
on Microeconomics 
By:  Joseph Y. Halpern; Yuval Heller; Eyal Winter 
Abstract:  We study the strategic advantages of coarsening one's utility by clustering nearby payoffs together (i.e., classifying them the same way). Our solution concept, coarseutility equilibrium (CUE) requires that (1) each player maximizes her coarse utility, given the opponent's strategy, and (2) the classifications form best replies to one another. We characterize CUEs in various games. In particular, we show that there is a qualitative difference between CUEs in which only one of the players clusters payoffs, and those in which all players cluster their payoffs, and that the latter type induce players to treat coplayers better than in Nash equilibria in the large class of games with monotone externalities. 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2201.10141&r= 
By:  Peter Bayer (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Ani Guerdjikova (GAEL  Laboratoire d'Economie Appliquée de Grenoble  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement  UGA  Université Grenoble Alpes  Grenoble INP  Institut polytechnique de Grenoble  Grenoble Institute of Technology  UGA  Université Grenoble Alpes) 
Abstract:  We analyze a model of endogenous twosided network formation where players are affected by uncertainty in their opponents' decisions. We model this uncertainty using the notion of equilibrium under ambiguity. Unlike the set of Nash equilibria, the set of equilibria under ambiguity does not always include underconnected and thus inefficient networks such as the empty network. On the other hand, it may include networks with unreciprocated, oneway links, which comes with an efficiency loss as linking efforts are costly. We characterize equilibria under ambiguity and provide conditions under which increased player optimism comes with an increase in connectivity and realized benefits in equilibrium. Next, we analyze network realignment under a myopic updating process with optimistic shocks, and derive a global stability condition of efficient networks. Under this condition, called ‘aligned preferences', a subset of the Pareto optimal equilibrium networks is reached, specifically, networks that maximize the players' total benefits of connections. 
Date:  2022–01–25 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03542373&r= 
By:  S. Nageeb Ali; Navin Kartik; Andreas Kleiner 
Abstract:  We study sequential bargaining between a proposer and a veto player. Both have singlepeaked preferences, but the proposer is uncertain about the veto player's ideal point. The proposer cannot commit to future proposals. When players are patient, there can be equilibria with Coasian dynamics: the veto player's private information can largely nullify proposer's bargaining power. Our main result, however, is that there are also equilibria in which the proposer obtains the high payoff that he would with commitment power. The driving force is that the veto player's singlepeaked preferences give the proposer an option to "leapfrog", i.e., to secure agreement from only lowsurplus types early on to credibly extract surplus from high types later. Methodologically, we exploit the connection between sequential bargaining and static mechanism design. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.02462&r= 
By:  Daniel F. Garrett (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Renato Gomes (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Lucas Maestri (FGVEPGE  Universidad de Brazil) 
Abstract:  We study competition by firms that simultaneously post (potentially nonlinear) taris to consumers who are privately informed about their tastes. Market power stems from informational frictions, in that consumers are heterogeneously informed about firms' oers. In the absence of regulation, all firms oer quantity discounts. As a result, relative to Bertrand pricing, imperfect competition benefits disproportionately more consumers whose willingness to pay is high, rather than low. Regulation imposing linear pricing hurts the former but benefits the latter consumers. While consumer surplus increases, firms' profits decrease, enough to drive down utilitarian welfare. By contrast, improvements in market transparency increase utilitarian welfare, and achieve similar gains on consumer surplus as imposing linear pricing, although with limited distributive impact. On normative grounds, our analysis suggests that banning price discrimination is warranted only if its distributive benefits have a weight on the societal objective. 
Keywords:  Asymmetric information,Informational frictions,Linear pricing,Nonlinear pricing,Oligopoly 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03515749&r= 
By:  Peter Bayer (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); György Kozics (Unknown); Nora Gabriella Szöke (Unknown) 
Abstract:  We study public goods games played on networks with possibly nonreciprocal relationships between players. Examples for this type of interactions include onesided relationships, mutual but unequal relationships, and parasitism. It is well known that many simple learning processes converge to a Nash equilibrium if interactions are reciprocal, but this is not true in general for directed networks. However, by a simple tool of rescaling the strategy space, we generalize the convergence result for a class of directed networks and show that it is characterized by transitive weight matrices and quadratic bestresponse potentials. Additionally, we show convergence in a second class of networks; those rescalable into networks with weak externalities. We characterize the latter class by the spectral properties of the absolute value of the network's weight matrix and by another bestresponse potential structure. 
