nep-mic New Economics Papers
on Microeconomics
Issue of 2021‒06‒21
twenty-six papers chosen by
Jing-Yuan Chiou
National Taipei University

  1. Strategic information transmission with sender's approval: the single-crossing case By Sémirat, S.; Forges, F.
  2. Monopoly strategy with purchase dependent preferences and endogenous preference change By Stéphane Lemarié; Cecilia Vergari
  3. Intransitive indifference with direction-dependent sensitivity By Nobuo Koida
  4. Solving Strong-Substitutes Product-Mix Auctions By Baldwin, Elizabeth; Goldberg, Paul; Klemperer, Paul; Lock, Edwin
  5. Between Commitment and Flexibility: Revealing Anticipated Regret and Elation By Daniele Pennesi
  6. Obfuscation in competitive markets By Ernst Fehr; Keyu Wu
  7. Aggregating Opinions By Salvador Barberà; Walter Bossert
  8. Interactive Communication in Bilateral Trade By Jieming Mao; Renato Paes Leme; Kangning Wang
  9. An algebraic approach to revealed preferences By Mikhail Freer; Cesar Martinelli
  10. Robust Merging of Information By Henrique de Oliveira; Yuhta Ishii; Xiao Lin
  11. Optimal Contest Design: A General Approach By Letina, Igor; Liu, Shuo; Netzer, Nick
  12. Compromising on Compromise Rules By Salvador Barberà; Danilo Coelho
  13. Rotation as Contagion Mitigation By Ely, Jeffrey; Galeotti, Andrea; Steiner, Jakub
  14. The impact of targeting technologies and consumer multi-homing on digital platform competition By Evensen, Charlotte Bjørnhaug; Haugen, Atle
  15. An Implementation Approach to Rotation Programs By Ville Korpela; Michele Lombardi; Riccardo D. Saulle
  16. Bargaining over a divisible good in the market for lemons By Gerardi, Dino; Maestri, Lucas; Monzon, Ignacio
  17. Characterization of equilibrium existence and purification in general Bayesian games By Wei He; Xiang Sun; Yeneng Sun; Yishu Zeng
  18. Asymmetric All-Pay Contests with Spillovers By Maria Betto; Matthew W. Thomas
  19. Misinformation: Strategic Sharing, Homophily, and Endogenous Echo Chambers By Daron Acemoglu; Asuman Ozdaglar; James Siderius
  20. The Optimal Length of Political Terms By Gersbach, Hans; Jackson, Matthew O.; Tejada, Oriol
  21. Electoral Competition with Costly Policy Changes: A Dynamic Perspective By Gersbach, Hans; Jackson, Matthew O.; Muller, Philippe; Tejada, Oriol
  22. The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects By Baldwin, Elizabeth; Edhan, Omer; Jagadeesan, Ravi; Klemperer, Paul; Teytelboym, Alex
  23. Coinsurance vs. copayments: reimbursement rules for a monopolistic medical product with competitive health insurers By Cremer, Helmuth; Lozachmeur, Jean-Marie
  24. Core and Stable Sets of Exchange Economies with Externalities By Maria Gabriella Graziano; Claudia Meo; Nicholas C. Yannelis
  25. The Value of a Coordination Game By Kets, Willemien; Kager, Wouter; Sandroni, Alvaro
  26. Optimal Lockdown in a Commuting Network By Fajgelbaum, Pablo; Khandelwal, Amit; Kim, Wookun; Mantovani, Cristiano; Schaal, Edouard

  1. By: Sémirat, S.; Forges, F.
    Abstract: We consider a sender-receiver game, in which the sender has finitely many types and the receiver's decision is a real number. We assume that utility functions are concave, single-peaked and single-crossing. After the cheap talk phase, the receiver makes a decision, which requires the sender's approval to be implemented. Otherwise, the sender "exits". At a perfect Bayesian equilibrium without exit, the receiver must maximize his expected utility subject to the participation constraints of all positive probability types. This necessary condition may not hold at the receiver's prior belief, so that a non-revealing equilibrium may fail to exist. Similarly, a fully revealing equilibrium may not exist either due to the sender's incentive compatibility conditions. We propose a constructive algorithm that always achieves a perfect Bayesian equilibrium without exit.
