
on Microeconomics 
By:  Dirk Bergemann (Cowles Foundation, Yale University); Benjamin Brooks (Dept. of Economics, University of Chicago); Stephen Morris (Dept. of Economics, Princeton University) 
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:  Optimal auction, common values, revenue maximization, revenue equivalence, rstprice auction, secondprice auction, resale, posted price, maximum value game, wallet game, descending auction, local incentive constraints, global incentive constraints 
JEL:  C72 D44 D82 D83 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2064&r=mic 
By:  Attar, Andrea; Mariotti, Thomas; Salanié, François 
Abstract:  We study a discriminatory limitorder book in which uninformed market makers compete in nonlinear tariffs to serve an informed insider. Our model allows for general nonparametric specifications of preferences and for arbitrary discrete distributions for the insider's private information. We show that adverse selection severely restricts possible equilibrium outcomes: in any purestrategy equilibrium, tariffs must be linear and at most one type may trade, leading to an extreme form of market breakdown. As a result, such equilibria only exist under exceptional circumstances. The Bertrandlike logic underlying these results markedly differs from Cournotlike analyses of the limitorder book that postulate a continuum of types. We argue that these contrasting outcomes can be reconciled when one considers "equilibria of either the game with a large number of market makers or the game with a large number of insider types. Mixedstrategy equilibria, by contrast, lead to a new class of equilibrium predictions that calls for further analysis. 
Keywords:  Adverse Selection, Competing Mechanisms, LimitOrder Book. 
JEL:  D43 D82 D86 
Date:  2016–11 
URL:  http://d.repec.org/n?u=RePEc:ide:wpaper:31204&r=mic 
By:  Isaac Loh (Northwestern University); Gregory Phelan (Williams College) 
Abstract:  When information is of lower dimension than the model generating the data, Bayesian learning need not converge to the truth. Because the information is of lower dimension than the model, agents face an identification problem, affecting the role of data in inference. We provide conditions under which Bayesian learning is asymptotically inconsistent with positive probability, and sometimes almost surely. Robustly, two agents with differing priors who observe identical, unambiguous data may disagree forever, with stronger disagreement the more data is observed. Agents rationally use common observations to differentially update beliefs about different parameters. 
Keywords:  beliefs, polarization, learning, Bayesian updating 
JEL:  D10 D80 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:wil:wileco:201618&r=mic 
By:  Dirk Bergemann (Cowles Foundation, Yale University); Stephen Morris (Dept. of Economics, Princeton University) 
Abstract:  We propose an incomplete information analogue of rationalizability. An action is said to be belieffree rationalizable if it survives the following iterated deletion process. At each stage, we delete actions for a type of a player that are not a best response to some conjecture that puts weight only on profiles of types of other players and states that that type thinks possible, combined with actions of those types that have survived so far. We describe a number of applications. This solution concept characterizes the implications of equilibrium when a player is known to have some private information but may have additional information. It thus answers the "informational robustness" question of what can we say about the set of outcomes that may arise in equilibrium of a Bayesian game if players may observe some additional information. 
Keywords:  Incomplete Information, Informational Robustness, Bayes Correlated Equilibrium, Interim Correlated Rationalizability, BeliefFree Rationalizability 
JEL:  C72 C79 D82 D83 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2066&r=mic 
By:  Dirk Bergemann (Cowles Foundation, Yale University); Benjamin Brooks (Dept. of Economics, University of Chicago); Stephen Morris (Dept. of Economics, Princeton University) 
Abstract:  A single unit of a good is to be sold by auction to one of two buyers. The good has either a high value or a low value, with known prior probabilities. The designer of the auction knows the prior over values but is uncertain about the correct model of the buyers’ beliefs. The designer evaluates a given auction design by the lowest expected revenue that would be generated across all models of buyers’ information that are consistent with the common prior and across all Bayesian equilibria. An optimal auction for such a seller is constructed, as is a worstcase model of buyers’ information. The theory generates upper bounds on the seller’s optimal payoff for general manyplayer and commonvalue models. 
