
on Microeconomics 
By:  Dirk Bergemann (Cowles Foundation, Yale University); Philipp Strack (Cowles Foundation, Yale University) 
Abstract:  A single seller faces a sequence of buyers with unit demand. The buyers are forwardlooking and longlived but vanish (and are replaced) at a constant rate. The arrival time and the valuation is private information of each buyer and unobservable to the seller. Any incentive compatible mechanism has to induce truthtelling about the arrival time and the evolution of the valuation. We derive the optimal stationary mechanism, characterize its qualitative structure, and derive a closedform solution. As the arrival time is private information, the buyer can choose the time at which he reports his arrival. The truthtelling constraint regarding the arrival time can be represented as an optimal stopping problem. The stopping time determines the time at which the buyer decides to participate in the mechanism. The resulting value function of each buyer cannot be too convex and must be continuously differentiable everywhere, reflecting the option value of delaying participation. The optimal mechanism thus induces progressive participation by each buyer: he participates either immediately or at a future random time. 
Keywords:  Dynamic Mechanism Design, Observable Arrival, Unobservable Arrival, Repeated Sales, Interim Incentive Constraints, Interim Participation Constraints, Stopping Problem, Option Value, Progressive Participation 
JEL:  D44 D82 D83 
Date:  2019–08 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2189r&r=all 
By:  Sarah Auster; Nenad Kos; Salvatore Piccolo 
Abstract:  We study a model of optimal pricing where the right to propose a mechanism is determined endogenously: a privately informed buyer covertly invests to increase the probability of offering a mechanism. We show that higher types get to propose a mechanism more often, enabling the seller to learn from the trading process. In any equilibrium, the seller either offers the price he would have offered if he was always the one to make an offer or randomises over prices. Pure strategy equilibria may fail to exist, even when types are continuously distributed. A full characterization of equilibria is provided in the model with two types, where the seller's profit is shown to be nonmonotonic in the share of highvalue buyers. 
Keywords:  Optimal Pricing, Bargaining Power 
JEL:  D82 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2020_151&r=all 
By:  Yasuaki Wasa (Department of Electrical Engineering and Bioscience, Waseda University, Tokyo 1698555, Japan.); KenIchi Akao (Graduate School of Social Sciences, Waseda University, Tokyo 1698050, Japan.); Kenko Uchida (Research Institute for Science and Engineering, Waseda University, Tokyo 1698555, Japan.) 
Abstract:  This paper investigates an optimal dynamic incentive contract between a riskaverse principal (system operator) and multiple riskaverse agents (subsystems) with independently local controllers in continuoustime controlled Markov processes, which can represent various cyberphysical systems. The principal fs incentive design and the agents f decisionmakings under asymmetric information structure are known as the principalagent (PA) problems in economic field. However, the standard framework in economics cannot be directly applied to the realistic control systems including largescale cyberphysical systems and complex networked systems due to some unrealistic assumptions for an engineering perspective. In this paper, using a constructive approach based on the techniques of the classical stochastic control theory, we propose and solve a novel dynamic control/incentive synthesis for the PA problem under moral hazard. 
Keywords:  Principalagent problems, Moral hazard, Cyberphysical systems, Multiagent systems, Dynamic programming, Risksensitive stochastic control, Differential games 
JEL:  C61 C73 D82 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:was:dpaper:2001&r=all 
By:  Asseyer, Andreas 
Abstract:  This paper studies how information control affects incentives for collusion and optimal organizational structures in principalsupervisoragent relationships. I consider a model in which the principal designs the supervisor's signal on the productive agent's private information and the supervisor and agent may collude. I show that the principal optimally delegates the interaction with the agent to the supervisor if either the supervisor's budget is large or the value of production is small. The principal prefers direct communication with the supervisor and agent if the supervisor's budget is sufficiently small and the value of production is high. 