    JEL: C72 D82
    Date: 2021
  2. By: Stéphane Lemarié; Cecilia Vergari
    Abstract: We study the optimal monopoly pricing when consumers may buy one or two units of a good over two successive periods and their preferences evolve depending on past purchases and preference persistence. If the monopolist cannot discriminate between past and new buyers, he refrains from intertemporal price discrimination. Selling over two periods improves the monopoly profit as compared to the benchmark one-period equilibrium only for high preference persistence. Conversely, if the monopoly can discriminate between second period buyers, behavior-based price discrimination becomes profitable only for low preference persistence.
    Keywords: Repeated purchases, monopoly dynamic pricing, vertical differentiation
    JEL: L10 Q10
    Date: 2021–03–01
  3. By: Nobuo Koida (Faculty of Policy Studies, Iwate Prefectural University)
    Abstract: Much of the literature has argued that intransitive indifference is more likely to occur when alternatives have con icting criteria than when one alternative dominates the other. To study such a phenomenon, we first axiomatize the essentially unique expected utility with direction-dependent sensitivity (EUDS) representation on the set of lotteries which extend the classic models of imperfect discrimination (e.g., Fishburn, 1970a; Luce, 1956) to enable a direction-dependent just-noticeable di erence function. The key axioms in this characterization are irresolute independence, wherein mixing lternatives with another may (or may not) alter a strict preference for indifference while preserving indifference, and strict preference convexity, which obtains the convexity of strict upper and lower contour sets. Thereafter, we indicate that intransitive indifference in EUDS can be divided into that caused by imperfect discrimination (Fishburn, 1970a; Luce, 1956) and that caused by uncertainty about tastes (Dubra et al., 2004) by considering the transitive core (Nishimura, 2018) of EUDS. We also obtain two special cases of our model, i.e., one-directional and categorical sensitivity.
    Keywords: intransitive indifference, direction-dependence, incomplete preference, transitive core
    JEL: D81
    Date: 2021–06
  4. By: Baldwin, Elizabeth; Goldberg, Paul; Klemperer, Paul; Lock, Edwin
    Abstract: This paper develops algorithms to solve strong-substitutes product-mix auctions: it finds competitive equilibrium prices and quantities for agents who use this auction's bidding language to truthfully express their strong-substitutes preferences over an arbitrary number of goods, each of which is available in multiple discrete units. Our use of the bidding language, and the information it provides, contrasts with existing algorithms that rely on access to a valuation or demand oracle. We compute market-clearing prices using algorithms that apply existing submodular minimisation methods. Allocating the supply among the bidders at these prices then requires solving a novel constrained matching problem. Our algorithm iteratively simplifies the allocation problem, perturbing bids and prices in a way that resolves tie-breaking choices created by bids that can be accepted on more than one good. We provide practical running time bounds on both price-finding and allocation, and illustrate experimentally that our allocation mechanism is practical.
    Keywords: bidding language; Competitive Equilibrium; convex optimisation; product-mix auction; strong substitutes; submodular minimisation; Walrasian Equilibrium
    JEL: D44
    Date: 2020–06
  5. By: Daniele Pennesi (Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino, Italy)
    Abstract: This paper introduces and characterizes behaviorally a model of choice over menus of actions in which the individual experiences regret or elation if, after uncertainty resolves, the choice from the menu is inferior or superior to available alternatives. The revealed preference charac- terization of the model combines two contrasting forces: a preference for having fewer options in order to reduce ex post regret, and a preference for having more options in order to increase ex post elation. An application of the model to information acquisition shows that instrumen- tal information is always valuable. Anticipated elation drives an apparently irrational aversion to delegate choices to an informed agent. Lastly, anticipated elation also generates a desire to include options that will not be selected from the menu, a behavior that is often ascribed to naive time-inconsistency.
    Keywords: Regret, Elation, Flexibility, Commitment, Information.
