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on Microeconomics |
| By: | Dirk Bergemann (Yale University); Benjamin Brooks (University of Chicago); Stephen Morris (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 take-it-or-leave-it-offer in the secondary market under complete information. |
| JEL: | C72 D44 D82 D83 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:085_2016&r=mic |
| By: | Stephen Morris (Princeton University); Ming Yang (Duke University) |
| Abstract: | We study a coordination game where players choose what information to acquire about payoffs prior to the play of the game. We allow general information acquisition technologies, modeled by a cost functional defined on information structures. A cost functional satisfies continuous choice if players choose a continuous decision rule even in a decision problem with discontinuous payoffs. If continuous choice holds, there is a unique equilibrium; if it fails, there are multiple equilibria. We show how continuous choice captures the idea that it is sufficiently harder to distinguish states that are close to each other relative to far away states. |
| Keywords: | coordination, endogenous information acquisition, continuous choice, higher order beliefs |
| JEL: | C72 D82 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:087_2017&r=mic |
| By: | Dirk Bergemann (Yale University); Benjamin Brooks (University of Chicago); Stephen Morris (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 worst-case model of buyers' information. The theory generates upper bounds on the seller's optimal payoff for general many-player and common-value models. |
| Keywords: | Optimal auctions, common values, information structure, mo del 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:pri:metric:084_2016&r=mic |
| By: | Gisèle Umbhauer |
| Abstract: | The paper is about mixed strategy Nash equilibria in discrete second price all-pay auctions with a limit budget. Two players fight over a prize of value V. Each player submits a bid lower or equal to M, the limit budget. The prize goes to the highest bidder but both bidders pay the lowest bid. V, M and the bids are integers. The paper studies the convergence of the mixed Nash equilibrium probability distribution in the discrete auction to the mixed Nash equilibrium probability distribution in the more well-known continuous second price all-pay auction –or static war of attrition. We establish that the- expected- convergence between discrete and continuous equilibrium distributions is in no way automatic. Both distributions converge for V odd and large, but, for even values of V, the discrete distribution is quite strange and obeys a singular yoyo phenomenon: the probabilities assigned to two adjacent bids are quite different, one probability being much lower than the continuous one, the adjacent probability being much larger. So the discrete probabilities, for V even, don’t converge to the continuous ones. Yet there is a convergence, when turning to sums: the sums of the discrete probabilities of two adjacent bids converge to the sums of the continuous probabilities of the same two bids for large values of V. It is shown in the paper that the yoyo phenomenon doesn’t disappear - it is even strengthened- when switching to lower natural bid increments, like 0.5 or 0.1. More generally, it is shown that convergence is an exception rather than the rule and that it requires a special link between V, M and the bid increment. It follows a lack of continuity between the discrete Nash equilibria and the continuous Nash equilibria. |
| Keywords: | discrete game, continuous game, second price all-pay auction, Nash equilibrium, increment. |
| JEL: | C72 D44 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2017-14&r=mic |
| By: | Dirk Bergemann (Yale University); Stephen Morris (Princeton University) |
| Abstract: | A set of players have preferences over a set of outcomes. We consider the problem of an "information designer" who can choose an information structure for the players to serve his ends, but has no ability to change the mechanism (or force the players to make particular action choices). We describe a unifying perspective for information design. We consider a simple example of Bayesian persuasion with both an uninformed and informed receiver. We extend information design to many player and relate it to the literature on incomplete information correlated equilibrium. |
| Keywords: | Information Design, Bayesian Persuasion, Bayes Correlated Equilibrium, Information Structure |
| JEL: | D82 D83 C72 |
| Date: | 2016–01 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:076_2016&r=mic |
| By: | Stephen Morris (Princeton University); Ming Yang (Duke University) |
| Abstract: | We study a coordination game where players simultaneously acquire information prior to the play of the game. We allow general information acquisition technologies, modeled by a cost functional mapping from information structures. Costly local distinguishability is a property requiring that the cost of distinguishing nearby states is hard relative to distinguishing distant states. This property is not important in decision problems, but is crucial in determining equilibrium outcomes in games. If it holds, there is a unique equilibrium; if it fails, there are multiple equilibria close to those that would exist if there was complete information. We study these issues in the context of a regime change game with a continuum of players. We also provide a common belief foundation for equilibria of this game. This allows us to distinguish cases where the players could (physically) acquire information giving rise to multiple equilibria, but choose not to, and situations where players could not physically have acquired information in a way consistent with multiple equilibria. Our analysis corresponds to the former case, while the choosing precision of additive noise corresponds to the latter case. |