Keywords:  Collusion,Information design,Delegation 
JEL:  D73 D83 D86 H57 M55 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:zbw:fubsbe:20203&r=all 
By:  Salvador Barberà; Geoffroy de Clippel; Alejandro Neme; Kareen Rozen 
Abstract:  A decision maker (DM) may not perfectly maximize her preference over the feasible set. She may feel it is good enough to maximize her preference over a sufficiently large consideration set; or just require that her choice is sufficiently wellranked (e.g., in the top quintile of options); or even endogenously determine a threshold for what is good enough, based on an initial sampling of the options. Heuristics such as these are all encompassed by a common theory of Orderk Rationality, which relaxes perfect optimization by only requiring choices from a set S to fall within the set’s top k(S) elements according to the DM’s preference ordering. Heuristics aside, this departure from rationality offers a natural way, in the classic ‘as if’ tradition, to gradually accommodate more choice patterns as k increases. We characterize the empirical content of Orderk Rationality (and related theories), and provide a tractable testing method which is comparable to the method of checking SARP. 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:bro:econwp:202010&r=all 
By:  René van den Brink (VU University Amsterdam); Dinko Dimitrov (Saarland University [Saarbrücken]); Agnieszka Rusinowska (CNRS  Centre National de la Recherche Scientifique, CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics) 
Abstract:  We study the issue of assigning weights to players that identify winning coalitions in plurality voting democracies. For this, we consider plurality games which are simple games in partition function form such that in every partition there is at least one winning coalition. Such a game is said to be precisely supportive if it possible to assign weights to players in such a way that a coalition being winning in a partition implies that the combined weight of its members is maximal over all coalitions in the partition. A plurality game is decisive if in every partition there is exactly one winning coalition. We show that decisive plurality games with at most four players, majority games with an arbitrary number of players, and almost symmetric decisive plurality games with an arbitrary number of players are precisely supportive. Complete characterizations of a partition's winning coalitions are provided as well. 
Abstract:  Nous étudions la question de l'attribution de pondérations aux acteurs qui identifient les coalitions gagnantes dans les démocraties à la pluralité des suffrages. Pour cela, nous considérons les jeux à la pluralité qui sont de simples jeux sous forme de partition, de telle sorte que dans chaque partition, il existe au moins une coalition gagnante. On dit qu'un tel jeu est justement favorable s'il est possible d'attribuer des pondérations aux joueurs de telle sorte qu'une coalition gagnante dans une partition implique que le poids combiné de ses membres est maximal par rapport à toutes les coalitions de la partition. Un jeu à la pluralité est décisif si dans chaque partition il y a exactement une coalition gagnante. Nous montrons que les jeux à la pluralité décisive avec au plus quatre joueurs, les jeux à la majorité avec un nombre arbitraire de joueurs et les jeux à la pluralité décisive presque symétriques avec un nombre de joueurs arbitraire sont précisément favorables. Des caractérisations complètes des coalitions gagnantes d'une partition sont également fournies. 
Keywords:  plurality game,plurality voting,precise support,simple game in partition function form,winning coalition,jeu à la pluralité,vote à la pluralité,soutien précis,jeu simple sous forme de partition,coalition gagnante 
Date:  2019–07 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs02346134&r=all 
By:  Armstrong, Mark; Vickers, John 
Abstract:  We explore patterns of price competition in an oligopoly where consumers vary in the set of suppliers they consider for their purchase. In the case of "nested reach" we find equilibria, unlike those in existing models, in which price competition is segmented: small firms offer only low prices and large firms only offer high prices. We characterize equilibria in the threefirm case using correlation measures of interaction between pairs of firms. We show how entry, merger and market expansion can affect patterns of price competition in novel ways. 
Keywords:  Bertrand competition, price dispersion, consideration sets, mixed strategies 
JEL:  C72 D43 D83 L13 L15 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:98346&r=all 
By:  Chiaki Hara (Institute of Economic Research, Kyoto University) 
Abstract:  Given two pairs of expected utility functions, we formalize the notion that one expected utility function is more riskaverse than the other in the first pair to a greater extent than in the second pair. We do so by assuming that the utility functions are twice continuously differentiable and satisfy the Inada condition, and, in each of the two pairs, using the function that transforms the derivatives of one expected utility function to the derivatives of the other, rather than the function that transforms one expected utility function to the other. This definition allows us to interpret the quantitative results on the ambiguity aversion coefficients of the smooth ambiguity model of Klibanoff, Marinacci, and Mukerji (2005) in some cases not covered by the moreambiguityaversethan relation that they conceived. 
