
on Microeconomics 
By:  Gonzalo Cisternas; Aaron Kolb 
Abstract:  We study dynamic signaling when the informed party does not observe the signals generated by her actions. A longrun player signals her type continuously over time to a myopic second player who privately monitors her behavior; in turn, the myopic player transmits his private inferences back through an imperfect public signal of his actions. Preferences are linearquadratic and the information structure is Gaussian. We construct linear Markov equilibria using belief states up to the longrun player's $\textit{secondorder belief}$. Because of the private monitoring, this state is an explicit function of the longrun player's past play. A novel separation effect then emerges through this secondorder belief channel, altering the traditional signaling that arises when beliefs are public. Applications to models of leadership, reputation, and trading are examined. 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2007.15514&r=all 
By:  Salvadori, Neri; De Francesco, Massimo A. 
Abstract:  This paper studies BertrandEdgeworth competition among firms producing a homogeneous commodity under efficient rationing and constant (andidentical across firms) marginal cost until full capacity utilization is reached. Our focus is on a subset of the no purestrategy equilibrium region of the capacity space in which, in a welldefined sense, some firms are large and the others are small. We characterize equilibria for such subset. For each firm, the payoffs are the same at any equilibrium and, for each type of firm, they are proportional to capacity. While there is a single profile of equilibrium distributions for the large firms, there is a continuum of equilibrium distributions for the small firms: what is uniquely determined, for the latter, is the capacityweighted sum of their equilibrium distributions and hence the union of the supports of their equilibrium strategies. 
Keywords:  BertrandEdgeworth oligopoly; mixed strategy equilibrium; large and small firms 
JEL:  C72 D43 L13 
Date:  2020–08–05 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:102274&r=all 
By:  Egor Starkov (University of Copenhagen) 
Abstract:  This paper explores a model of dynamic signaling without commitment. It is known that separating equilibria do not exist if the sender cannot commit to future costly actions, since no single action can have enough weight to be an effective signal. This paper, however, shows that informative and payoffrelevant signaling can occur even without commitment and without resorting to unreasonable offpath beliefs. Such signaling can only happen through attrition, when the weakest type mixes between revealing own type and pooling with the stronger types. The possibility of full information revelation in the limit hence depends crucially on the assumptions about the state space. We illustrate the results by exploring a model of dynamic price signaling and show that prices may be informative of product quality even if the seller cannot commit to future prices, with both high and low prices being able to signal high quality. 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2007.09568&r=all 
By:  Wei Zhao; Claudio Mezzetti; Ludovic Renou; Tristan Tomala 
Abstract:  We consider a dynamic moral hazard problem between a principal and an agent, where the sole instrument the principal has to incentivize the agent is the disclosure of information. The principal aims at maximizing the (discounted) number of times the agent chooses a particular action, e.g., to work hard. We show that there exists an optimal contract, where the principal stops disclosing information as soon as its most preferred action is a static best reply for the agent or else continues disclosing information until the agent perfectly learns the principal's private information. If the agent perfectly learns the state, he learns it in finite time with probability one; the more patient the agent, the later he learns it. 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2007.05983&r=all 
By:  Franz Dietrich (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics, CNRS  Centre National de la Recherche Scientifique) 
Abstract:  Can a group be a standard rational agent? This would require the group to hold aggregate preferences which maximise expected utility and change only by Bayesian updating. Group rationality is possible, but the only preference aggregation rules which support it (and are minimally Paretian and continuous) are the lineargeometric rules, which combine individual tastes linearly and individual beliefs geometrically. 
Keywords:  Bayesian aggregation,preference aggregation under uncertainty,expected utility hypothesis for groups,Bayesian revision,rational group agents,linear versus geneometric opinion pooling 
Date:  2020–06 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs02905409&r=all 
By:  Sean Horan (Université de Montréal and CIREQ); Yves Sprumont (Université de Montréal and CIREQ) 
Abstract:  We propose a class of decisive collective choice rules that rely on an exogenous linear ordering to partition the majority relation into two acyclic relations. The first relation is used to obtain a shortlist of the feasible alternatives while the second is used to make a final choice. In combination with faithfulness to the underlying majority relation, rules in this class are characterized by two desirable rationality properties: Sen’s expansion consistency and a version of Manzini and Mariotti’s weak WARP. The rules also satisfy natural adaptations of Arrow’s independence of irrelevant alternatives and May’s positive responsiveness. 
