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on Microeconomics |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Francisco Castro (Graduate School of Business, Columbia University); Gabriel Weintraub (Graduate School of Business, Stanford University) |
| Abstract: | We study the classic sequential screening problem under ex-post participation constraints. Thus the seller is required to satisfy buyers’ ex-post participation constraints. A leading example is the online display advertising market, in which publishers frequently cannot use up-front fees and instead use transaction-contingent fees. We establish when the optimal selling mechanism is static (buyers are not screened) or dynamic (buyers are screened), and obtain a full characterization of such contracts. We begin by analyzing our model within the leading case of exponential distributions with two types. We provide a necessary and sufficient condition for the optimality of the static contract. If the means of the two types are sufficiently close, then no screening is optimal. If they are sufficiently apart, then a dynamic contract becomes optimal. Importantly, the latter contract randomizes the low type buyer while giving a deterministic allocation to the high type. It also makes the low type worse-off and the high type better-off compared to the contract the seller would offer if he knew the buyer’s type. Our main result establishes a necessary and sufficient condition under which the static contract is optimal for general distributions. We show that when this condition fails, a dynamic contract that randomizes the low type buyer is optimal. |
| Keywords: | Sequential screening, Ex-post participation constraints, Static contract, Dynamic contract |
| JEL: | C72 D82 D83 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2078&r=mic |
| By: | Bergemann, Dirk; Morris, Stephen |
| 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 persua- sion (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: | Bayesian persuasion; correlated equilibrium; incomplete information; information design; information structure.; robust predictions |
| JEL: | C72 D82 D83 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11867&r=mic |
| By: | Asseyer, Andreas |
| Abstract: | This paper studies optimal information disclosure under the threat of collusion. A prin- cipal seeks to procure a good from one of two agents who can collude against the principal. The first agent has a publicly known cost of production and the second agent’s cost is his private information. The principal decides how much information the first agent receives about the costs of the second agent. In the choice of the optimal disclosure policy, the principal faces a trade-off: More information disclosure makes the elicitation of private in- formation easier but facilitates collusion at the same time. It is optimal for the principal to partially disclose information. Under the optimal information structure, none of the agents receives a positive information rent. |
| JEL: | D82 D83 D86 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc16:145779&r=mic |
| By: | Antelo, Manel; Antonio, Sampayo |
| Abstract: | This paper examines the licensing of an innovation—by a patent holder to one or more users—when the innovation’s value (high or low) is known, after the contract is signed, by each user. In this setup, we analyze the patent holder’s joint decision concerning the number of licenses and the type of contracts. Our first main finding is that, depending on how uncertain is the efficiency of users exploiting the innovation, both shut-down contracts and screening contracts can emerge in equilibrium. Second, shut-down contracts amount to fixed fees under exclusive licensing but are two-part contracts under non-exclusive licensing. Third, there is distorted production at the bottom of the innovation value’s distribution under exclusive licensing as well as distortion at both the bottom and the top of that distribution under non-exclusive licensing. Fourth, asymmetric information favors the latter (i.e., issuing multiple licenses) except when the patent holder uses a screening contract, since then the need to distort production at both the bottom and the top renders non-exclusive licensing less profitable. Our final result is that the number of licenses issued by the patent holder is more likely to maximize aggregate surplus under asymmetric information than under symmetric information. |
| Keywords: | exclusive and non-exclusive licensing, symmetric and asymmetric information, screening, fixed-fee and two-part contracts, welfare analysis |
| JEL: | D43 D82 L24 |
| Date: | 2017–03–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:77252&r=mic |
| By: | Szalay, Dezsö; Deimen, Inga |