Keywords:  Expected utility functions, risk aversion, ambiguity aversion, smooth ambiguity model 
JEL:  C38 D81 G11 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:kyo:wpaper:1019&r=all 
By:  Raghul S Venkatesh (AixMarseille Univ., CNRS, EHESS, Centrale Marseille, AMSE) 
Abstract:  An informed and an uninformed agent both contribute to a joint coordination game such that their actions are substitutable and constrained. When agents are allowed to share information prior to the coordination stage, in the absence of commitment , there is full information revelation as long as constraints are not binding. The presence of binding constraints results in only partial revelation of information in equilibrium. The most informative equilibrium is strictly pareto dominant. Allowing for limited commitment strictly increases (ex ante) welfare of both agents. I completely characterize the optimal commitment mechanism for the uninformed agent. Finally, I apply the theoretical results to the problem of information sharing and binding agreements in international alliances. 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:aim:wpaimx:1856&r=all 
By:  Alcalde, José (IUDESP); Dahm, Matthias (Department of Economics,) 
Abstract:  We study the effects of affirmative action through endogenous setasides. We propose a share auction for dual sourcing in which more intensive affirmative action strengthens the favoured provider. This induces potentially more competitive procurement overall. Our main result considers a complete information setting and provides a condition under which affirmative action not only guarantees very substantial minority representation, but also reduces the buyer's provision cost compared to a firstprice auction. We also consider extensions of the benchmark model, including to a setting in which providers have private information about their costs. 
Keywords:  Affirmative Action; Bidding Credits; Bidding Preferences; SetAsides 
JEL:  D44 D47 H57 J15 
Date:  2020–02–11 
URL:  http://d.repec.org/n?u=RePEc:ris:qmetal:2020_001&r=all 
By:  Marco Rogna (Free University of Bolzano‐Bozen, Faculty of Economics and Management, Italy) 
Abstract:  The paper presents a coalitional bargaining model with a peculiar type of partial breakdown: the Burning Coalition Bargaining Model. Rather than triggering the end of all negotiations or the exclusion of some players from the game, as already proposed in the literature, in this model the rejection of a proposal causes the possibility of the proposed coalition to vanish. Under this type of partial breakdown and adopting a standard rejecterproposes protocol, 0normalized, 3players games are examined for extreme values of the breakdown probability. When such probability is equal to one, efficiency is more difficult to obtain than in models adopting discounting. Furthermore, when an efficient outcome is attained, the final payoffs distribution reflects the strength of players in the game, with strength being defined by belonging to more valuable coalitions. The same feature is retained when considering a probability of breakdown approaching zero. 
Keywords:  Bargaining Theory; Bargaining protocols; Coalition formation; Efficiency; Partial breakdown. 
JEL:  C71 C78 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:bzn:wpaper:bemps69&r=all 
By:  de Haan, Thomas (University of Bergen, Department of Economics) 
Abstract:  I introduce a new method to incentivise the elicitation of belief distributions, the Random Partitions method. With this method, an agent’s payoff not only depends on the realised state and the elicited distribution, but also on a randomised twolevel partitioning of the statespace. The method creates a binary lottery payoff structure where reports closer to an agent’s true belief distribution generate a higher probability to earn a high payout. The randomisation of the statespace partitioning ensures that the agent is incentivised to report correctly across the entire belief distribution. I compare the introduced Random Partitions method with both the well known Quadratic Scoring Rule, and a method based on the BeckerDeGrootMarschak procedure and argue that the Random Partitions method gives substantially stronger truthtelling incentives to agents in situations where there are many states/bins. 
Keywords:  Belief elicitation; randomized state/event Space; partitioning; proper scoring rules. 
