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on Microeconomics |
| By: | Matthew Ryan (School of Economics, Auckland University of Technology) |
| Abstract: | The Condorcet Jury Theorem formalises the “wisdom of crowds”: binary decisions made by majority vote are asymptotically correct as the number of voters tends to infinity. This classical result assumes like-minded, expected utility maximising voters who all share a common prior belief about the right decision. Ellis (2016) shows that when voters have ambiguous prior beliefs – a (closed, convex) set of priors – and follow maxmin expected utility (MEU), such wisdom requires that voters’ beliefs satisfy a “disjoin posteriors” condition: difference private signals lead to posterior sets with disjoint interiors. Both the original theorem and Ellis’s generalisation assume symmetric penalties for wrong decisions. If, as in the jury context, errors attract asymmetric penalties, then it is natural to consider voting rules that raise the hurdle for the decision carrying the heavier penalty for error (such as conviction in jury trials). In a classical model, Feddersen and Pesendorfer (1998) have shown that, paradoxically, raising this hurdle may actually increase the likelihood of the more serious error. In particular, crowds are not wise under the unanimity rule: the probability of the more serious error does not vanish as the crowd size tends to infinity. We show that this “Jury Paradox” persists in the presence of ambiguity, whether or not juror beliefs satisfy Ellis’s “disjoint posteriors” condition. We also characterise the strictly mixed equilibria of this model and study their properties. Such equilibria cannot exist in the absence of ambiguity but may exist for arbitrarily large jury size when ambiguity is present. In addition to “uninformative” strictly mixed equilibria, analogous to those exhibited by Ellis (2016), there may also exist strictly mixed equilibria which are “informative” about voter signals. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:aut:wpaper:201907&r=all |
| By: | David McCarthy (Department of Philosophy, University of Hong Kong); Kalle Mikkola (Department of Mathematics and Systems Analysis, Aalto University); Teruji Thomas (Global Priorities Institute, University of Oxford) |
| Abstract: | We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown to be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling. |
| Date: | 2019–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1911.00872&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 Panthéon-Sorbonne - 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:cesptp:halshs-02346134&r=all |
| By: | Bhaskar Dutta (University of Warwick and Ashoka University); Hannu Vartiainen (University of Helsinki and Helsinki Graduate School of Economics) |
| Abstract: | Farsighted formulations of coalitional formation, for instance by Harsanyi (1974) and Ray and Vohra(2015), have typically been based on the von NeumannMorgenstern (1944) stable set. These farsighted stable sets use a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional 'moves' in which each coalition that is involved in the sequence eventually stands to gain. Dutta and Vohra(2016) point out that these solution concepts do not require coalitions to make optimal moves. Hence, these solution concepts can yield unreasonable predictions. Dutta and Vohra (2016) restricted coalitions to hold common, history independent expectations that incorporate optimality regarding the continuation path. This paper extends the Dutta-Vohra analysis by allowing for history dependent expectations. The paper provides characterization results for two solution concepts corresponding to two versions of optimality. It demonstrates the power of history dependence by establishing nonemptyness results for all ï¬ nite games as well as transferable utility partition function games. The paper also provides partial comparisons of the solution concepts to other solutions. |
| Keywords: | Coalition |
| Date: | 2018–07 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:02&r=all |
| By: | Luis Miguel Cândido Dias (CeBER and Faculty of Economics, University of Coimbra); Rudolf Vetschera (Faculty of Business, Economics and Statistics, University of Vienna) |
| Abstract: | The Zeuthen-Hicks bargaining model connects strategic and axiomatic bargaining models by providing a description of the behavior of each party,and showing that the entire process leads to the axiomatically founded Nash bargaining solution. In its original formulation, the model treats parties asymmetrically by considering different decision alternatives of the focal party (who can either accept the opponent's offer or make a counteroffer, but not quit the negotiation) and the opponent (who can accept the focal party's offer or quit the negotiation, but not make a counteroffer). We extend the model to consider the full set of possible actions from both sides, which requires explicit modeling of the expectations of the parties concerning outcomes and outside options that become available during the process. We show analytically that under the assumption of concave utilities of both parties, the bargaining process converges to the nonsymmetric Nash bargaining solution. This result provides a new interpretation of the parameters of the nonsymmetric Nash bargaining solution, linking them to behavior in the bargaining process. Furthermore,we perform a simulation study to analyze the outcomes for non-concave utilities. |
| Keywords: | Zeuthen-Hicks bargaining, Nonsymmetric Nash bargaining solution, negotiator confidence. |
| JEL: | C72 C78 C44 C63 |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:gmf:papers:2019-05&r=all |
| By: | Lubik, Thomas A. (Federal Reserve Bank of Richmond); Matthes, Christian (Federal Reserve Bank of Richmond); Mertens, Elmar (Deutsche Bundesbank) |
| 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. We show that for parameter values that imply a unique equilibrium under full information, the limited information rational expectations equilibrium can be 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; Kalman filter; belief shocks |
| JEL: | C11 C32 E52 |
| Date: | 2019–10–08 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedrwp:19-17&r=all |
| By: | Francis Bloch (Université Paris 1 and Paris School of Economics); Bhaskar Dutta (University of Warwick and Ashoka University); Mihai Manea (Stony Brook University) |
| Abstract: | We analyze the formation of partnerships in social networks. Players need favors at random times and ask their neighbors in the network to form exclusive long-term partnerships that guarantee reciprocal favor exchange. Refusing to provide a favor results in the automatic removal of the underlying link. Players agree to provide the ï¬ rst favor in a partnership only if they otherwise face the risk of eventual isolation. In equilibrium, players essential for realizing every maximum matching can avoid this risk and enjoy higher payoffsthaninessentialplayers.Althoughthesearchforpartnersisdecentralizedandreflects local partnership opportunities, the strength of essential players drives efficient partnership formation in every network. Equilibrium behavior is determined by the classiï¬ cation of nodes in the Gallai-Edmonds decomposition of the underlying network. |