| Abstract: | Two divisions of a firm, overarched by a headquarters, are engaged in a decision problem. Division one obtains information and informs division two who has the formal authority to make the decision. Headquarters guides the decision process by affecting the quality of information that division one obtains. In equilibrium, division one honestly communicates the inferences drawn from its observations, but not the underlying observations themselves and division two takes the advice at face value. The communication equilibrium involves smooth strategies and is outcome equivalent to delegation: the informed party gets its way, regardless of the allocation of formal authority. |
| JEL: | D82 D83 D86 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc16:145668&r=mic |
| By: | Tymofiy Mylovanov; Andriy Zapechelnyuk |
| Abstract: | We study the problem of allocating a prize to one of several agents. The social value of giving the prize to an agent is privately known by this agent. The allocation rule chooses the winner of the prize based on the agents’ reports about these values. After the prize is allocated, the social value of giving the prize to the winner becomes commonly known and the agent can be penalized for lies about the value. We show that, if the number of agents is low, the optimal allocation rule takes the form of a restricted-bid procedure; otherwise, it takes the form of a shortlisting procedure. Examples of applications of this model are grant competitions, scholarship allocations, and hiring for a fixed-salary post. |
| Keywords: | mechanism design without transfers, Matthews-Border constraint, short- listing procedure, verification, limited penalty |
| JEL: | D82 D86 |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:gla:glaewp:2016_21&r=mic |
| By: | Bernardo Guimaraes (Sao Paulo School of Economics); Kevin D. Sheedy (Economics Department London School of Economics (LSE); Centre for Macroeconomics (CFM)) |
| Abstract: | This paper presents a theory of political specialization in which some countries uphold the rule of law while others consciously choose not to do so, even though they are ex ante identical. This is borne out of two key insights: for incumbents in each country, (i) the first steps to the rule of law have the greatest private cost, and (ii) steps taken by some countries in the direction of the rule of law make it less attractive for others to follow the same path. The world equilibrium features a symbiotic relationship between despotic and rule-of-law economies: by producing technology-intensive goods that require protection of property rights, rule-of-law economies raise the relative price of natural resources and increase incentives for despotism in other countries; while the choice of despotism entails a positive externality because cheap oil makes the rule of law more attractive elsewhere in the world. |
| Keywords: | Rule of Law, Power Sharing, International Trade, Resource Curse, Development |
| JEL: | D74 F43 O43 P48 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:cfm:wpaper:1710&r=mic |
| By: | Letina, Igor; Benkert, Jean-Michel |
| Abstract: | This paper considers the optimal design of dynamic research tournaments when the buyer can set time-dependent prizes. We derive the buyer-optimal tournament and show that it entails an increasing prize schedule. Remarkably, this allows the buyer to implement a global stopping rule. In particular, the optimal tournament attains the first-best. More generally, we show that global stopping rules can be implemented robustly and compare them to individual stopping rules which have been analyzed in the existing literature. We conclude by discussing policy implications of our findings and highlight that global stopping rules combine the best aspects of innovation races and fixed prize tournaments. |
| JEL: | O32 D02 L19 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc16:145738&r=mic |
| By: | Krishna Dasaratha; Kevin He |
| Abstract: | We study a model of sequential learning with naive agents on a network. The key behavioral assumption is that agents wrongly believe their predecessors act based on only private information, so that correlation between observed actions is ignored. We provide a simple linear formula characterizing agents' actions in terms of paths in the network and use this formula to determine when society learns correctly in the long-run. Because early agents are disproportionately influential, standard network structures can lead to herding on incorrect beliefs. The probability of mislearning increases when link densities are higher and when networks are more integrated. When actions can only communicate limited information, segregated networks often lead to persistent disagreement between groups. |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1703.02105&r=mic |
| By: | Koichi Futagami (Graduate School of Economics, Osaka University); Toshihiro Matsumura (Institute of Social Science, The University of Tokyo); Kizuku Takao (Department of Economics, Aomori Public University) |