Keywords:  Optimal auctions, common values, information structure, model uncertainty, ambiguity aversion, robustness, Bayes correlated equilibrium, revenue maximization, revenue equivalence, information rent 
JEL:  C72 D44 D82 D83 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2065&r=mic 
By:  Zhijun Chen; Patrick Rey 
Abstract:  Crosssubsidization arises naturally when firms with different comparative ad vantages compete for consumers with diverse shopping patterns. Firms then face a form of coopetition, being substitutes for onestop shoppers and complements for multistop shoppers. Competition for onestop shoppers then drives total prices down to cost, but firms subsidize weak products with the profit made on strong products. While firms and consumers would bene.t from cooperation limiting cross subsidization (e.g., through price caps), banning belowcost pricing instead increases firms profits at the expense of onestop shoppers; this calls for a cautious use of belowcost pricing regulations in competitive markets. 
Keywords:  crosssubsidization, shopping patterns, multiproduct competition,coopetition. 
JEL:  L11 L41 
Date:  2016–11 
URL:  http://d.repec.org/n?u=RePEc:mos:moswps:201624&r=mic 
By:  Zhijun Chen; Greg Shaffer 
Abstract:  Contracts that reference rivals have long been a focus of antitrust law and the subject of intense scholarly debate. This paper compares two such contracts, exclusivedealing contracts and marketshare contracts, in a model of naked exclusion. We discuss the different mechanisms through which each works and identify the fundamental tradeoff that arises: marketshare contracts are better at maximizing a seller’s benefit from foreclosure whereas exclusive dealing is better at minimizing a seller’s cost of foreclosure. We give settings in which each is the more profitable contract and show that welfare can be worse with marketshare contracts. 
Keywords:  Exclusive dealing, Marketshare contracts, Dominant Firm, Foreclosure 
JEL:  L13 L41 L42 K21 D86 
Date:  2016–11 
URL:  http://d.repec.org/n?u=RePEc:mos:moswps:201644&r=mic 
By:  Kvaløy, Ola (UiS Business School, University of Stavanger); Olsen, Trond E. (Dept. of Business and Management Science, Norwegian School of Economics) 
Abstract:  We analyze relational contracting between a principal and a team of agents where only aggregate output is observable. We deduce optimal team incentive contracts under di¤erent set of assumptions, and show that the principal can use team size and team composition as instruments in order to improve incentives. In particular, the principal can strengthen the agents' incentives by composing teams that utilize stochastic dependencies between the agents' outputs. We also show that more agents in the team may under certain conditions increase each team member's effort incentives, in particular if outputs are negatively correlated. 
Keywords:  Relational contracts; team incentive scheme 
JEL:  D00 D20 D21 D80 D86 
Date:  2016–12–16 
URL:  http://d.repec.org/n?u=RePEc:hhs:nhhfms:2016_023&r=mic 
By:  F. Zagonari 
Abstract:  This paper identifies the globally stable conditions under which an individual facing the same choice in many subsequent times learns to behave as prescribed by the expectedutility model. To do so, the analysis moves from the relevant behavioural models suggested by psychology (i.e., weighted probabilities applied to regret and rejoice theory), and by updating probability estimations and outcome preferences according to the learning models suggested by neuroscience (i.e., adaptive learning aimed at reducing surprises), and analogous to Bayesian updating. The search context is derived from experimental economics, whereas the learning framework is borrowed from theoretical economics. Analytical results show that obstinate and lucky individuals are better off in the shortrun (i.e., a low density of events in the reference period), but they do not learn, and this is true to a greater extent in a simple context; in contrast, reactive and unlucky individuals are worse off in the shortrun, but they learn and are better off in the longrun (i.e., all individuals are equally lucky or unlucky), and this is true to a greater extent in a complex context. The expectedutility model explains real behaviours in the longrun whenever unlucky events are more likely than lucky events. 
JEL:  D83 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:bol:bodewp:wp1090&r=mic 
By:  Benoît Julien; Sephorah Mangin 
Abstract:  This paper generalizes the wellknown Hosios (1990) efficiency condition to dynamic search and matching environments where the expected match output depends on the market tightness. Such environments give rise to a novel externality – the output externality – which may be either positive or negative. The generalized Hosios condition is simple: entry is constrained efficient when buyers’ surplus share equals the matching elasticity plus the surplus elasticity (i.e. the elasticity of the expected joint match surplus with respect to buyers). This intuitive condition captures both the standard externalities generated by the frictional matching process and the output externality. 
