Prasad, Suraj
    Abstract: We study an agent's incentives to discover where her talents lie before putting them to productive use. In our setting, an agent can specialize and learn about the same type of talent repeatedly, or experiment and learn about different types of talent. When talents are normally and symmetrically distributed we find that experimentation is efficient, regardless of one's initial draw of talent. Competitive labor markets encourage experimentation whereas monopsonistic labor markets induce specialization. Relaxing our assumptions of normality and symmetry in the distribution of talents, and allowing for human capital acquisition, provides a role for specialization in discovering talents.
    Date: 2019–09
  20. By: Jos\'e Cl\'audio do Nascimento
    Abstract: This paper shows that the $q$-exponential function rationally evaluate the time discounting. When we consider two processes of wealth accumulation with different frequencies, then the discount rate and the relative frequency between them are essentials to choose the best process. In this context, the exponential discounting is a particular case, where one of the processes has a much higher frequency related to the other. In addition, one can note that some behaviors observed empirically in decision makers, such as subadditivity, magnitude effect, and preference reversal, are consistent with processes which have a low relative frequency.
    Date: 2019–10
  21. By: Jacob Leshno (University of Chicago Booth School of Business); Philipp Strack (Cowles Foundation, Yale University)
    Abstract: A key part of decentralized consensus protocols is a procedure for random selection, which is the source of the majority of miners cost and wasteful energy consumption in Bitcoin. We provide a simple economic model for random selection mechanism and show that any PoW protocol with natural desirable properties is outcome equivalent to the random selection mechanism used in Bitcoin.
    Keywords: Bitcoin, Random Selection, Proportional Selection Rule, Impossibility Theorem
    JEL: C72 D02
    Date: 2019–02
  22. By: Annie Liang; Xiaosheng Mu; Vasilis Syrgkanis
    Abstract: An agent has access to multiple data sources, each of which provides information about a different attribute of an unknown state. Information is acquired continuously--where the agent chooses both which sources to sample from, and also how to allocate resources across them--until an endogenously chosen time, at which point a decision is taken. We show that the optimal information acquisition strategy proceeds in stages, where resource allocation is constant over a fixed set of providers during each stage, and at each stage a new provider is added to the set. We additionally apply this characterization to derive results regarding: (1) endogenous information acquisition in a binary choice problem, and (2) equilibrium information provision by competing news sources.
    Date: 2019–10
  23. By: Francesco Cerigioni; Fabrizio Germano; Pedro Rey-Biel; Peio Zuazo-Garin
    Keywords: Rationality, higher-order rationality, revealed rationality, levels of thinking.
    JEL: C70 C72 C91 D01
    Date: 2019–08

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