| Abstract: | Previous studies in differential games reveal that intertemporal strategic behaviors have an important role for various economic problems. However, most of their analyses are limited to cases where objective functions are identical among agents. In this paper, we characterize the open-loop Nash equilibrium and the Markov perfect Nash equilibrium of a mixed duopoly game where a fully or partially state-owned firm and a fully private firm compete in the quantities of homogeneous goods with sticky prices. We show that in the Markov perfect Nash equilibrium, an increase in the governments f share-holdings of the state-owned firm has a non-monotonic effect on the price, and in a wide range of parameter spaces, it increases the price. These results are derived from the interaction of an asymmetric structure of agents f objectives and inter-temporal strategic behaviors, which are in sharp contrast with those in the open-loop Nash equilibrium. We provide new implications for privatizationpolicies in the presence of dynamic interactions, against the static analyses. |
| Keywords: | Mixed Duopoly, Open-loop Nash equilibrium, Markov Perfect Nash equilibrium |
| JEL: | C73 D43 L32 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:osk:wpaper:1703&r=mic |
| By: | Karl H. Schlag; Andriy Zapechelnyuk |
| Abstract: | We study decision making in complex discrete-time dynamic environments where Bayesian optimization is intractable. A decision maker is equipped with a finite set of benchmark strategies. She aims to perform similarly to or better than each of these benchmarks. Furthermore, she cannot commit to any decision rule, hence she must satisfy this goal at all times and after every history. We find such a rule for a sufficiently patient decision maker and show that it necessitates not to rely too much on observations from distant past. In this sense we find that it can be optimal to forget. |
| Keywords: | Dynamic consistency, experts, regret minimization, forecast com- bination, non-Bayesian decision making. |
| JEL: | C44 D81 |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:gla:glaewp:2016_20&r=mic |
| By: | Anton Kolotilin; Tymofiy Mylovanov; Andriy Zapechelnyuk; Ming Li |
| Abstract: | We study persuasion mechanisms in linear environments. A privately informed receiver chooses between two actions. A sender designs a persuasion mech- anism that can condition the information disclosed to the receiver on the receiver’s report about his type. We establish the equivalence of implementation by persua- sion 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, mech- anism design without transfers, experiments, persuasion mechanisms, media |
| JEL: | D82 D83 L82 |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:gla:glaewp:2016_22&r=mic |
| By: | Takashi Hayashi; Michele Lombardi |
| Abstract: | This paper aims to address two issues related to simultaneous aggregation of utilities and beliefs. The Örst one is related to how to integrate both inequality and uncertainty considerations into social decision-making. The second one is related to how individuals should be responsible for their own beliefs. To accomplish this, whereas individuals are assumed to abide by Savage modelís of subjective expected utility, society is assumed to prescribe, either to each individual when the ex ante individual well-being is favored or to itself when the ex post individual well-being is favored, acting in accordance with the maximin expected utility theory of Gilboa and Schmeidler (1989). Furthermore, it adapts an ex ante Pareto-type condition proposed by Gayer et al. (2014), which says that a prospect Pareto dominates another one if the former gives a higher expected utility than the latter one, for each individual, for all individualsíbeliefs. In the context where the ex ante individual welfare is favored, our ex ante Pareto-type condition is shown to be equivalent to social utility taking the form of a MaxMinMin social welfare function, as well as to the individual set of priors being contained within the range of individual beliefs. However, when the ex post individual welfare is favored, the same Pareto-type condition is shown to be equivalent to social utility taking the form of a MaxMinMin social welfare function, as well as to the social set of priors containing only weighted averages of individual beliefs. |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:gla:glaewp:2016_19&r=mic |
| By: | Fausto, Cavalli; Mario, Gilli; Ahmad, Naimzada; |