Keywords:  majority rule, decisiveness, IIA, monotonicity, rational shortlist methods 
JEL:  D71 D72 
Date:  2020–05 
URL:  http://d.repec.org/n?u=RePEc:mtl:montec:132020&r=all 
By:  Shaofei Jiang 
Abstract:  Evidence games study situations where a sender persuades a receiver by selectively disclosing hard evidence about an unknown state of the world. Evidence games often have multiple equilibria. Hart et al. (2017) propose to focus on truthleaning equilibria, i.e., perfect Bayesian equilibria where the sender prefers disclosing truthfully when indifferent, and the receiver takes offpath disclosure at face value. They show that a truthleaning equilibrium is an equilibrium of a perturbed game where the sender has an infinitesimal reward for truthtelling. We show that, when the receiver's action space is finite, truthleaning equilibrium may fail to exist, and it is not equivalent to equilibrium of the perturbed game. To restore existence, we introduce a disturbed game with a small uncertainty about the receiver's payoff. A purifiable equilibrium is a truthleaning equilibrium in an infinitesimally disturbed game. It exists and features a simple characterization. A truthleaning equilibrium that is also purifiable is an equilibrium of the perturbed game. 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2007.06403&r=all 
By:  Siddhartha Bandyopadhyay; Antonio Cabrales 
Abstract:  We consider a model where agents differ in their `types' which determines their voluntary contribution towards a public good. We analyze what the equilibrium composition of groups are under centralized and centralized choice. We show that there exists a topdown sorting equilibrium i.e. an equilibrium where there exists a set of prices which leads to groups that can be ordered by level of types, with the first k types in the group with the highest price and so on. This exists both under decentralized and centralized choosing. We also analyze the model with endogenous group size and examine under what conditions is topdown sorting socially efficient. We illustrate when integration (i.e. mixing types so that each group's average type if the same) is socially better than topdown sorting. Finally, we show that top down sorting is efficient even when groups compete among themselves. 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2008.03102&r=all 
By:  Dylan Possama\"i; Nizar Touzi 
Abstract:  This paper provides a complete review of the continuoustime optimal contracting problem introduced by Sannikov, in the extended context allowing for possibly different discount rates of both parties. The agent's problem is to seek for optimal effort, given the compensation scheme proposed by the principal over a random horizon. Then, given the optimal agent's response, the principal determines the best compensation scheme in terms of running payment, retirement, and lumpsum payment at retirement. A Golden Parachute is a situation where the agent ceases any effort at some positive stopping time, and receives a payment afterwards, possibly under the form of a lumpsum payment, or of a continuous stream of payments. We show that a Golden Parachute only exists in certain specific circumstances. This is in contrast with the results claimed by Sannikov, where the only requirement is a positive agent's marginal cost of effort at zero. Namely, we show that there is no Golden Parachute if this parameter is too large. Similarly, in the context of a concave marginal utility, there is no Golden Parachute if the agent's utility function has a too negative curvature at zero. In the general case, we provide a rigorous analysis of this problem, and we prove that an agent with positive reservation utility is either never retired by the principal, or retired above some given threshold (as in Sannikov's solution). In particular, different discount factors induce naturally a facelifted utility function, which allows to reduce the whole analysis to a setting similar to the equaldiscount rates one. Finally, we also confirm that an agent with small reservation utility does have an informational rent, meaning that the principal optimally offers him a contract with strictly higher utility value. 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2007.05529&r=all 
By:  Achille Basile; Surekha Rao; K. P. S. Bhaskara Rao 
Abstract:  Let $V$ be society whose members express preferences about two alternatives, indifference included. Identifying anonymous binary social choice functions with binary functions $f=f(k,m)$ defined over the integer triangular grid $G=\{(k,m)\in \mathbb{N}_0\times\mathbb{N}_0 : k+m\le V\} $, we show that every strategyproof, anonymous social choice function can be described geometrically by listing, in a sequential manner, groups of segments of G, of equal (maximum possible) length, alternately horizontal and vertical, representative of preference profiles that determine the collective choice of one of the two alternatives. Indeed, we show that every function which is anonymous and strategyproof can be described in terms of a sequence of nonnegative integers $(q_1, q_2, \cdots, q_s)$ corresponding to the cardinalities of the mentioned groups of segments. We also analyze the connections between our present representation with another of our earlier representations involving sequences of majority quotas. A Python code is available with the authors for the implementation of any such social choice function. 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2008.02041&r=all 
By:  Ruzica Savivc; Dimitrios Xefteris 
Abstract:  We study electoral competition under the, socalled, Apostolic voting rule (AVR) in the framework of the HotellingDowns model (Osborne, 1993). The AVR is a twostage election procedure composed of a voting stage and a lottery stage: the voters vote for the candidate they like best, and each of the two mostvoted candidates is elected with even probability. Under standard assumptions regarding the voters' preferences, we show that the AVR leads to a unique up to permutations of the players' identities equilibrium: only two candidates enter in the electoral race and they choose distinct policy platforms. This is the first rule which is proved to support an essentially unique equilibrium in this popular model. Our analysis highlights that as long as candidates do not compete for a single first place (as in standard plurality or runoff elections), but for a number of them (as under the AVR), strategic incentives alter dramatically and lead to stable and predictable configurations. 