Keywords:  constrained efficiency, search and matching, directed search, competitive search, Nash bargaining, Hosios condition 
JEL:  C78 D83 E24 J64 
Date:  2016–11 
URL:  http://d.repec.org/n?u=RePEc:mos:moswps:201628&r=mic 
By:  F. Delbono; L. Lambertini 
Abstract:  We challenge the global optimality of oneshot punishments in infi nitely repeated games with discounting. Speci fically, we show that the stickandcarrot punishment à la Abreu (1986) may not be globally optimal. We prove our result by investigating tacit collusion in the infi nite repetition of a linear Cournot game. We illustrate the existence of the stickandcarrot globally optimal punishment for large cartels, and fully characterise it. Then, we show that for mall cartels, global optimality may be reached only with twoperiod punishments. 
JEL:  C73 L13 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:bol:bodewp:wp1091&r=mic 
By:  Luca Savorelli (School of Economics and Finance, University of St Andrews); Jacob Seifert (University of Manchester) 
Abstract:  We consider a spatial duopoly with nonmonotonic network effects and extend the literature by endogenizing firms' location decisions. We show that the existence of equilibrium is ruled out due to displacement incentives at the location stage whenever network effects are sufficiently strong. Furthermore, unlike in exogenous location models, neither vertical product differentiation nor a monopoly outcome can arise endogenously in equilibrium. Relative to monotonic network effect models, our framework provides an additional rationale for a duopolistic market structure to be welfarepreferred to monopoly: for large population sizes, splitting demand between two firms can reduce the disutility from crowding. 
Keywords:  product differentiation, network effects, welfare. 
JEL:  L14 D62 
Date:  2016–12–23 
URL:  http://d.repec.org/n?u=RePEc:san:wpecon:1615&r=mic 
By:  Rothenhäusler, Dominik; Schweizer, Nikolaus; Szech, Nora 
Abstract:  This paper analyzes how moral costs affect individual support of morally difficult group decisions. We study a threshold public good game with moral costs. Motivated by recent empirical findings, we assume that these costs are heterogeneous and consist of three parts. The first one is a standard cost term. The second, shared guilt, decreases in the number of supporters. The third hinges on the notion of being pivotal. We analyze equilibrium predictions, isolate the causal effects of guilt sharing, and compare results to standard utilitarian and nonconsequentialist approaches. As interventions, we study information release, feedback, and fostering individual moral standards. 
Keywords:  Moral Decision Making,Committee Decisions,Diffusion of Responsibility,Shared Guilt,Being Pivotal,Division of Labor,Institutions and Morals 
JEL:  D02 D03 D23 D63 D82 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:zbw:kitwps:99&r=mic 
By:  Boom, Anette (Department of Economics, Copenhagen Business School) 
Abstract:  This paper examines the effect of bid regulations on the range of potential equilibrium prices in a multiunit uniform price auction with heterogenous bidders. General bid caps destroy equilibria with prices above the bid cap and create new equilibria with prices way below the cap. A cap only for larger firms does not guarantee market prices below that cap. A sufficiently high bid floor only for smaller firms destroys some or all pure strategy equilibria despite their prices being above the bid floor. With a general bid floor this happens only with considerably higher bid floors. 
Keywords:  Multiunit Auctions; Heterogenous Bidders; Bid Regulation 
JEL:  D43 D44 L12 L13 L51 
Date:  2016–12–01 
URL:  http://d.repec.org/n?u=RePEc:hhs:cbsnow:2016_001&r=mic 
By:  Gao, Jianwei; Zhao, Feng 
Abstract:  This paper develops some new stochastic dominance (SD) rules for ranking transformations on a random variable, which is the first time to study ranking approach for transformations on the discrete framework. By using the expected utility theory, the authors first present a sufficient condition for general transformations by first degree SD (FSD), and further develop it into the necessary and sufficient condition for the monotonic transformations. For the second degree SD (SSD) case, the authors divide the monotonic transformations into increasing and decreasing ones, and respectively derive the necessary and sufficient conditions for the two situations. For two different discrete random variables with the same possible states, they obtain the sufficient and necessary condition for FSD and SSD, respectively. The feature of the new SD rules is that each FSD condition is represented by the transformation functions and each SSD condition is characterized by the transformation functions and the probability distributions of the random variable. This is different from the existing SD approach where they are described by cumulative distribution functions. In this way, the authors construct a new theoretical paradigm for transformations on the discrete random variable. Finally, a numerical example is provided to show the effectiveness of the new SD rules. 