    JEL: D01 D91
    Date: 2021–06
  6. By: Ernst Fehr; Keyu Wu
    Abstract: In many markets, firms make their products complex through add-ons, thus making them difficult to evaluate and compare. How does this product obfuscation affect competition, sellers’ profits, and buyers’ welfare? We study these questions in a competitive experimental market in which sellers have the opportunity to obfuscate by add-on features, and buyers endogenously decide how much time to spend on searching for the best product. We show that stable obfuscation levels emerge that reduce buyers’ welfare by ensuring that total prices are substantially above marginal cost and by inducing buyers to make mistakes and to waste their time searching. Competition operates through lowering salient headline prices, but sellers are able to appropriate a considerable share of the surplus with expensive add-on features. In contrast, prices quickly converge to marginal cost if we remove obfuscation opportunities. We thus provide direct causal evidence that obfuscation mitigates competition and generates positive profits because buyers typically search only a small share of the product space. Our results also suggest that purely exploitative obfuscation tends to be much less stable than obfuscation by surplus-enhancing add-on features because buyers’ aversion to complicated products may have a non-negligible impact on sellers’ obfuscation decisions.
    Date: 2021–06
  7. By: Salvador Barberà; Walter Bossert
    Abstract: In a world admitting a fixed finite set of alternatives, an opinion is an ordered pair of alternatives. Such a pair expresses the idea that one alternative is superior to another in some sense, and an opinion aggregator assigns a social relation on the set of alternatives to every possible multiset of opinions. Our primary motivation is to extend some basic results of social choice theory to a more general model in which no specific reference to agents generating or holding opinions is needed. It turns out that, although our analysis has some bearing on those cases where opinions reflect the preferences of agents in a society, it is not limited to them. In addition to the preference interpretation, opinions can also be used to represent other forms of comparative assessments. The main results of the paper provide characterizations of suitably defined versions of the Borda rule and the majority rule.
    Keywords: opinions, aggregation, majority rule, Borda rule, monotonicity
    JEL: D71 D72
    Date: 2021–06
  8. By: Jieming Mao; Renato Paes Leme; Kangning Wang
    Abstract: We define a model of interactive communication where two agents with private types can exchange information before a game is played. The model contains Bayesian persuasion as a special case of a one-round communication protocol. We define message complexity corresponding to the minimum number of interactive rounds necessary to achieve the best possible outcome. Our main result is that for bilateral trade, agents don't stop talking until they reach an efficient outcome: Either agents achieve an efficient allocation in finitely many rounds of communication; or the optimal communication protocol has infinite number of rounds. We show an important class of bilateral trade settings where efficient allocation is achievable with a small number of rounds of communication.
    Date: 2021–06
  9. By: Mikhail Freer; Cesar Martinelli
    Abstract: We propose and develop an algebraic approach to revealed preference. Our approach dispenses with non algebraic structure, such as topological assumptions. We provide algebraic axioms of revealed preference that subsume previous, classical revealed preference axioms, as well as generate new axioms for behavioral theories, and show that a data set is rationalizable if and only if it is consistent with an algebraic axiom.
    Date: 2021–05
  10. By: Henrique de Oliveira; Yuhta Ishii; Xiao Lin
    Abstract: When multiple sources of information are available, any decision must take into account their correlation. If information about this correlation is lacking, an agent may find it desirable to make a decision that is robust to possible correlations. Our main results characterize the strategies that are robust to possible hidden correlations. In particular, with two states and two actions, the robustly optimal strategy pays attention to a single information source, ignoring all others. More generally, the robustly optimal strategy may need to combine multiple information sources, but can be constructed quite simply by using a decomposition of the original problem into separate decision problems, each requiring attention to only one information source. An implication is that an information source generates value to the agent if and only if it is best for at least one of these decomposed problems.
