
on Microeconomics 
By:  Fabrizio Germano; Jonathan Weinstein; Peio ZuazoGarin 
Abstract:  Predictions under common knowledge of payoffs may differ from those under arbi trarily, but finitely, many orders of mutual knowledge; Rubinstein’s (1989) Email game is a seminal example. Weinstein and Yildiz (2007) showed that the discontinuity in the example generalizes: for all types with multiple rationalizable (ICR) actions, there exist similar types with unique rationalizable action. This paper studies how a wide class of departures from common belief in rationality impact Weinstein and Yildiz’s discontinuity. We weaken ICR to ICR?, where ? is a sequence whose nth term is the probability players attach to (n  1)th order belief in rationality. We find that Weinstein and Yildiz’s discontinuity holds when higherorder belief in rationality remains above some threshold (constant ?), but fails when higherorder belief in rationality eventually becomes low enough (? converging to 0). 
Keywords:  robustness, Rationalizability, bounded rationality, Incomplete Information, belief hierarchies 
JEL:  C72 D82 D83 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:bge:wpaper:947&r=mic 
By:  Besanko, David; Tong, Jian; Wu, Jianjun 
Abstract:  Conventional Bayesian games of incomplete information are limited in their ability to represent severe incompleteness of information. Using an illustrative example of (seller offer) sequential bargaining with onesided incomplete information, we analyze a dynamic game under ambiguity. The novelty of our model is the stark assumption that the seller has complete ignorancerepresented by the set of all plausible prior distributionsover the buyer's type. We propose a new equilibrium conceptPerfect Objectivist Equilibrium (POE)in which multiple priors and full Bayesian updating characterize the belief system, and the uninformed player maximizes the infimum expected utility over nonweaklydominated strategies. We provide a novel justification for refining POE through Markov perfection, and obtain a unique refined equilibrium. This results in a New "Coase Conjecture"a competitive outcome arising from an apparent monopoly, which does not require the discount rate to approach zero, and is robust to reversion caused by reputation equilibria. 
Date:  2016–12–16 
URL:  http://d.repec.org/n?u=RePEc:stn:sotoec:1606&r=mic 
By:  Bergemann, Dirk; Brooks, Benjamin A; Morris, Stephen 
Abstract:  We study auction design when bidders have a pure common value equal to the maximum of their independent signals. In the revenue maximizing mechanism, each bidder makes a payment that is independent of his signal and the allocation discriminates in favor of bidders with lower signals. We provide a necessary and sufficient condition under which the optimal mechanism reduces to a posted price under which all bidders are equally likely to get the good. This model of pure common values can equivalently be interpreted as model of resale: the bidders have independent private values at the auction stage, and the winner of the auction can make a takeitorleaveitoffer in the secondary market under complete information. 
Keywords:  common values; descending auction; global incentive constraints; local incentive constraints; maximum value game; Optimal auction; posted price; resale; revenue maximization; wallet game 
JEL:  C72 D44 D82 D83 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:11783&r=mic 
By:  Becker, Johannes Gerd; Gersbach, Hans 
Abstract:  We consider an infinitely repeated reappointment game in a principalagent relationship and examine the consequences of threshold contracts, which forbid reappointment if the principal's utility is too low. Typical examples are voterpolitician or governmentpublic servant relationships. The agent chooses costly effort and enjoys being in office until he is deselected. The principal observes a noisy signal of the agent's effort and decides whether to reappoint the agent or not. We analyse the stationary Markovian equilibria of this game with and without threshold contracts. We identify the circumstances under which such threshold contracts are welfareimproving or beneficial for the principal, which, in turn, may justify attempts to introduce such contracts in politics. 