Keywords:  Apostolic Voting, HotellingDowns model, manipulation, lotteries, unique equilibrium 
JEL:  D72 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:ucy:cypeua:082020&r=all 
By:  Charles Hodgson (Cowles Foundation, Yale University); Gregory Lewis (Microsoft Research) 
Abstract:  We develop a model of consumer search with spatial learning in which sampling the payoff of one product causes consumers to update their beliefs about the payoffs of other products that are nearby in attribute space. Spatial learning gives rise to path dependence, as each new search decision depends on past experiences through the updating process. We present evidence of spatial learning in data that records online search for digital cameras. Consumers' search paths tend to converge to the chosen product in attribute space, and consumers take larger steps away from rarely purchased products. We estimate the structural parameters of the model and show that these patterns can be rationalized by our model, but not by a model without spatial learning. Eliminating spatial learning reduces consumer welfare by 12%: crossproduct inferences allow consumers to locate better products in a shorter time. Spatial learning has important implications for the power of search intermediaries. We use simulations to show that consumeroptimal product recommendations are that are most informative about other products. 
Keywords:  Consumer search, Platforms, Online markets, Industrial organization 
JEL:  D12 L81 L0 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2246&r=all 
By:  David K Levine; Andrea Mattozzi 
Date:  2020–08–17 
URL:  http://d.repec.org/n?u=RePEc:cla:levarc:786969000000001563&r=all 
By:  Ishita Chakraborty (Yale School of Management); Joyee Deb (Cowles Foundation, Yale University); Aniko Oery (Cowles Foundation, Yale University) 
Abstract:  The propensity of consumers to engage in wordofmouth (WOM) differs after good versus bad experiences, which can result in positive or negative selection of usergenerated reviews. We show how the dispersion of consumer beliefs about quality (brand strength), informativeness of good and bad experiences, and price can affect selection of WOM in equilibrium. WOM is costly: Early adopters talk only if they can affect the receiverâ€™s purchase. Under homogeneous beliefs, only negative WOM can arise. Under heterogeneous beliefs, the type of WOM depends on the informativeness of the experiences. We use data from Yelp.com to validate our predictions. 
Keywords:  Costly communication, Recommendation engines, Review platforms, Word of mouth 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2254&r=all 
By:  Leandro Gorno; Alessandro Rivello 
Abstract:  We extend Berge's Maximum Theorem to allow for incomplete preferences (i.e., reflexive and transitive binary relations which fail to be complete). We show that if, in addition to the traditional continuity assumptions, a new continuity property for the domains of comparability holds, the limits of maximal elements along a sequence of decision problems are maximal elements in the limit problem. While this new continuity property for the domains of comparability is sufficient, it is not generally necessary. However, we provide conditions under which it is necessary and sufficient for maximality and minimality to be preserved by limits. 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2007.09781&r=all 
By:  Trivikram Dokka Venkata Satyanaraya; Herve Moulin; Indrajit Ray; Sonali Sen Gupta 
Abstract:  In a public good provision or a public bad abatement situation, the noncooperative interplay of the participants typically results in low levels of provision or abatement. In the familiar class of nperson quadratic games, we show that Coarse Correlated equilibria (CCEs)  simple mediated communication devices that do not alter the strategic structure of the game  can significantly outperform the Nash equilibrium in terms of the policy objective above. 
Keywords:  Quadratic game, Coarse correlated equilibrium, Abatement level, Efficiency gain 
JEL:  C72 Q52 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:lan:wpaper:301895429&r=all 
By:  Evan M. Calford 
Abstract:  We study the use of mixed strategies in games by ambiguity averse agents with a preference for randomization. Applying the decision theoretic model of Saito (2015) to games, we establish that the set of rationalizable strategies grows larger as preferences for randomization weaken. An agentâ€™s preference for randomization is partially observable: given the behavior of an agent in a game, we can determine an upper bound on the strength of randomization preferences for that agent. Notably, data in previous experiments on ambiguity aversion in games is not consistent with a maximal preference for randomization for approximately 30% of subjects. 