    Date: 2021–05
  11. By: Letina, Igor; Liu, Shuo; Netzer, Nick
    Abstract: We consider the design of contests for n agents when the principal can choose both the prize profile and the contest success function. Our framework includes Tullock contests, Lazear-Rosen tournaments and all-pay contests as special cases, among others. We show that the optimal contest has an intermediate degree of competitiveness in the contest success function, and a minimally competitive prize profile with n-1 identical prizes. The optimum can be achieved with a nested Tullock contest. We extend the model to allow for imperfect performance measurement and for heterogeneous agents. We relate our results to a recent literature which has asked similar questions but has typically focused on the design of either the prize profile or the contest success function.
    Keywords: contest design; optimal contests; tournaments
    JEL: D02 D82 M52
    Date: 2020–06
  12. By: Salvador Barberà; Danilo Coelho
    Abstract: We propose three mechanisms to reach compromise between two opposing par- ties. They are based on the use of Rules of k Names, whereby one of the parties proposes a shortlist and the other chooses from it. Methods of this class are used in practice to appoint Supreme Court justices and have been recently proposed for arbitration selection processes. Our mechanisms are flexible and allow the parties to participate in the endogenous determination of the role of proposer and the shortlist size. They involve few stages, weakly implement the Unanimity Compromise Set and are robust to the strategic inclusion of candidates.
    Keywords: The Unanimity Compromise Set, Compromise Rule of k Names, shortlisting contest, alternate shortlists, shortlisting, voting by alternating offers, and vetoes and fallback bargaining
    JEL: D02 D71 D72
    Date: 2021–06
  13. By: Ely, Jeffrey; Galeotti, Andrea; Steiner, Jakub
    Abstract: We study rotation schemes that govern individuals' activities within an organization during an epidemic. We optimize the frequency of rotation and degree of cross-mixing of the rotating subpopulations. Frequency affects risk over the length of diffusion within the infected subpopulation until the organization detects and/or reacts to the infection. If the reaction time is short, then such risk is undesirable since the growth of the prevalence is initially convex in time. Frequent rotation, which acts as insurance against exposure time risk, is then optimal. Infrequent rotation becomes optimal if the organization reacts slowly. Mixing of the rotating subpopulations is detrimental because it increases the share of interactions between sick and healthy individuals. However, the effect of mixing is small if the terminal prevalence is low in the absence of mixing.
    Keywords: epidemic mitigation; rotation
    JEL: I18
    Date: 2020–06
  14. By: Evensen, Charlotte Bjørnhaug (Dept. of Economics, Norwegian School of Economics and Business Administration); Haugen, Atle (Dept. of Economics, Norwegian School of Economics and Business Administration)
    Abstract: Abstract In this paper, we address how targeting and consumer multi-homing impact platform competition and market equilibria in two-sided markets. We analyze platforms that are financed by both advertising and subscription fees, and let them adopt a targeting technology with increasing performance in audience size: a larger audience generates more consumer data, which improves the platforms’ targeting ability and allows them to extract more ad revenues. Targeting therefore increases the importance of attracting consumers. Previous literature has shown that this could result in fierce price competition if consumers subscribe to only one platform (i.e. single-home). Surprisingly, we find that pure single-homing possibly does not constitute a Nash equilibrium. Instead, platforms might rationally set prices that induce consumers to subscribe to more than one platform (i.e. multi-home). With multi-homing, a platform’s audience size is not restricted by the number of subscribers on rival platforms. Hence, multi-homing softens the competition over consumers. We show that this might imply that equilibrium profit is higher with than without targeting, in sharp contrast to what previous literature predicts.
    Keywords: Two-sided markets; digital platforms; targeted advertising; incremental pricing; consumer multi-homing.
    JEL: D11 D21 L13 L82
    Date: 2021–06–10
  15. By: Ville Korpela; Michele Lombardi; Riccardo D. Saulle
    Abstract: We study rotation programs within the standard implementation frame-work under complete information. A rotation program is a myopic stableset whose states are arranged circularly, and agents can effectively moveonly between two consecutive states. We provide characterizing conditionsfor the implementation of efficient rules in rotation programs. Moreover,we show that the conditions fully characterize the class of implementablemulti-valued and efficient rules
    Date: 2021–05
  16. By: Gerardi, Dino; Maestri, Lucas; Monzon, Ignacio
    Abstract: We study bargaining with divisibility and interdependent values. A buyer and a seller trade a durable good divided into finitely many units. The seller is privately informed about the good's quality, which can be either high or low. Gains from trade are positive and decreasing in the number of units traded by the parties. In every period, the buyer makes a take-it-or-leave-it offer that specifies a price and a number of units. Divisibility introduces a new channel of competition between the buyer's present and future selves. The buyer's temptation to split the purchases of the high-quality good is detrimental to him. As bargaining frictions vanish and the good becomes arbitrarily divisible, the high-quality good is traded smoothly over time and the buyer's payoff shrinks to zero.