JEL:  D82 D83 
Date:  2020–01–06 
URL:  http://d.repec.org/n?u=RePEc:hhs:bergec:2020_001&r=all 
By:  Federico Boffa (Free University of Bolzano‐Bozen, Faculty of Economics and Management); Alessandro Fedele (Free University of Bolzano‐Bozen, Faculty of Economics and Management); Alberto Iozzi (Università di Roma 'Tor Vergata' and SOAS University of London) 
Abstract:  Following the development of autonomous vehicles (AVs) and GPS systems, fleets will gain prominence over private vehicles. We analyze the welfare effects of the transition from a fully decentralized regime, in which all travelers are atomistic and do not internalize the congestion externality, to a centralized regime, where all travelers are supplied by a fl eet of AVs controlled by a monopolist. In our model, heterogeneous individuals differing in the disutility from congestion may travel on one of two lanes, which may endogenously differ in the level of congestion, or they may not travel. We show that the monopolist sorts travelers across the two lanes differently than the decentralized regime. Moreover, depending on the severity of congestion costs, it may also exclude some travelers. We find that centralization is always welfare detrimental when the monopolist does not ration travel. If instead rationing occurs, centralization may be welfare beneficial, provided that congestion costs are sufficiently high. We then analyze how to restore first best with road taxes. While congestion charges are optimal under decentralization, taxes differ markedly in a centralized regime, where restoring first best may require subsidizing the monopolist. 
Keywords:  Autonomous vehicles; congestion externality; eets; sorting; rationing 
JEL:  R41 R11 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:bzn:wpaper:bemps67&r=all 
By:  Olga Gorelkina 
Abstract:  This paper studies collusion via information sharing in the context of auctions. The model of collusion via information sharing builds on Aumann’s (1976) description of knowledge. Robustness of auction mechanisms to collusion via information sharing is defined as the impossibility of an agreement to collude. A cartel can agree to collude on a contract if it is common knowledge within that cartel that the contract is incentive compatible and individually rational. Robust mechanisms are characterized in a number of settings where some, all, or no bidders are bound by limited liability. Finally, the characterization is used in a simple IPV setting to design a mechanism that is both optimal and robust to collusion. 
Keywords:  Bidder collusion, mechanism design, communication design, notrade theorem 
JEL:  D82 D44 C72 
Date:  2018–08 
URL:  http://d.repec.org/n?u=RePEc:liv:livedp:20182&r=all 
By:  Gregorio Curello; Ludvig Sinander 
Abstract:  A committee ranks a set of alternatives by sequentially voting on pairs, in an order chosen by the committee's chair. Although the chair has no knowledge of voters' preferences, we show that she can do as well as if she had perfect information. We characterise strategies with this 'regretfreeness' property in two ways: (1) they are efficient, and (2) they avoid two intuitive errors. One regretfree strategy is a sorting algorithm called insertion sort. We show that it is characterised by a lexicographic property, and is outcomeequivalent to a recursive variant of the muchstudied amendment procedure. 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2001.11341&r=all 
By:  Giovanni Paolo Crespi; Davide Radi; Matteo Rocca 
Abstract:  A robust game is a distributionfree model to handle ambiguity generated by a bounded set of possible realizations of the values of players' payoff functions. The players are worstcase optimizers and a solution, called robustoptimization equilibrium, is guaranteed by standard regularity conditions. The paper investigates the sensitivity to the level of uncertainty of this equilibrium. Specifically, we prove that it is an epsilonNash equilibrium of the nominal counterpart game, where the epsilonapproximation measures the extra profit that a player would obtain by reducing his level of uncertainty. Moreover, given an epsilonNash equilibrium of a nominal game, we prove that it is always possible to introduce uncertainty such that the epsilonNash equilibrium is a robustoptimization equilibrium. An example shows that a robust Cournot duopoly model can admit multiple and asymmetric robustoptimization equilibria despite only a symmetric Nash equilibrium exists for the nominal counterpart game. 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2002.00225&r=all 
By:  Marco Buso (Department of Economics and Finance, Catholic University of Sacred Heart, Milan and Interuniversity Centre for Public Economics (CRIEP)); Michele Moretto (DSEA, University of Padova); Dimitrios Zormpas (Department of Mathematics, University of Bologna) 
Abstract:  We study the optimal design of PublicPrivate Partnerships (PPPs) when there is unobservable action on the private partyâ€™s side. We show that if the private party does not have negotiating power over the projectâ€™s surplus, no inefficient delays are attributable to the moral hazard issue. However, if the private party has negotiating power, the firstbest timing is not guaranteed. This time discrepancy is shown to be costly in terms of overall project efficiency. The explicit consideration of the private partyâ€™s negotiating power can explain empirical evidence showing that private parties in PPPs reap excess returns. 