Keywords:  Potential games,Local public goods,Externalities,Networks,Nonreciprocal relations 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03542533&r= 
By:  Charlson, G. 
Abstract:  A platform holds information on the demographics of its users and wants maximise total surplus. The data generates a probability over which of two products a buyer prefers, with different data segmentations being more or less informative. The platform reveals segmentations of the data to two firms, one popular and one niche, preferring to reveal no information than completely revealing the consumer's type for certain. The platform can improve profits by revealing to both firms a segmentation where the niche firm is relatively popular, but still less popular than the other firm, potentially doing even better by revealing information asymmetrically. The platform has an incentive to provide more granular data in markets in which the niche firm is particularly unpopular or in which broad demographic categories are not particularly revelatory of type, suggesting that the profit associated with big data techniques differs depending on market characteristics. 
Keywords:  Strategic interaction, network games, interventions, industrial organisation, platforms, hypergraphs 
JEL:  D40 L10 L40 
Date:  2021–08–19 
URL:  http://d.repec.org/n?u=RePEc:cam:camjip:2104&r= 
By:  Jiehua Chen; Martin N\"ollenburg; Sofia Simola; Ana\"is Villedieu; Markus Wallinger 
Abstract:  A preference profile with $m$ alternatives and $n$ voters is $d$Manhattan (resp. $d$Euclidean) if both the alternatives and the voters can be placed into the $d$dimensional space such that between each pair of alternatives, every voter prefers the one which has a shorter Manhattan (resp. Euclidean) distance to the voter. Following Bogomolnaia and Laslier [Journal of Mathematical Economics, 2007] and Chen and Grottke [Social Choice and Welfare, 2021] who look at $d$Euclidean preference profiles, we study which preference profiles are $d$Manhattan depending on the values $m$ and $n$. First, we show that each preference profile with $m$ alternatives and $n$ voters is $d$Manhattan whenever $d$ $\geq$ min($n$, $m$$1$). Second, for $d = 2$, we show that the smallest non $d$Manhattan preference profile has either three voters and six alternatives, or four voters and five alternatives, or five voters and four alternatives. This is more complex than the case with $d$Euclidean preferences (see [Bogomolnaia and Laslier, 2007] and [Bulteau and Chen, 2020]. 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2201.09691&r= 
By:  Ding, S.; Dziubinski, M.; Goyal, S. 
Abstract:  A recurring theme in the study of society is the concentration of influence and power that is driven through unequal membership of groups and associations. In some instances these bodies constitute a small world while in others they are fragmented into distinct cliques. This paper presents a new model of clubs and networks to understand the sources of individual marginalization and the origins of different club networks. In our model, individuals seek to become members of clubs while clubs wish to have members. Club value is increasing in its size and in the strength of ties with other clubs. We show that a stable membership profile exhibits marginalization of individuals and that this is generally not welfare maximizing. Our second result shows that if returns from strength of ties are convex (concave) then stable memberships support fragmented networks with strong ties (small worlds held together by weak ties). We illustrate the value of these theoretical results through case studies of interlocking directorates, boards of editors of journals, and defence and R&D alliances. 
Date:  2021–10–25 
URL:  http://d.repec.org/n?u=RePEc:cam:camjip:2109&r= 
By:  Saglam, Ismail 
Abstract:  Can a monopoly persist by expanding its operation to a new market after strategically bidding for an exclusive license under the threat of supply function competition with a potential entrant? The answer may be yes or no depending on how the monopolist's existing product and the new product are related. The monopolist can win the bidding for the new market and thus expand its operation if the marginal cost (to produce a unit output) is sufficiently low with respect to the degree of product differentiation, while its likelihood of winning is higher if the two products are substitutes than if they are complements. 
Keywords:  Monopoly persistence; supply function competition; strategic bidding. 