| Abstract: | The purpose of this paper is to propose a symmetric two player general contest model in order to study the relationship between equilibria and crucial structural parameters of the model. In particular, given a general specification of the players’ set of possible entries, of the agents’ utility functions, and of the rules that presides over outcomes, we aim to analyze the characteristics of the set of equilibria as a function of structural characteristics of the contest technology and of the outcome function. Focusing on three main cases, we study the effect of introducing spillover in the marginal productivity of agents’ efforts and in the polarization between agents’ goals. Firstly, we show that without spillover the equilibrium efforts’ intensity is uniquely connected to the ratio between marginal productivity of effort and polarization. Secondly, we are able to connect existence of multiple symmetric and asymmetric equilibria to the intensity of spillover effects into outcomes. Finally, we show that spillover in contest technology can imply the non-existence of equilibria. |
| Keywords: | symmetric contest, multiple equilibria, symmetric and asymmetric equilibria |
| JEL: | C72 D72 D74 |
| Date: | 2017–03–03 |
| URL: | http://d.repec.org/n?u=RePEc:mib:wpaper:364&r=mic |
| By: | Rabah Amir; Sergei Belkov; Igor V. Evstigneev |
| Abstract: | We analyze the concept of correlated equilibrium in the framework of two-player two-strategy games. This simple framework makes it possible to clearly demonstrate the characteristic features of this concept. We develop an intuitive and easily memorizable test for equilibrium conditions and provide a complete classification of symmetric correlated equilibria in symmetric games. |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:man:sespap:1706&r=mic |
| By: | Luke Boosey (Department of Economics, Florida State University); Philip Brookins (Max Planck Institute for Research on Collective Goods); Dmitry Ryvkin (Department of Economics, Florida State University) |
| Abstract: | We consider group contests where the number of competing groups is fixed but group sizes are uncertain. Under group-level uncertainty, when players observe the size of their own group, we show that under very general conditions the contest has a semi-symmetric equilibrium where aggregate investment is invariant with respect to group size uncertainty. In contrast, under individual-level uncertainty, when players do not observe the size of their own group, the equilibrium investment is always lower than in a symmetric group contest where the same expected group size is commonly known. The reduction in investment due to population uncertainty is stronger the larger the variance in appropriately defined relative group impacts. |
| Keywords: | group contest, stochastic group size |
| JEL: | C72 D72 D82 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:fsu:wpaper:wp2017_03_01&r=mic |
| By: | Z. Emel Ozturk |
| Abstract: | We consider a collective choice problem in which the number of alternatives and the number of voters may vary. The two fundamental axioms in such a setting are reinforcement and composition-consistency. The former guarantees that the social choice rule cannot be manipulated by partitioning the electorate into sub-electorates. The latter guarantees that the rule cannot be manipulated by altering the set of alternatives entering an election via a procedure called cloning. Brandl et al. (2016) show that reinforcement and composition-consistency are incompatible. We propose a plausible weakening of composition-consistency called composition-consistency for dominated clones. We show that there is only one social choice rule that satisfies reinforcement, unanimity and composition- consistency for dominated clones. The rule is the well-known plurality rule which selects the alternatives top-ranked by the largest number of voters. |
| Keywords: | Plurality rule, cloning-consistency, composition-consistency, reinforcement |
| JEL: | D70 D71 D72 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:gla:glaewp:2017_04&r=mic |
| By: | Hirbod Assa (Institute for Financial and Actuarial Mathematics and Institute for Risk and Uncertainty, University of Liverpool, Center for Doctoral Training, Chadwick Building, Liverpool, UK); Alexander Zimper (Department of Economics, University of Pretoria, South Africa, and Kiel Institute for the World Economy, Germany) |
| Abstract: | We consider preferences over all random variables on a given nonatomic probability space. We show that non-trivial and complete preferences cannot simultaneously satisfy the two fundamental principles of convexity and continuity. As an implication of this incompatibility result there cannot exist any non-trivial continuous utility representations over all random variables that are either quasi-concave or quasi-convex. This rules out risk-averse (or seeking) expected utility representations and, more generally, risk- and uncertainty-averse (or seeking) Choquet expected utility representations for this large space of random variables. |
| Keywords: | Large Space, Preference for Diversification, Utility Representation, Risk Measures |
