nep-mic New Economics Papers
on Microeconomics
Issue of 2021‒11‒08
eight papers chosen by
Jing-Yuan Chiou
National Taipei University

  1. Keeping the Agents in the Dark: Private Disclosures in Competing Mechanisms By Andrea Attar; Eloisa Campioni; Thomas Mariotti; Alessandro Pavan
  2. Public-Good Provision with Macro Uncertainty about Preferences: Efficiency, Budget Balance, and Robustness By Martin F. Hellwig
  3. Characterizing Robust Solutions in Monotone Games By Anne-Christine Barthel; Eric Hoffmann; Tarun Sabarwal
  4. Bitcoin selection rule and foundational game theoretic representation of mining competition By A. Mantovi
  5. Social Choice in Large Populations with Single-Peaked Preferences By Martin F. Hellwig
  6. A Sufficient Statistics Approach for Welfare Analysis of Oligopolistic Third-Degree Price Discrimination By Takanori ADACHI; Michal FABINGER
  7. Crowding in School Choice By William PHAN; Ryan TIERNEY; Yu ZHOU
  8. Effects of Defensive and Proactive Measures on Competition Between Terrorist Groups By Subhayu Bandyopadhyay; Todd Sandler

  1. By: Andrea Attar (CEIS & DEF University of Rome "Tor Vergata" and Toulouse School of Economics); Eloisa Campioni (CEIS & DEF University of Rome "Tor Vergata" and Toulouse School of Economics); Thomas Mariotti (Toulouse School of Economics, CNRS); Alessandro Pavan (Northwestern University, Evanston)
    Abstract: We study games in which several principals contract with several privately-informed agents. We show that enabling the principals to engage in contractible private disclosures {by sending private signals to the agents about how the mechanisms will respond to the agents' messages { can significantly affect the predictions of such games. Our first result shows that private disclosures may generate equilibrium outcomes that cannot be supported in any game without private disclosures, no matter the richness of the message spaces and the availability of public randomizing devices. The result thus challenges the canonicity of the universal mechanisms of Epstein and Peters (1999). Our second result shows that equilibrium outcomes of games without private disclosures need not be sustainable when private disclosures are allowed. The result thus challenges the robustness of the \folk theorems" of Yamashita (2010) and Peters and Troncoso-Valverde (2013). These findings call for a novel approach to the analysis of competing-mechanism games.
    Keywords: Incomplete Information, Competing Mechanisms, Private Disclosures, Signals, Universal Mechanisms, Folk Theorems.
    JEL: D82
    Date: 2021–10–21
  2. By: Martin F. Hellwig (Max Planck Institute for Research on Collective Goods)
    Abstract: The paper studies efficient public-good provision in a model with private values whose distribution depends on a macro shock; conditionally on this shock, values are independent and identically distributed. A generalization of the Bayesian mechanism of d'Aspremont and Gérard-Varet is shown to implement an efficient provision rule with budget balance. However, first-best implementation and budget balance are incompatible with a reqruirement of weak robustness whereby incentive compatibility of the mechanism is independent of the stochastic specification within the class of specifications defined by the structure of the model. Budget imbalances with robust implementation are small if there are many participants, as surplus from the Clarke-Groves mechanism converges to zero in probability when the number of participants becomes large. In the limit, with a continuum of agents, a first-best provision rule with equal cost sharing is robustly incentive-compatible. In this limit, information about the macro shock, which is the only thing that matters for public-good provision, can be elicited without any efficiency loss.
    Keywords: Efficient public-good provision, incomplete information, conditionally independent private values, macro uncertainty, budget balance, weakly robust incentive compatibility
    Date: 2021–10–13
  3. By: Anne-Christine Barthel (Department of Economics, *West Texas A&M University, Canyon, TX 79016, USA); Eric Hoffmann (Department of Economics, *West Texas A&M University, Canyon, TX 79016, USA); Tarun Sabarwal (Department of Economics, University of Kansas, Lawrence, KS 66045, USA)
    Abstract: In game theory, p-dominance and its set-valued generalizations serve as important robust solution concepts. We show that in monotone games, (which include the broad classes of super-modular games, sub-modular games, and their combinations,) these concepts can be characterized in terms of pure strategy Nash equilibria in an auxiliary game of complete information. The auxiliary game is constructed in a transparent manner that is easy to follow and retains a natural connection to the original game. Our results show explicitly how to map these concepts to a corresponding Nash equilibrium thereby identifying a new bijection between robust solutions in the original game and equilibrium notions in the auxiliary game. Moreover, our characterizations lead to new results about the structure of entire classes of such solution concepts. In games with strategic complements, these classes are complete lattices. More generally, they are totally unordered. We provide several examples to highlight these results.
    Keywords: p-dominance, p-best response set, minimal p-best response set, strategic complements, strategic substitutes