JEL:  D42 D43 L13 
Date:  2022–02–04 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:111829&r= 
By:  Hiroki Shinozaki 
Abstract:  We consider the problem of allocating multiple units of an indivisible object among a set of agents and collecting payments. Each agent can receive multiple units of the object, and has a (possibly) nonquasilinear preference on the set of (consumption) bundles. We assume that preferences exhibit both nonincreasing marginal valuations and nonnegative income effects. We propose a new property of fairness: no price envy. It extends the standard no envy test (Foley, 1967) over bundles to prices (perunit payments), and requires no agent envy other agents' prices to his own in the sense that if he has a chance to receive some units at other agents' prices, then he gets better off than his own bundle. First, we show that a rule satisfies no price envy and no subsidy for losers if and only if it is an inverse uniformprice rule. Then, we identify the unique maximal domain for no price envy, strategyproofness, and no subsidy for losers: the domain with partly constant marginal valuations. We further establish that on the domain with partly constant marginal valuations, a rule satisfies no price envy, strategyproofness, and no subsidy for losers if and only if it is a minimum inverse uniformprice rule. Our maximal domain result implies that no rule satisfies no price envy, strategyproofness, and no subsidy for losers when agents have preferences with nonincreasing marginal valuations. Given this negative observation, we look for a minimally manipulable rule among the class of rules satisfying both no price envy and no subsidy for losers in the case of preferences with nonincreasing marginal valuations. We show that a rule is minimally manipulable among the class of rules satisfying no price envy and no subsidy for losers if and only if it is a minimum inverse uniformprice rule. Our results provide a rationale for the use of the popular minimum uniformprice rule in terms of fairness and nonmanipulability. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:dpr:wpaper:1164&r= 
By:  Emilien Macault 
Abstract:  We propose a stochastic model of opinion exchange in networks. A finite set of agents is organized in a fixed network structure. There is a binary state of the world and each agent receives a private signal on the state. We model beliefs as urns where red balls represent one possible value of the state and blue balls the other value. The model revolves purely around communication and beliefs dynamics. Communication happens in discrete time and, at each period, agents draw and display one ball from their urn with replacement. Then, they reinforce their urns by adding balls of the colors drawn by their neighbors. We show that for any network structure, this process converges almostsurely to a stable state. Futher, we show that if the communication network is connected, this stable state is such that all urns have the same proportion of balls. This result strengthens the main convergence properties of nonBayesian learning models. Yet, contrary to those models, we show that this limit proportion is a fullsupport random variable. This implies that an arbitrarily small proportion of misinformed agents can substantially change the value of the limit consensus. We propose a set of conjectures on the distribution of this limit proportion based on simulations. In particular, we show evidence that the limit belief follows a beta distribution and that its average value is independent from the network structure. 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2201.12100&r= 
By:  M\'ario S. Alvim; Konstantinos Chatzikokolakis; Yusuke Kawamoto; Catuscia Palamidessi 
Abstract:  A common goal in the areas of secure information flow and privacy is to build effective defenses against unwanted leakage of information. To this end, one must be able to reason about potential attacks and their interplay with possible defenses. In this paper, we propose a gametheoretic framework to formalize strategies of attacker and defender in the context of information leakage, and provide a basis for developing optimal defense methods. A novelty of our games is that their utility is given by information leakage, which in some cases may behave in a nonlinear way. This causes a significant deviation from classic game theory, in which utility functions are linear with respect to players' strategies. Hence, a key contribution of this paper is the establishment of the foundations of information leakage games. We consider two kinds of games, depending on the notion of leakage considered. The first kind, the QIFgames, is tailored for the theory of quantitative information flow (QIF). The second one, the DPgames, corresponds to differential privacy (DP). 
Date:  2020–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2012.12060&r= 
By:  Pavel Ilinov; Ole Jann 
Abstract:  We consider two types of models: (i) a rational inattention problem (as known from the literature) and (ii) a conformity game, in which fully informed players find it costly to deviate from average behavior. We show that these problems are equivalent to each other both from the perspective of the participant and the outside observer: Each individual faces identical tradeoffs in both situations, and an observer would not be able to distinguish the two models from the choice data they generate. We also establish when individual behavior in the conformity game maximizes welfare. 
Keywords:  conformity; equivalence; rational inattention; social norms; 
JEL:  D81 D83 D91 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:cer:papers:wp719&r= 
By:  Chiara Fumagalli (Università Bocconi, CSEF and CEPR); Massimo Motta (ICREAUniversitat Pompeu Fabra and Barcelona Graduate School of Economics); Emanuele Tarantino (Luiss University, EIEF and CEPR) 
Abstract:  A startup and an incumbent negotiate over an acquisition price under asymmetric information about the startup's ability to succeed in the market. The acquisition may result in the shelving of the startup's project or the development of a project that would otherwise never reach the market because of financial constraints. Despite this possible procompetitive effect, the optimal merger policy commits to standards of review that prohibit highprice takeovers, even if they may be welfarebeneficial ex post. Ex ante this pushes the incumbent to acquire startups lacking the financial resources to develop independently, and increases expected welfare. 
Keywords:  Optimal merger policy, selection effect, nascent competitors. 
JEL:  L41 L13 K21 
Date:  2022–02–09 
URL:  http://d.repec.org/n?u=RePEc:sef:csefwp:637&r= 