Keywords:  asymmetric information; commitment.; principalagent model; reappointment; repeated game; stationary Markovian strategies; threshold contracts; threshold strategies 
JEL:  C83 D82 D86 H11 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:11766&r=mic 
By:  Bezerra Bisneto, João Lídio 
Abstract:  This paper analyses how to design a communication policy in a setting with both incomplete information and uncertainty about the future. In the model developed, both agents and the information authority have only noisy knowledge of the state of the world and the degree of uncertainty of the authority is unknown to the agents. The information authority chooses how much information to provide to private agents and how precise, or disperse, such information will be. Agents faces costs on information acquisition and choose how much of it to obtain. In the model developed in this paper, the presence of incomplete information does not alter the equilibrium choices, as a separating equilibrium can be achieved. In all cases analysed, the information authority would prefer to offer signals with the lowest dispersion possible 
Date:  2016–10–19 
URL:  http://d.repec.org/n?u=RePEc:fgv:eesptd:431&r=mic 
By:  Besanko, David; Tong, Jian; Wu, Jianjun 
Abstract:  We study government optimal subsidy policies for research programs in the face of servere information asymmetrywhen firms have private information about the likelihood of project viability but the government cannot form a unique prior belief about this likelihood. The paper makes two contributions. First, we show that the way in which R&D is subsidized matters. Under both monopoly R&D (i.e., a single firm conducts R&D in isolation) and R&D competition, different types of subsidies (e.g., earmarked, unrestricted subsidies, and pure matching subsidies) have significantly different effects on firms' R&D investment incentives. Second, we show that a simple subsidy scheme works even when the government is unable to form a unique prior belief about the firm's private information on project viability. If the shadow cost of public funds is zero, under monopoly R&D, there exists a pure matching subsidy that induces the firm to follow the firstbest R&D policy irrespective of its prior beliefs about the viability of the project, meaning it is a (belieffree) ex post equilibrium policy; under R&D competition, the firstbest outcome can also be achieved through a simple combination of a matching subsidy and an unrestricted subsidy. If the shadow cost of public funds is positive, an ex post equilibrium in general does not exist either under monopoly or competition. We then consider two alternative policy decision criteria that are appropriate for belieffree games: rationalizability and maxmin criteria. We argue that the maxmin criteria is preferable in our context, and by way of doing so establish that the set of maxmin subsidy policies under either monopoly or competitive R&D consists entirely of simple pure matching subsidies. We further establish that allowing firms to form an R&D consortium reduces the matching rate for the highest maxmin subsidy, suggesting that cooperative R&D has the potential to economize on the shadow costs of public funding of subsidies. 
Date:  2016–07–13 
URL:  http://d.repec.org/n?u=RePEc:stn:sotoec:1605&r=mic 
By:  Bergemann, Dirk; Brooks, Benjamin A; Morris, Stephen 
Abstract:  We explore the impact of private information in sealedbid firstprice auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winningbid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning bids and for the informationally robust comparison of alternative bidding mechanisms. 
Keywords:  Bayes correlated equilibrium; common values; Firstprice auction; information structure; interdependent values; private values; reserve price.; revenue; surplus; welfare bounds 
JEL:  C72 D44 D82 D83 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:11782&r=mic 
By:  Paraskevas Lekeas; Giorgos Stamatopoulos (Department of Economics, University of Crete, Greece) 
Abstract:  Cooperative game theory studies situations where groups or coalitions of players act collectively by signing binding agreements. The starting point of the theory is to determine the worth each coalition can achieve when its members act independently of the players outside the coalition. In games with orthogonal coalitions, i.e., coalitions that do not affect one another, this task is quite straightforward, as it suffices to study the actions of the insiders only. However, when orthogonality is absent, or in other words, when there are intercoalitional externalities, the specification of the worth of a coalition requires the studying of the actions of the players in all coalitions. Therefore, when a number of players contemplate to form a coalition in an environment with externalities they need to have a theory, or a conjecture, about the actions of the players outside the proposed coalition. Clearly, different conjectures lead to different specifications of the worth or value of the coalition, which in turn affects the outcome of the game. In particular, these conjectures determine the core of the cooperative game. The core is the set of all outcomes (allocations of the value that the entire society of players generates) that no coalition has incentive to block and act on its own. Nonemptiness of the core means that cooperation among all players in the game is feasible. The literature on cooperative games with externalities has proposed a number of such coalitional conjectures, each giving rise to a specific core notion. According to Î± and Î²conjectures (Aumann 1959), the members of a coalition compute their worth assuming that the outside players select their strategies so as to minimize the payoff of the coalition; the Î± and Î²core are then defined with respect to the resulting coalitional payoffs. According to Î³conjectures (Chander&Tulkens 1997), it is assumed that the outsiders select individual best strategies, i.e., they form only singleton coalitions; the Î³core is then accordingly defined. The same approach can be followed under the additional assumption that each coalition assumes for itself the role of Stackelberg