| JEL: | D81 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:pre:wpaper:201714&r=mic |
| By: | Bernhard von Stengel |
| Abstract: | We consider a sequential inspection game where an inspector uses a limited number of inspections over a larger number of time periods to detect a violation (an illegal act) of an inspectee. Compared with earlier models, we allow varying rewards to the inspectee for successful violations. As one possible example, the most valuable reward may be the completion of a sequence of thefts of nuclear material needed to build a nuclear bomb. The inspectee can observe the inspector, but the inspector can only determine if a violation happens during a stage where he inspects, which terminates the game; otherwise the game continues. Under reasonable assumptions for the payoffs, the inspector’s strategy is independent of the number of successful violations. This allows to apply a recursive description of the game, even though this normally assumes fully informed players after each stage. The resulting recursive equation in three variables for the equilibrium payoff of the game, which generalizes several other known equations of this kind, is solved explicitly in terms of sums of binomial coefficients. We also extend this approach to nonzero-sum games and “inspector leadership” where the inspector commits to (the same) randomized inspection schedule, but the inspectee acts legally (rather than mixes as in the simultaneous game) as long as inspections remain. |
| Keywords: | inspection game; multistage game; recursive game; Stackelberg leadership; binominal coefficients |
| JEL: | C72 |
| Date: | 2016–03–02 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:68299&r=mic |
| By: | Galasso, Alberto; Mitchell, Matthew; Virag, Gabor |
| Abstract: | The past decade has witnessed a resurgence in innovation awards, in particular of Grand Innovation Prizes (GIPs) which are rewards to innovators developing technologies reaching performance goals and requiring breakthrough solutions. GIPs typically do not preclude the winner also obtaining patent rights. This is in stark contrast with mainstream economics of innovation theories where prizes and patents are substitute ways to generate revenue and encourage innovation. Building on the management of innovation literature which stresses the difficulty to specify ex-ante all the technical features of the winning technologies, we develop a model in which innovative effort is multi-dimensional and only a subset of innovation tasks can be measured and contracted upon. We show that in this environment patent rights and cash rewards are complements, and that GIPs are often preferable to patent races or prizes requiring technologies to be placed in the public domain. Moreover, our model uncovers a tendency for patent races to encourage speed of discovery over quality of innovation, which can be corrected by GIPs. We explore robustness to endogenous entry, costly public funds, and incomplete information by GIP organizers on the surplus created by the technology. |
| Keywords: | innovation; patent; prizes |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11860&r=mic |
| By: | Schumacher, Heiner; Karle, Heiko; Volund, Rune |
| Abstract: | We analyze how early settlement offers affect Nash bargaining outcomes when agents are asymmetrically informed about the distribution of bargaining powers and exhibit expectations-based loss-aversion preferences. Before the start of the bargaining process, the sender has private information about the receiver’s bargaining power. His settlement offers may convey this private information so that they change the receiver’s expectations and, by loss aversion, preferences. We show that the sender can exploit this mechanism by making non-binding settlement offers, i.e., the receiver is free to accept them at any time, even after learning her true bargaining value. |
| JEL: | C78 D03 K12 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc16:145772&r=mic |
| By: | Ana-Isabel Guerra; Ferran Sancho |
| Abstract: | The message of this note is that in a general equilibrium setting the compensating variation is numéraire dependent. In contrast, the equivalent variation is neutral regarding the choice of value units. We illustrate with a simple example and propose an even simpler solution to overcome this bias in the compensating variation; all that is required to have a correct welfare estimate is to compensate the compensating variation by normalization with a price index. This type of correction is necessary to overcome the often blind implementation of welfare measures in numerical general equilibrium. |
| Keywords: | Compensating variation, equivalent variation, Konüs index, computable general equilibrium. |
| JEL: | D11 D12 D60 |
| Date: | 2017–02–16 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:961.17&r=mic |