    Keywords: Bargaining; Coase conjecture; divisible objects; gradual sale; interdependent valuations; market for lemons
    Date: 2020–06
  17. By: Wei He; Xiang Sun; Yeneng Sun; Yishu Zeng
    Abstract: This paper studies Bayesian games with general action spaces, correlated types and interdependent payoffs. We introduce the condition of ``decomposable coarser payoff-relevant information'', and show that this condition is both sufficient and necessary for the existence of pure-strategy equilibria and purification from behavioral strategies. As a consequence of our purification method, a new existence result on pure-strategy equilibria is also obtained for discontinuous Bayesian games. Illustrative applications of our results to oligopolistic competitions and all-pay auctions are provided.
    Date: 2021–06
  18. By: Maria Betto; Matthew W. Thomas
    Abstract: When opposing parties compete for a prize, the sunk effort players exert during the conflict can affect the value of the winner's reward. These spillovers can have substantial influence on the equilibrium behavior of participants in applications such as lobbying, warfare, labor tournaments, marketing, and R&D races. To understand this influence, we study a general class of asymmetric, two-player all-pay contests where we allow for spillovers in each player's reward. The link between participants' efforts and rewards yields novel effects -- in particular, players with higher costs and lower values than their opponent sometimes extract larger payoffs.
    Date: 2021–06
  19. By: Daron Acemoglu; Asuman Ozdaglar; James Siderius
    Abstract: We present a model of online content sharing where agents sequentially observe an article and must decide whether to share it with others. The article may contain misinformation, but at a cost, agents can fact-check it to determine whether its content is entirely accurate. While agents derive value from future shares, they simultaneously fear getting caught sharing misinformation. With little homophily in the “sharing network”, misinformation is often quickly identified and brought to an end. However, when homophily is strong, so that agents anticipate that only those with similar beliefs will view the article, misinformation spreads more rapidly because of echo chambers. We show that a social media platform that wishes to maximize content engagement will propagate extreme articles amongst the most extremist users, while not showing these articles to ideologically opposed users. This creates an endogenous echo chamber—filter bubble—that makes misinformation spread virally. We use this framework to understand how regulation can encourage more fact-checking by online users and mitigate the consequences of filter bubbles.
    JEL: D83 D85 P16
    Date: 2021–06
  20. By: Gersbach, Hans; Jackson, Matthew O.; Tejada, Oriol
    Abstract: We analyze the optimal length of political terms (equivalently, the optimal frequency with which elections should be held) when the candidates of two polarized parties compete for office and the median voter shifts over time. Office-holders determine policy and experience persistent random shocks to their valence. Policy changes are costly for citizens and politicians. Optimal term-length balances the frequency of costly policy changes when parties change office with the incumbent's average valence during tenure. We find that optimal term-length increases with party polarization, with the degree to which the median voter cares about valence, and with the frequency and the size of swings in the electorate. In contrast, optimal term-length decreases when candidates for office undergo less scrutiny or when parties care more about future outcomes. Finally, with small swings in the electorate and large polarization, optimal term-length increases if checks and balances increase.