leader (Currarini&Marini 2003). The rtheory (Huang&Sjostrom 2003; Koczy 2007) proposes that the members of a coalition compute their worth by looking recursively on the subgames played among the outsiders; the rcore arises when the solution concept employed in these subgames is the core itself. Economists often restore to cooperative games with externalities to model various economic environments. Applications include the use of Î± and Î²core in oligopolistic markets (Zhao 1999; Norde et al. 2002; Lardon 2010); the use of Î³core in economies with production externalities (Chander&Tulkens 1997; Chander 2007; Helm 2012), in oligopolies (Rajan 1989; Lardon 2010; Lardon 2012) or in extensiveform games (Chander&Wooders 2012); the use of sequential Î³core for cooperative games with strategic complements (Currarini&Marini 2003) or for economies with enviromental externalities (Marini 2013), etc. The main focus of these papers is to find conditions under which the core is nonempty. The current paper focuses too on cooperative games with externalities but takes a different route. It assumes that when a group of players S contemplate to break off from the rest of the society, they are uncertain about the partition that the players outside S will form. Hence, they assign various probability distributions on the set of all possible partitions. These probabilistic beliefs do not necessarily reflect the behavior of the outsiders, i.e., beliefs need not be consistent with actual choices. Given the beliefs, no natter how they form, one can compute the expected worth of S and define the core of the resulting cooperative game. The task that arises then is to find conditions on the data of the game (i.e., payoff functions and probability distributions) that guarantee the nonemptiness of the core, or, in other words, guarantee that the cooperation of all players in the game is feasible. The motivation of our paper is twofold. First, we are intersted in generalizing (some of) the existing approaches on the definition of the core. For example, the Î³core notion is a special case of our approach that arises when each coalition assigns probability one to the event that the outsiders will form only singleton coalitions. Secondly, our paper could be read as a work on bounded rationality in its relation to cooperative games. The assignment of a (nonequilibrium) probability distribution on the set of parititions of the outsiders may reflect the cognitive inability of the members of a coalition to accurately deduce the outsiders' equilibrium partition. In this sense, probabilistic beliefs act as a rule of thumb. This approach is particularly relevant for games with a large number of players, where the number of different partitions can be very large. We apply the above framework to cooperative games generated by (symmetric) aggregative normal form games, i.e., games where the payoff of a player depends on his strategy and on the sum of the strategies of all players. Many economic models have an aggregative structure, such as oligopoly models, rentseeking games, contest games, etc. We focus, in particular, on aggregative games that satisfy the following properties: (a) each player's payoff function has a bilinear form (this gives us the family of linear aggregative games introduced by Martimort&Stole 2010); (b) each player's payoff and marginal payoff decrease in the aggregate value of all players' strategies. The bilinear form assumption, in particular, is used as it allows us to simplify considerably the objective function of each coalition. 
Keywords:  aggregative game; cooperative game; core; stochastic dominance 
JEL:  C71 
Date:  2016–09–22 
URL:  http://d.repec.org/n?u=RePEc:crt:wpaper:1605&r=mic 
By:  Camera, Gabriele; Gioffré, Alessandro 
Abstract:  Studies of cooperation in infinitely repeated matching games focus on homogeneous economies, where full cooperation is efficient and any defection is collectively sanctioned. Here we study heterogeneous economies where occasional defections are part of efficient play, and show how to support those outcomes through contagious punishments 
Keywords:  cooperation,repeated games,social dilemmas 
JEL:  C6 C7 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:zbw:safewp:162&r=mic 
By:  Zvika Neemam (Tel Aviv University); Aniko Ory (Cowles Foundation, Yale University); Jungju Yu (Yale School of Management) 
Abstract:  We study a model of collective reputation and use it to analyze the benefit of collective brands. Consumers form beliefs about the quality of an experience good that is produced by one firm that is part of a collective brand. Consumers’ limited ability to distinguish among firms in the collective and to monitor firms’ investment decisions creates incentives to freeride on other firms’ investment efforts. Nevertheless, we show that collective brands induce stronger incentives to invest in quality than individual brands under two types of circumstances: if the main concern is with quality control and the baseline reputation of the collective is low, or if the main concern is with the acquisition of specialized knowledge and the baseline reputation of the collective is high. We also contrast the socially optimal information structure with the profit maximizing choice of branding if branding is endogenous. Our results can be applied to countryoforigin, agricultural appellation, and other collective brands. 
Keywords:  Branding, Collective reputation, Commitment, Country of origin 
JEL:  C70 D21 D40 D70 L10 L50 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2068&r=mic 
By:  Yuval Heller (BarIlan University) 
Abstract:  Various papers have presented folk theorem results for repeated games with private monitoring that rely on belieffree equilibria. I show that these equilibria are not robust against small perturbations in the behavior of potential opponents. Specifically, I show that essentially none of the belieffree equilibria is evolutionarily stable, and that in generic games none of these equilibria is neutrally stable. Moreover, in a large family of games (which includes many public good games), the belieffree equilibria fail to satisfy even a very mild stability refinement. 