Keywords:  Ambiguity Aversion, Mixed Strategies, Game Theory 
JEL:  D81 C70 C72 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:acb:cbeeco:2020675&r=all 
By:  Hassan Benchekroun; Miao Dai; Ngo Van Long 
Abstract:  We examine the profitability of crossownership in an oligopolistic industry where firms compete as Cournot rivals. We consider a symmetric crossownership structure in which a subset of k firms engage in crossshareholding and each firm has an equal silent financial interest in the other firms, while the remaining (n – k) firms stay independent. We show that a symmetric crossownership is never profitable for any levels of noncontrolling minority shareholdings if the participation ratio (k/n) is less than or equal to (n+1)/(2n), while there exists a large range of crossownership for which it can be profitable beyond that participation ratio. This result may be called a crossownership paradox, analogous to the merger paradox. With the presence of stock constraints, however, we find some of the results from the crossownership paradox do not carry over to the case of nonrenewable resource industries. The profitability of a symmetric crossownership can be positive even when the participation ratio (k/n) is less than or equal to (n+1)/(2n) and is always positive when the participation ratio (k/n) is greater than (n+1)/(2n), provided that the initial resource stock owned by each firm is small enough. We also highlight that crossownership can be preferable to a horizontal merger under Cournot competition. Not only is it more profitable to do so, more importantly, it constitutes a shrewd strategy to avoid possible legal challenges. Nous examinons la rentabilité de la propriété croisée dans une industrie oligopolistique où les entreprises se font concurrence en tant que rivales de Cournot. Nous considérons une structure de propriété croisée symétrique dans laquelle un sousensemble de k entreprises s'engagent dans des participations croisées, chaque entreprise ayant un intérêt financier silencieux égal dans les autres (k1) entreprises du sousensemble, alors que (n  k) entreprises restent indépendantes. Nous montrons qu'une participation croisée symétrique n'est jamais rentable si le ratio de participation (k /n) est inférieur ou égal à (n + 1) / (2n), alors qu’il existe un large domaine de valeurs de k/n audelà de (n+1)/(2n) pour lesquelles la participation croisée est rentable. Ce résultat peut être qualifié de paradoxe de la propriété croisée, analogue au paradoxe de la fusion. Cependant, dans le cas des industries de ressources nonrenouvelables, avec la présence de contraintes de stock, nous constatons que certains des résultats du paradoxe de la propriété croisée ne se répercutent pas. La rentabilité d'une propriété croisée symétrique peut être positive même lorsque le taux de participation (k / n) est inférieur ou égal à (n + 1) / (2n) et est toujours positive lorsque le taux de participation (k / n) est supérieur à (n +1) / (2n), à condition que le stock initial de ressources détenu par chaque entreprise soit suffisamment petit. Nous soulignons également que la propriété croisée peut être préférable à une fusion horizontale sous la concurrence de Cournot. Non seulement il est plus rentable de le faire, mais surtout, cela constitue une stratégie astucieuse pour éviter d'éventuelles contestations judiciaires. 
Keywords:  Crossownership,Profitability,Oligopoly,Nonrenewable Resources,Resource Stock,Horizontal Merger,Competition Policy,Antitrust Laws, Propriété croisée,Rentabilité,Oligopole,Ressources nonrenouvelables,Stock de ressources,Fusion horizontale,Politique de la concurrence,Lois antitrust 
JEL:  L13 L41 Q3 
Date:  2020–08–11 
URL:  http://d.repec.org/n?u=RePEc:cir:cirwor:2020s43&r=all 
By:  Anastasios G. Karantounias 
Abstract:  This paper analyzes optimal policy in setups where both the leader and the follower have doubts about the probability model of uncertainty. I illustrate the methodology in two environments: a) an industry populated with a large firm and many small firms in a competitive fringe, where both types of firms doubt the probability model of demand shocks, and b) a general equilibrium economy, where a policymaker taxes linearly the labor income of a representative household in order to finance an exogenous stream of stochastic spending shocks. The policymaker can distrust the probability model of spending shocks more, the same, or less than the household. Whenever there are doubts about the model, cautious agents form endogenous worstcase beliefs by assigning high probability on low profitability or lowutility events. There are two forces that shape optimal policy results: the manipulation of the endogenous beliefs of the follower to the benefit of the leader, and the discrepancy (if any) in the pessimistic beliefs between the leader and the follower. Depending on the application, the leader may amplify or mitigate the worstcase beliefs of the follower. 