| Keywords: | coordination, endogenous information acquisition, costly local distinguishability, higher order beliefs |
| JEL: | C72 D82 |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:079_2016&r=mic |
| By: | Dirk Bergemann (Yale University); Stephen Morris (Princeton University) |
| Abstract: | Fixing a game with uncertain payoffs, information design identifies the information structure and equilibrium that maximizes the payoff of an information designer. We show how this perspective unifies existing work, including that on communication in games (Myerson (1991)), Bayesian persuasion (Kamenica and Gentzkow (2011)) and some of our own recent work. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures. |
| JEL: | C72 C82 D83 C79 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:086_2016&r=mic |
| By: | Dirk Bergemann (Yale University); Stephen Morris (Princeton University) |
| Abstract: | Fixing a game with uncertain payoffs, information design identifies the information structure and equilibrium that maximizes the payoff of an information designer. We show how this perspective unifies existing work, including that on communication in games (Myerson (1991)), Bayesian persuasion (Kamenica and Gentzkow (2011)) and some of our own recent work. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures. |
| Keywords: | Information design, Bayesian persuasion, correlated equilibrium, incomplete informa- tion, robust predictions, information structure |
| JEL: | C72 D82 D83 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:089_2017&r=mic |
| By: | Stephen Morris (Princeton University); Hyun Song Shin (Bank for International Settlements); Muhamet Yildiz (M.I.T.) |
| Abstract: | We study coordination games under general type spaces. We characterize rationalizable actions in terms of the properties of the belief hierarchies and show that there is a unique rationalizable action played whenever there is approximate common certainty of rank beliefs, defined as the probability the players assign to their payoff parameters being higher than their opponents'. We argue that this is the driving force behind selection results for the specific type spaces in the global games literature. |
| JEL: | C70 D83 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:069_2015&r=mic |
| By: | Victor Arshavskiy |
| Abstract: | When a debt covenant is violated the lender has the right to demand immediate repayment of the loan. Using this right, the lender can extract certain concessions from the borrower (manager), which may be inefficient. I propose a theory that explains why, despite this inefficiency, tight and often violated debt covenants may be optimal. In a repeated moral hazard problem combined with an incomplete contract set-up, the debt overhang prevents the manager from exercising optimal effort. I deviate from the standard incomplete contract set-up by allowing outside market participants to observe the uncontractable outcome. I model the manager's outside option as the opportunity to refinance his debt on a competitive loan market. In this situation, the market independently evaluates the manager's performance based on observable parameters. The value of the outside option has an important impact on the covenant design. A strict covenant will severely punish the manager if his outside option is low. If the covenant is violated the lender will have control over the manager's assets and the manager will face a renegotiation game in which the lender has all the bargaining power. In this case a high outside option allows the manager to retain some rents. The manager will exercise effort to increase his chances to have a high outside option. |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:bel:wpaper:37&r=mic |
| By: | Giovanni Immordino (Università di Napoli Federico II and CSEF); Gülen Karakoç-Palminteri (Università di Milano Bicocca); Salvatore Piccolo (Università di Bergamo and CSEF) |
| Abstract: | We study a simple mechanism design problem that describes the optimal behavior of a country targeted by a foreign terrorist group. The country is uncertain about the terrorists’ strength and may decide to acquire such information from the community hosting the terrorists. We highlight a novel trade-off between target hardening – i.e., mitigating the incidence of an attack by strengthening internal controls and improving citizens’ protection – and preemptive military measures aimed at eradicating the problem at its root – i.e., a strike in the terrorists’ hosting country. We show that, conditional on being informed about the terrorists’ strength, the country engages in a preemptive attack only when it faces a sufficiently serious threat and when the community norms favoring terrorists are weak. Yet, in contrast with the existing literature, we show that it is optimal for the country to acquire information only when these norms are strong enough and when its prior information about the terrorists’ strength is sufficiently poor. |
