14,917 research outputs found

    Informational Substitutes

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    We propose definitions of substitutes and complements for pieces of information ("signals") in the context of a decision or optimization problem, with game-theoretic and algorithmic applications. In a game-theoretic context, substitutes capture diminishing marginal value of information to a rational decision maker. We use the definitions to address the question of how and when information is aggregated in prediction markets. Substitutes characterize "best-possible" equilibria with immediate information aggregation, while complements characterize "worst-possible", delayed aggregation. Game-theoretic applications also include settings such as crowdsourcing contests and Q\&A forums. In an algorithmic context, where substitutes capture diminishing marginal improvement of information to an optimization problem, substitutes imply efficient approximation algorithms for a very general class of (adaptive) information acquisition problems. In tandem with these broad applications, we examine the structure and design of informational substitutes and complements. They have equivalent, intuitive definitions from disparate perspectives: submodularity, geometry, and information theory. We also consider the design of scoring rules or optimization problems so as to encourage substitutability or complementarity, with positive and negative results. Taken as a whole, the results give some evidence that, in parallel with substitutable items, informational substitutes play a natural conceptual and formal role in game theory and algorithms.Comment: Full version of FOCS 2016 paper. Single-column, 61 pages (48 main text, 13 references and appendix

    Robust Predictions in Games with Incomplete Information

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    We analyze games of incomplete information and offer equilibrium predictions which are valid for all possible private information structures that the agents may have. Our characterization of these robust predictions relies on an epistemic result which establishes a relationship between the set of Bayes Nash equilibria and the set of Bayes correlated equilibria. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior information of the analyst refines the set of equilibrium distribution. As an application, we obtain new results regarding the optimal information sharing policy of firms under demand uncertainty. Finally, we reverse the perspective and investigate the identification problem under concerns for robustness to private information. We show how the presence of private information leads to partial rather than complete identification of the structural parameters of the game. As a prominent example we analyze the canonical problem of demand and supply identification.Incomplete information, Correlated equilibrium, Robustness to private information, Moments restrictions, Identification, Information bounds

    Optimal Procurement Contracts with Pre–Project Planning

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    The paper studies procurement contracts with pre–project investigations in the presence of adverse selection and moral hazard. To model the procurer’s roblem, we extend a standard sequential screening model to endogenous information acquisition with moral hazard. The optimal contract displays systematic distortions in information acquisition. Due to a rent effect, adverse selection induces too much information acquisition to prevent cost overruns and too little information acquisition to prevent false project cancelations. Moral hazard mitigates the distortions related to cost overruns yet exacerbates those related to false negatives. The optimal mechanism is a menu of option contracts that achieves the dual goal of providing incentives for information acquisition and truthful information revelation

    Information in Mechanism Design

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    We survey the recent literature on the role of information for mechanism design. We specifically consider the role of endogeneity of and robustness to private information in mechanism design. We view information acquisition of and robustness to private information as two distinct but related aspects of information management important in many design settings. We review the existing literature and point out directions for additional future work.Mechanism Design, Information Acquisition, Ex Post Equilibrium, Robust Mechanism Design, Interdependent Values, Information Management

    Allocative and Informational Externalities in Auctions and Related Mechanisms

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    We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

    "Combinatorial Bootstrap Inference IN in Prtially Identified Incomplete Structural Models"

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    We propose a computationally feasible inference method infinite games of complete information. Galichon and Henry (2011) and Beresteanu, Molchanov, and Molinari (2011) show that such models are equivalent to a collection of moment inequalities that increases exponentially with the number of discrete outcomes. We propose an equivalent characterization based on classical combinatorial optimization methods that alleviates this computational burden and allows the construction of confidence regions with an effcient combinatorial bootstrap procedure that runs in linear computing time. The method can also be applied to the empirical analysis of cooperative and noncooperative games, instrumental variable models of discrete choice and revealed preference analysis. We propose an application to the determinants of long term elderly care choices.

    Abstention, ideology and information acquisition

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    We consider an election in which each voter can collect information of different precision. Voters have asymmetric information and preferences that vary both in terms of ideology and intensity. In contrast to all other models of voting with endogenous information, in equilibrium voters collect information of different qualities. We show that information and abstention are not necessarily negatively correlated: some voters are more likely to abstain the more informed they are. We also discuss the manner in which incentives to acquire information are non-monotonic in terms of both ideology and the level of intensity. © 2013 Elsevier Inc
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