    JEL: C62 C72
    Date: 2021–02
  4. By: A. Mantovi
    Abstract: The Bitcoin selection rule shapes the basic mining (rent-seeking) competition, whose unique Nash equilibrium has been thoroughly investigated in terms of best responses to the overall scale of activity and entry thresholds. It is the aim of the present contribution to deepen such game theoretic aspects of Proof-of-Work and provide a unifying perspective on approaches employing absolute and relative levels of activity, and envision a ‘map’ of strategic space that may frame and cross-fertilize more realistic refinements of mining competition and blockchain phenomenology. The additive aggragation property of the selection rule has pivotal implications for thorough investigations of best response dynamics. Potential lines of progress are briefly sketched.
    Keywords: Blockchain; Proof-of-Work; Rent Seeking; Nash Equilibrium; Additive Aggregation;Best Response Dynamics
    JEL: C72 D82 E42 O33
    Date: 2021
  5. By: Martin F. Hellwig (Max Planck Institute for Research on Collective Goods)
    Abstract: Anonymous social choice function for a large atomless population maps cross-section distributions of preferences into outcomes. Because any one individual is too insignificant to a¤ect these distributions, every anonymous social choice function is individually strategy-proof. However, not every anonymous social choice function is group strategy-proof. If the set of outcomes is linearly ordered and participants have single-peaked preferences, an anonymous social choice function is group strategy-proof if and only if it can be implemented by a mechanism involving binary votes between neighbouring outcomes with nondecreasing thresholds for "moving higher up". Such a mechanism can be interpreted as a version of Moulin's (1980) generalized median-voter mechanism for a large population.
    Keywords: Social choice, large populations, strategy proofness, group strategy proofness, single-peaked preferences
    Date: 2021–10–13
  6. By: Takanori ADACHI; Michal FABINGER
    Abstract: This paper proposes a sufficient statistics approach to welfare analysis of third-degree price discrimination in differentiated oligopoly. Specifically, our sufficient conditions for price discrimination to increase or decrease aggregate output, social welfare, and con-sumer surplus simply entail a cross-market comparison of multiplications of two or three of the sufficient statistics—pass-through, conduct, and profit margin—that are functions of first-order and second-order elasticities of the firm’s demand. Notably, these results are derived under a general class of demand, and can be readily be extended to accom-modate heterogeneous firms. These features suggest that our approach has potential for conducting welfare analysis without a full specification of an oligopoly model.
    Keywords: Third-Degree Price Discrimination; Oligopoly; Sufficient Statistics.
    JEL: D43 L11 L13
    Date: 2021–10
  7. By: William PHAN; Ryan TIERNEY; Yu ZHOU
    Abstract: We consider the problem of matching students to schools when students are able to express preferences over crowding. For example, schools have varying per capita expenditures, average teacherstudent ratios, etc. These characteristics of a school are now endogenously determined—matchings with more students to a particular school decrease each of the variables above. We propose a new equilibrium notion, the Rationing Crowding Equilibrium (RCE), that accommodates crowding, noenvy, and respect for priorities. We prove the existence of RCE under mild domain conditions, and establish a Rural Hospitals Theorem and welfare lattice result on the set of RCE. The latter implies the existence of a maximal RCE, and that such RCE are studentoptimal. Moreover, the mechanism defined by selection from the maximal RCE correspondence is strategyproof. We also identify an algorithm to find a maximal RCE for a natural subdomain.
    Keywords: School choice with crowding; Rationing crowding equilibrium; Student optimality;Strategyproofness
    JEL: C78 D47 D62 I20
    Date: 2021–10
  8. By: Subhayu Bandyopadhyay; Todd Sandler
    Abstract: A two-stage game investigates how counterterrorism measures affect within-country competition between two rival terrorist groups. Although such competition is commonplace (e.g., al-Nusra Front and Free Syria Army; Revolutionary Armed Forces of Colombia and the National Liberation Army; and al-Fatah and Hamas), there is no theoretical treatment of how proactive and defensive measures influence this interaction. Previous studies on rival terrorist groups are solely empirical concerning group survival, outbidding, and terrorism level, while ignoring the role that government countermeasures exert on the rival groups’ terrorism. In a theoretical framework, alternative counterterrorism actions have diverse impacts on the level of terrorism depending on relative group sizes and government-targeting decisions. In the two-stage game, optimal counterterrorism policy rules are displayed in terms of how governments target symmetric and asymmetric terrorist groups. Comparative statics show how parameter changes affect Nash or subgame perfect equilibrium outcomes.
    Keywords: competitive terrorist groups; defensive and proactive counterterrorism; two-stage game; comparative statics; outbidding between rival groups
    Date: 2021–06–17

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