| Keywords: | Counter-terrorism, Striking Rules, Target Hardening, Terrorism |
| JEL: | D02 D74 D73 D78 |
| Date: | 2017–04–07 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:470&r=mic |
| By: | Anton Kolotilin (School of Economics, UNSW Business School, UNSW); Tymofiy Mylovanov (University of Pittsburgh, Department of Economics); Andriy Zapechelnyuk (Adam Smith Business School, University of Glasgow); Ming Li (Concordia University and CIREQ) |
| Abstract: | We study persuasion mechanisms in linear environments. A privately informed receiver chooses between two actions. A sender designs a persuasion mechanism that can condition the information disclosed to the receiver on the receiver’s report about his type. We establish the equivalence of implementation by persuasion mechanisms and by experiments. We also characterize the optimal persuasion mechanisms. In particular, if the density of the receiver’s type is log-concave, then the optimal persuasion mechanism reveals the state if and only if the state is below a threshold. We apply our results to the design of media censorship policies. |
| Keywords: | Bayesian persuasion, information disclosure, information design, mechanism design without transfers, experiments, persuasion mechanisms, media |
| JEL: | D82 D83 L82 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:swe:wpaper:2016-21&r=mic |
| By: | Dilip Abreu (Princeton University); Benjamin Brooks (Becker Friedman Institute and Univ ersity of Chicago); Yuliy Sannikov (Princeton University) |
| Abstract: | We study the subgame perfect equilibria of two player stochastic games with perfect monitoring and geometric discounting. A novel algorithm is developed for calculating the discounted payoffs that can be attained in equilibrium. This algorithm generates a sequence of tuples of payoffs vectors, one payoff for each state, that move around the equilibrium payoff sets in a clockwise manner. The trajectory of these "pivot" payoffs asymptotically traces the boundary of the equilibrium payoff correspondence. We also provide an implementation of our algorithm, and preliminary simulations indicate that it is more efficient than existing methods. The theoretical results that underlie the algorithm also yield a bound on the number of extremal equilibrium payoffs. |
| JEL: | C63 C72 C73 D90 |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:78_2016&r=mic |
| By: | Nicolás Hernández Santibáñez (DIM - Departamento de Ingeniera Matematica [Santiago] - Universidad de Chile [Santiago], CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique); Dylan Possamaï (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique); Chao Zhou (NUS - National University of Singapore) |
| Abstract: | In this paper, we extend the optimal securitization model of Pagès [41] and Possamaï and Pagès [42] between an investor and a bank to a setting allowing both moral hazard and adverse selection. Following the recent approach to these problems of Cvitanić, Wan and Yang [12], we characterize explicitly and rigorously the so-called credible set of the continuation and temptation values of the bank, and obtain the value function of the investor as well as the optimal contracts through a recursive system of first-order variational inequalities with gradient constraints. We provide a detailed discussion of the properties of the optimal menu of contracts. |
| Keywords: | moral hazard,bank monitoring, securitization, adverse selection, principal-agent problem |
| Date: | 2017–01–14 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01435460&r=mic |
| By: | Alia Gizatulina (Max Planck Institute for Research on Collective Goods); Martin Hellwig (Max Planck Institute for Research on Collective Goods) |
| Abstract: | McAfee and Reny (1992) have given a necessary and sufficient condition for full surplus extraction in naive type spaces with a continuum of payoff types. We generalize their characterization to arbitrary abstract type spaces and to the universal type space and show that in each setting, full surplus extraction is generically possible. We interpret the McAfee-Reny condition as a much stronger version of injectiveness of belief functions and prove genericity by arguments similar to those used to prove the classical embedding theorem for continuous functions. Our results can be used to also establish the genericity of common priors that admit full surplus extraction. |
| Keywords: | mechanism design, surplus extraction,abstract type spaces, universal type space, genericity, correlated values, correlated information, strategic continuity |
| JEL: | D40 D44 D80 D82 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:mpg:wpaper:2017_02&r=mic |
| By: | Christopher J. Tyson (Queen Mary University of London) |
| Abstract: | The class of preferences over opportunity sets ("menus") rationalizable by underlying preferences over the alternatives is characterized for the general case in which the dataset is unrestricted. In particular, both the universal set of alternatives and the domain of menus over which preferences are asserted by the decision maker are arbitrary. The key "Cover Dominance" axiom states that any menu strictly preferred to a collection of menus must be strictly preferred to any menu covered by the collection. The method of characterization relies upon transitivity of menu preferences, but completeness can be relaxed. |