    Keywords: costs of change; Elections; Polarization; term-length
    JEL: C72 C73 D72 D78
    Date: 2020–06
  21. By: Gersbach, Hans; Jackson, Matthew O.; Muller, Philippe; Tejada, Oriol
    Abstract: We analyze dynamic electoral competition policy changes. The costs of changing a policy increase with the extent of the shift and generate an incumbency advantage. We characterize the dynamics of Markov equilibria in terms of history and party polarization, and analyze how policies are influenced by the amplitude and convexity of costs of change, as well as by the degree of party and voter farsightedness. Regardless of the initial policy, party choices converge in the long run to a stochastic alternation between two (regions of) policies, with transitions occurring when office-holders suffer a shock to their capacity or valence. Although costs of change have a moderating effect on policies, full convergence to the median voter position does not take place.
    Keywords: costs of change; democracy; dynamic elections; Markov perfect equilibrium; Political Polarization
    JEL: C72 C73 D72 D78
    Date: 2020–06
  22. By: Baldwin, Elizabeth; Edhan, Omer; Jagadeesan, Ravi; Klemperer, Paul; Teytelboym, Alex
    Abstract: We show that, with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents' substitution effects, not their income effects. Our Equilibrium Existence Duality allows us to transport results on the existence of competitive equilibrium from settings with transferable utility to settings with income effects. One consequence is that net substitutability-which is a strictly weaker condition than gross substitutability-is sufficient for the existence of competitive equilibrium. We also extend the "demand types" classification of valuations to settings with income effects and give necessary and sufficient conditions for a pattern of substitution effects to guarantee the existence of competitive equilibrium.
    JEL: C62 D11 D44
    Date: 2020–06
  23. By: Cremer, Helmuth; Lozachmeur, Jean-Marie
    Abstract: This paper studies a market for a medical product in which there is perfect competition among health insurers, while the good is sold by a monopolist. Individuals di¤er in their severity of illness and there is ex post moral hazard. We consider two regimes: one in which insurers use coinsurance rates (ad valorem reimbursements) and one in which insurers use copayments (specic reimbursements). We show that the induced equilibrium with copayments involves a lower producer price and a higher level of wel- fare for consumers. This results provides strong support for a reference price based reimbursement policy.
    Keywords: Ex post moral hazard; health insurance competition; copayments; imper-; fect competition
    JEL: I11 I13 I18
    Date: 2021–05
  24. By: Maria Gabriella Graziano (Università di Napoli Federico II and CSEF); Claudia Meo (Università di Napoli Federico II); Nicholas C. Yannelis (University of Iowa)
    Abstract: It is known that the core of an economy with externalities may be empty. We consider two concepts of dominance that allow us to prove that the set formed by individually rational, Pareto optimal allocations is stable and coincides with the core that, consequently, is non-empty.
    Keywords: Other-regarding Preferences; Externalities; Stable Sets; Core.
    JEL: C71 D51 D70
    Date: 2021–06–16
  25. By: Kets, Willemien (University of Oxford); Kager, Wouter; Sandroni, Alvaro
    Abstract: The value of a game is the payoff a player can expect (ex ante) from playing the game. Understanding how the value changes with economic primitives is critical for policy design and welfare. However, for games with multiple equilibria, the value is difficult to determine. We therefore develop a new theory of the value of coordination games. The theory delivers testable comparative statics on the value and delivers novel insights relevant to policy design. For example, policies that shift behavior in the desired direction can make everyone worse off, and policies that increase everyone's payoffs can reduce welfare.
    Date: 2021–06–03
  26. By: Fajgelbaum, Pablo; Khandelwal, Amit; Kim, Wookun; Mantovani, Cristiano; Schaal, Edouard
    Abstract: We study optimal dynamic lockdowns against Covid-19 within a commuting network. Our framework combines canonical spatial epidemiology and trade models, and is applied to cities with varying initial viral spread: Seoul, Daegu and NYC-Metro. Spatial lockdowns achieve substantially smaller income losses than uniform lockdowns, and are not easily approximated by simple centrality-based rules. In NYM and Daegu-with large initial shocks-the optimal lockdown restricts inflows to central districts before gradual relaxation, while in Seoul it imposes low temporal but large spatial variation. Actual commuting responses were too weak in central locations in Daegu and NYM, and too strong across Seoul.
    Keywords: commuting; COVID-19; General Equilibrium; lockdown; optimal policy
    JEL: C6 R38 R4
    Date: 2020–06

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