Keywords:  model uncertainty; ambiguity aversion; multiplier preferences; misspecification; robustness; martingale; monopolist; competitive fringe; demand uncertainty; Ramsey taxation 
JEL:  D80 E62 H21 H63 
Date:  2020–07–31 
URL:  http://d.repec.org/n?u=RePEc:fip:fedawp:88478&r=all 
By:  Peyman Khezr (School of Economics, Finance and Marketing, RMIT University,); Flavio M. Menezes (School of Economics, University of Queensland) 
Abstract:  This paper explores the welfare implications of free entry when firms face known entry costs, but production costs are privately known. Upon entering, firms compete in prices to supply a homogeneous good. Our framework yields results that are more nuanced than those of the literature on free entry, where there is either insufficient or excessive entry. Depending on the distribution of costs, the value of the entry fee, and the number of potential entrants, it is possible to have both excessive and insufficient entry as parameters change. We also show that the existence of entry costs fundamentally changes one of the key results of Spulber (1995) on the convergence of the equilibrium price to the competitive equilibrium. Instead, with entry costs, we have shown that the probability of excessive entry goes to one as the number of potential firms goes to infinity. 
Keywords:  entry; Bertrand equilibrium; asymmetric information. 
JEL:  D21 D43 L1 
Date:  2020–08–07 
URL:  http://d.repec.org/n?u=RePEc:qld:uq2004:632&r=all 
By:  Yongmin Chen; Xinyu Hua; Keith E. Maskus 
Abstract:  We study the international protection of consumer data in a model where data usage benefits firms at the expense of their customers. We show that a multinational firm does not balance this tradeoff efficiently if its data usage lacks (full) transparency or if consumers’ privacy preference differs across countries. Unilateral data regulation by each country addresses the moralhazard problem associated with opacity, but may nevertheless reduce global welfare due to crosscountry externalities that distort output and data usage. The regulations may also cause excessive investment in data localization, even though localization mitigates the externalities. Our findings highlight the need for international coordination. though not necessarily uniformity. on regulations about data usage and protection. 
Keywords:  consumer data, data usage, privacy, multinational firm, regulation, data localization, international coordination 
JEL:  L15 L86 F12 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_8391&r=all 
By:  Ricardo Gonçalves (Católica Porto Business School, Universidade Catolica Portuguesa); Peyman Khezr (School of Economics, Finance and Marketing, RMIT University, Australia.); Flavio Menezes (School of Economics, University of Queensland, Brisbane, Australia) 
Abstract:  We examine the role of asymmetric information about costs on the impact of partial (noncontrolling) vertical integration on competition. We show that Greenlee and Raskovich (2006)’s invariance result that total downstream quantity (and, therefore, competition) is not impacted by such acquisitions holds in the case of privately known marginal costs and symmetric ownership shares. This invariance result provides a possible explanation for why partial acquisitions where downstream firms own equal shares in an upstream firm with market power are so uncommon. 
Keywords:  Vertical integration; partial acquisition; asymmetric information. 
JEL:  D4 L1 L2 L4 
Date:  2020–08–18 
URL:  http://d.repec.org/n?u=RePEc:qld:uq2004:634&r=all 
By:  Saki Bigio (UCLA); Liyan Shi (EIEF) 
Abstract:  We study repurchase options (repo contracts) in a competitive asset market with asymmetric information. Gains from trade emerge from a liquidity need, but private information about asset quality prevents the full realization of trade. We obtain a unique equilibrium, which features a pooling repo contract and full participation among borrowers. The equilibrium repo contract resolves adverse selection: the embedded repurchase option prevents the market unraveling that occurs in assetsale markets. However, the contract is inefficient due to cream skimming. Competition to attract highquality borrowers through the terms of the repurchase option inefficiently lowers liquidity. The equilibrium contract has a closed form and is portable to many applications. 
JEL:  D82 G23 G32 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:apc:wpaper:169&r=all 
By:  Gary W. Cox; Jon H. Fiva; Daniel M. Smith; Rune J. Sørensen 
Abstract:  How do parties motivate candidates to exert effort in closedlist elections? If each candidate’s primary goal is winning a seat, then those in safe and hopeless list positions have weak incentives to campaign. We present a model in which (i) candidates care about both legislative seats and the higher offices available when their party enters government; and (ii) parties commit to allocating higher offices monotonically with list rank. This model predicts that the volume and geodiversity of candidates’ campaign efforts will increase as their list rank improves. Using new data covering Norwegian parliamentary candidates’ use of mass and social media during the 2017 election, we find clear support for this prediction. As their list rank increases, candidates shift from intradistrict to extradistrict media exposure—which cannot help them win their own seats; but can improve their party’s chance of entering government, and thus their own potential share of the spoils. 
Keywords:  party lists, cabinet promotion, Gamson’s law, proportional representation, voter mobilization 
JEL:  D72 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_8357&r=all 