| Keywords: | General domains, Opportunity sets, Revealed preference, Transitivity |
| JEL: | D01 D11 |
| Date: | 2017–04 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp819&r=mic |
| By: | Llorente-Saguer, Aniol; Zultan, Ro'i |
| Abstract: | The theoretical literature on collusion in auctions suggests that the first-price mechanism can deter the formation of bidding rings. However, such analyses neglect to consider the effects of failed collusion attempts, wherein information revealed in the negotiation process may affect bidding behavior. We experimentally test a setup in which theory predicts no collusion and no information revelation in first-price auctions. The results reveal a hitherto overlooked failing of the first-price mechanism: failed collusion attempts distort bidding behavior, resulting in a loss of seller revenue and efficiency. Moreover, the first-price mechanism does not result in less collusion than the second-price mechanism. We conclude that, while the features of the first-price mechanism may have the potential to deter bidder collusion, the role of beliefs in guiding bidding behavior make it highly susceptible to distortions arising from the informational properties of collusive negotiation. Auction designers should take this phenomenon into account when choosing the auction mechanism. |
| Keywords: | auctions; Collusion; Experiment |
| JEL: | C72 C91 D44 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11944&r=mic |
| By: | Stephen Morris (Princeton University); Muhamet Yildiz (Massachusetts Institute of T echnology) |
| Abstract: | A coordination game with incomplete information is played through time. In each period, payoffs depend on a fundamental state and an additional idiosyncratic shock. Fundamentals evolve according to a random walk where the changes in fundamentals (namely common shocks) have a fat tailed distribution. We show that majority play shifts either if fundamentals reach a critical threshold or if there are large common shocks, even before the threshold is reached. The fat tails assumption matters because it implies that large shocks make players more unsure about whether their payoffs are higher than others. This feature is necessary for large shocks to matter |
| JEL: | E32 G01 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:083_2016&r=mic |
| By: | George J. Mailath (University of Pennsylvania); Stephen Morris (Princeton University); Andrew Postlewaite (University of Pennsylvania) |
| Abstract: | A law prohibiting a particular behavior does not directly change the payoff to an individual should he engage in the prohibited behavior. Rather, any change in the individual’s payoff, should he engage in the prohibited behavior, is a consequence of changes in other peoples' behavior. If laws do not directly change payoffs, they are “cheap talk,†and can only affect behavior because people have coordinated beliefs about the effects of the law. Beginning from this point of view, we provide definitions of authority in a variety of problems, and investigate how and when individuals can have, gain, and lose authority. |
| JEL: | K00 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:082_2016&r=mic |
| By: | Bar-Isaac, Heski; Shapiro, Joel |
| Abstract: | By introducing a shareholder with many votes (a blockholder) to a standard model of voting, we uncover several striking results. First, if a blockholder is unbiased, she may not vote with all of her shares. This is efficient, as it prevents her vote from drowning out the information provided by other votes. Second, if this blockholder can announce her vote before the vote takes place, other shareholders may ignore their information and vote with the blockholder to support her superior information. Third, if the blockholder is biased, some shareholders will try to counter the blockholder's vote. The results are robust to allowing for information acquisition and trade. This suggests that regulations discouraging or prohibiting abstention, strategic behavior, and/or coordination may reduce efficiency. |
| Keywords: | Blockholder; corporate governance; shareholder voting |
| JEL: | D72 G34 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11933&r=mic |
| By: | Marc Fleurbaey (Princeton University); Stephane Zuber (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:pri:metric:088_2017&r=mic |
| By: | Henry, Emeric; Ottaviani, Marco |
| Abstract: | An informer sequentially collects information at a cost to influence an evaluator's choice between rejection and approval. Payoffs and control rights are split between informer and evaluator depending on the organizational rules governing the approval process. We compare the performance of different organizations from a positive and normative perspective, depending on the commitment power of informer and evaluator. As a welfare benchmark we recover Wald's (1947) classic solution for a statistician with payoff equal to the sum of our informer and evaluator. We apply the analysis to the regulatory process for drug approval and to the market for new technologies. |
| Keywords: | Information; Opproval; Organization; Persuasion |
| JEL: | D83 M38 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11939&r=mic |