Keywords:  public projects, publicprivate partnerships, moral hazard, real options, investment timing 
JEL:  D81 D82 D86 H54 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:pad:wpaper:0246&r=all 
By:  Lubik, Thomas A.; Matthes, Christian; Mertens, Elmar 
Abstract:  We study equilibrium determination in an environment where two kinds of agents have different information sets: The fully informed agents know the structure of the model and observe histories of all exogenous and endogenous variables. The less informed agents observe only a strict subset of the full information set. All types of agents form expectations rationally, but agents with limited information need to solve a dynamic signal extraction problem to gather information about the variables they do not observe. In this environment, we identify a new channel that leads to equilibrium indeterminacy: Optimal information processing of the less informed agent introduces stable dynamics into the equation system that lead to selffulling expectations. For parameter values that imply a unique equilibrium under full information, the limited information rational expectations equilibrium is indeterminate. We illustrate our framework with a monetary policy problem where an imperfectly informed central bank follows an interest rate rule. 
Keywords:  limited information,rational expectations,signal extraction,belief shocks 
JEL:  C11 C32 E52 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:zbw:bubdps:012020&r=all 
By:  Ryoma KITAMURA (Faculty of Economics, Otemon Gakuin University); Tsuyoshi TOSHIMITSU (School of Economics, Kwansei Gakuin University) 
Abstract:  We develop a model of horizontally differentiated oligopolies with network externalities and reconsider a Stackelberg leader's incentive to invite entry, a problem previously examined by Economides (1996) and Kim (2002). We demonstrate that a Stackelberg leader has (does not have) an incentive to invite entry if the degree of network externalities is larger (smaller) than that of the product substitutability, such that a follower's profit increases (decreases). 
Keywords:  Network externality; Horizontally differentiated oligopoly; Stackelberg competition; Entry; Passive expectation; Responsive expectation 
JEL:  D21 D43 D62 L13 
URL:  http://d.repec.org/n?u=RePEc:kgu:wpaper:203&r=all 
By:  Ga\"etan Fournier; Karine Van Der Straeten; J\"orgen Weibull 
Abstract:  This paper studies a spatial competition game between two firms that sell a homogeneous good at some predetermined fixed price. A population of consumers is spread out over the real line, and the two firms simultaneously choose location in this same space. When buying from one of the firms, consumers incur the fixed price plus some transportation costs, which are increasing with their distance to the firm. Under the assumption that each consumer is ready to buy one unit of the good whatever the locations of the firms, firms converge to the median location: there is "minimal differentiation". In this article, we relax this assumption and assume that there is an upper limit to the distance a consumer is ready to cover to buy the good. We show that the game always has at least one Nash equilibrium in pure strategy. Under this more general assumption, the "minimal differentiation principle" no longer holds in general. At equilibrium, firms choose "minimal", "intermediate" or "full" differentiation, depending on this critical distance a consumer is ready to cover and on the shape of the distribution of consumers' locations. 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2001.11422&r=all 
By:  Mark Whitmeyer 
Abstract:  Always, if the number of states is equal to two; or if the number of receiver actions is equal to two and i. The number of states is three or fewer, or ii. The game is cheap talk, or ii. There are just two available messages for the sender. A counterexample is provided for each failure of these conditions. 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2001.09387&r=all 