Keywords:  stochastic dominance,transformation,utility theory,insurance 
JEL:  C51 D81 G1 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:zbw:ifwedp:201649&r=mic 
By:  HIRATA, Daisuke; KASUYA, Yusuke 
Abstract:  This paper studies stable and (onesided) strategyproof rules in manytoone matching markets with contracts. Not assuming any kind of substitutes condition or the law of aggregate demand, we obtain the following results. First, the number of stable and strategyproof rules is at most one. Second, the doctoroptimal stable rule, whenever it exists, is the unique candidate for a stable and strategyproof rule. Third, a stable and strategyproof rule, whenever it exists, is secondbest optimal for doctor welfare, in that no individually rational and strategyproof rule can dominate it. This last result is further generalized to nonwasteful and strategyproof rules. Due to the weak assumptions, our analysis covers a broad range of markets, including cases where a (unique) stable and strategyproof rule is not equal to the one induced by the cumulative offer process or the deferred acceptance algorithm. 
Keywords:  matching with contracts, stability, strategyproofness, uniqueness, efficiency, irrelevance of rejected contracts 
Date:  2016–12 
URL:  http://d.repec.org/n?u=RePEc:hit:econdp:201613&r=mic 
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:  We introduce the notion of stable sets with externalities and address the existence problem. The importance of this solution concept is related to the fact that the existence of core allocations for exchange economies is not in general assured in a framework with more than two traders. 
Keywords:  Stable sets; interdependent preferences; core; types of agents. 
JEL:  C71 D51 D70 
Date:  2016–12–17 
URL:  http://d.repec.org/n?u=RePEc:sef:csefwp:461&r=mic 
By:  S. CerreiaVioglio; F. Maccheroni; M. Marinacci; A. Rustichini 
Abstract:  We characterize consistent random choice rules in terms of the optimality of the support. We then proceed to study stochastic choice in a consumer theory setting. We prove a law of demand for stochastic choice. We then move to a temporal setting where we characterize the softmax decision criterion. 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:593&r=mic 
By:  Satoh, Atsuhiro; Tanaka, Yasuhito 
Abstract:  We examine maximin and minimax strategies for firms under symmetric oligopoly with differentiated goods. We consider two patterns of game; the Cournot game in which strategic variables of the firms are their outputs, and the Bertrand game in which strategic variables of the firms are the prices of their goods. We will show that the maximin strategy and the minimax strategy in the Cournot game, and the maximin strategy and the minimax strategy in the Bertrand game for the firms are all equivalent. However, the maximin strategy for the firms are not necessarily equivalent to their Nash equilibrium strategies in the Cournot game nor the Bertrand game. But in a special case, where the objective function of one firm is the opposite of the sum of the objective functions of other firms, the maximin and the minimax strategies for the firms constitute the Nash equilibrium both in the Cournot game and the Bertrand game. 
Keywords:  maximin strategy, minimax strategy, oligopoly 
JEL:  C72 D43 
Date:  2016–12–27 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:75837&r=mic 
By:  Pio Baake; Slobodan Sudaric 
Abstract:  We analyze pricing and competition under paid prioritization within a model of interconnected internet service providers (ISPs), heterogeneous content providers (CPs) and heterogeneous consumers. We show that prioritization is welfare superior to a regime without prioritization (network neutrality) and yields higher incentives for investment in network capacities. As ISPs price discriminate between onnet and offnet CPs, their bottleneck property is propagated and competition for consumers increases resulting in a potential prisoner's dilemma when deciding whether to offer prioritization. We show that peering for prioritized traffic emerges as a collusive outcome and present offnet prices as a further collusive instrument. 
Keywords:  interconnection, investment, network neutrality, prioritization 
JEL:  L13 L51 L96 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1629&r=mic 
By:  Emanuele Borgonovo; Veronica Cappelli; Fabio Maccheroni; Massimo Marinacci 
Abstract:  The purpose of this note is to discuss the relation between model uncertainty in risk analysis and decision theory. 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:592&r=mic 