Keywords:  Belieffree equilibrium, evolutionary stability, private monitoring, repeated Prisoner’s Dilemma, communication 
JEL:  C73 D82 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:biu:wpaper:201701&r=mic 
By:  de Meza, David; Reito, Francesco 
Abstract:  The equilibrium of a competitive market in which firms must choose prices ex ante and demand is stochastic is shown to be secondbest inefficient. Even under risk neutrality, equilibrium price exceeds the welfaremaximising predetermined price. Competition tends to eliminate rationing, but at the greater welfare cost of creating excess capacity. Entry incentives are also distorted. In low states, entrants obtain a share of revenue without increasing consumption, giving rise to a version of the common pool problem. In high states, firms do not appropriate the consumer surplus gained from marginal reductions in rationing. As a result of these o¤setting externalities, the number of firms may be excessive or insufficient. Inefficiency arises whether or not the rationing rule is efficient. 
Keywords:  stochastic demand, rationing, waste, e¢ ciency. 
JEL:  D61 D81 H23 
Date:  2016–01–10 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:76125&r=mic 
By:  Akerlof, Robert; Holden, Richard 
Abstract:  This paper explores the problem of assembling capital for projects. It can be difficult to assemble capital, when it is disaggregated, for a project that exhibits increasing returns. Small investors may be reluctant to participate, as they may question the ability of the project owner to raise the additional capital he requires. This suggests the possibility that agents with blocks of capital (capital that is already aggregated) might earn rents. Similarly, agents with "network capital"  that is, an ability to aggregate the capital of others  may earn rents. In this paper, we develop a theory of the rents attached to capital assembly, and discuss the implications for a range of issues from investment, to growth, to inequality. 
Keywords:  increasing returns; inequality; investment; network capital 
JEL:  D24 D30 D85 G30 L26 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:11763&r=mic 
By:  Tomohiro Uchiyama 
Abstract:  We present a complete characterization of the classical transfer problem for an exchange economy with an arbitrary finite number of traders. Our method is geometric, using an equilibrium manifold developed by Debreu, MasColell, and Balasko. We show that for a regular equilibrium the transfer problem arises if and only if the index at the equilibrium is $1$. This implies that the transfer problem does not happen if the equilibrium is Walras tatonnement stable. Our result generalizes Balasko's analogous result for an exchange economy with two traders. 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1701.04491&r=mic 
By:  Marc Fleurbaey (Woodrow Wilson School and Center for Human Values  Princeton University); Stéphane Zuber (Centre d'Economie de la Sorbonne  Paris School of Economics) 
Abstract:  Utilitarianism is a prominent approach to social justice that has played a central role in economic theory. A key issue for utilitarianism is to define how utilities should be measured and compared. This paper draws on Harsanyi's approach (Harsanyi, 1955) to derive utilities from choices in risky situations. We introduce a new normalization of utilities that ensures that: 1) a transfer from a rich to a poor is welfare enhancing, and 2) populations with more risk averse people have lower welfare. We propose normative principles that reflect these fairness requirements and characterize fair utilitarianism. We also study some implications of fair utilitarianism for risk sharing and collective risk aversion 
Keywords:  Fairness; utilitarianism; risk sharing; collective risk aversion 
JEL:  D63 D81 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:17005&r=mic 
By:  Nicolas Gravel; Brice Magdalou; Patrick Moyes 
Abstract:  What would be the analogue of the Lorenz quasiordering when the variable of interest is of a purely ordinal nature? We argue that it is possible to derive such a criterion by substituting for the PigouDalton transfer used in the standard inequality literature what we refer to as a Hammond progressive transfer. According to this criterion, one distribution of utilities is considered to be less unequal than another if it is judged better by both the lexicographic extensions of the maximin and the minimax, henceforth referred to as the leximin and the antileximax, respectively. If one imposes in addition that an increase in someone’s utility makes the society better off, then one is left with the leximin, while the requirement that society welfare increases as the result of a decrease of one person’s utility gives the antileximax criterion. Incidently, the paper provides an alternative and simple characterisation of the leximin principle widely used in the social choice and welfare literature. 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:lam:wpaper:1703&r=mic 