| Keywords: | networks, efficiency, decentralized markets, partnerships, favor exchange, maximum matchings, Gallai-Edmonds decomposition, under-demanded. |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:09&r=all |
| By: | Chiara Fumagalli; Massimo Motta |
| Abstract: | We show that the incentive to engage in exclusionary tying (of two complementary products) may arise even when tying cannot be used as a defensive strategy to protect the incumbent's dominant position in the primary market. By engaging in tying, an incumbent firm sacrifices current profits but can exclude a more efficient rival from a complementary market by depriving it of the critical scale it needs to be successful. In turn, exclusion in the complementary market allows the incumbent to be in a favorable position when a more efficient rival will enter the primary market, and to appropriate some of the rival's efficiency rents. The paper also shows that tying is a more profitable exclusionary strategy than pure bundling, and that exclusion is the less likely the higher the proportion of consumers who multi-home. |
| Keywords: | Inefficient foreclosure, Tying, Scale economies, Network Externalities |
| JEL: | K21 L41 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:baf:cbafwp:cbafwp19123&r=all |
| By: | Lefouili, Yassine; Toh, Ying Lei (Federal Reserve Bank of Kansas City) |
| Abstract: | This paper analyzes whether a privacy regulation that restricts a dominant firm’s data disclosure level harms the firm’s incentives to invest in service quality and thereby harms social welfare. We study how the regulation affects the privacy and quality choices of a monopoly service provider, who derives revenues solely from disclosing user data to third parties, as well as how those choices in turn affect consumers’ participation and information-sharing decisions. We show that the regulation does not always harm investment incentives; moreover, even when it does, it may still improve social welfare. |
| Keywords: | Privacy Regulation; Data Disclosure; Investment; Quality |
| JEL: | D83 L15 L51 |
| Date: | 2019–07–30 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedkrw:rwp19-05&r=all |
| By: | Prescott, Edward Simpson (Federal Reserve Bank of Cleveland); Jarque, Arantxa (Federal Reserve Bank of Richmond) |
| Abstract: | A multi-agent, moral-hazard model of a bank operating under deposit insurance and limited liability is used to analyze the connection between compensation of bank employees (below CEO) and bank risk. Limited liability with deposit insurance is a force that distorts effort down. However, the need to increase compensation to risk-averse employees in order to compensate them for extra bank risk is a force that reduces this effect. Optimal contracts use relative performance and are implementable as a wage with bonuses tied to individual and firm performance. The connection between pay for performance and bank risk depends on correlation of returns. If employee returns are uncorrelated, the form of pay is irrelevant for risk. If returns are perfectly correlated, a low wage can indicate risk. Connections to compensation regulation and characteristics of organizations are discussed. |
| Keywords: | incentive compensation; relative performance; bank regulation; |
| JEL: | D82 G21 G28 J33 |
| Date: | 2019–11–05 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwq:192000&r=all |
| By: | Yuqing Kong |
| Abstract: | In the setting where participants are asked multiple similar possibly subjective multi-choice questions (e.g. Do you like Panda Express? Y/N; do you like Chick-fil-A? Y/N), a series of peer prediction mechanisms are designed to incentivize honest reports and some of them achieve dominantly truthfulness: truth-telling is a dominant strategy and strictly dominate other "non-permutation strategy" with some mild conditions. However, a major issue hinders the practical usage of those mechanisms: they require the participants to perform an infinite number of tasks. When the participants perform a finite number of tasks, these mechanisms only achieve approximated dominant truthfulness. The existence of a dominantly truthful multi-task peer prediction mechanism that only requires a finite number of tasks remains to be an open question that may have a negative result, even with full prior knowledge. This paper answers this open question by proposing a new mechanism, Determinant based Mutual Information Mechanism (DMI-Mechanism), that is dominantly truthful when the number of tasks is at least 2C and the number of participants is at least 2. C is the number of choices for each question (C=2 for binary-choice questions). In addition to incentivizing honest reports, DMI-Mechanism can also be transferred into an information evaluation rule that identifies high-quality information without verification when there are at least 3 participants. To the best of our knowledge, DMI-Mechanism is the first dominantly truthful mechanism that works for a finite number of tasks, not to say a small constant number of tasks. |
| Date: | 2019–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1911.00272&r=all |
| By: | Lorenzo Bastianello; Jos\'e Heleno Faro |
| Abstract: | We study intertemporal decision making under uncertainty. We give the first full characterization of discounted expected utility in a framework \`a la Savage. Despite the popularity of this model, no characterization is available in the literature. The concept of stationarity, introduced by Koopmans for deterministic discounted utility, plays a central role for both attitudes towards time and towards uncertainty. We show that a strong stationarity axiom characterizes discounted expected utility. When hedging considerations are taken into account, a weaker stationarity axiom generalizes discounted expected utility to Choquet discounted expected utility, allowing for non-neutral attitudes towards uncertainty. |
| Date: | 2019–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1911.00370&r=all |
| By: | Péter Bayer; György Kozics; Nóra Szőke |
| Abstract: | We study public goods games played on networks with possibly non-reciprocal relationships between players. Examples for this type of interactions include one-sided relationships, mutual but unequal relationships, and parasitism. Directed cycles and parasitic relations lead to the emergence of best-response cycles, leading to non-convergence to the game's Nash equilibrium under best-response dynamics. It is well known that, in reciprocal interaction networks, best-response dynamics converge to a Nash equilibrium. We show that a class of non-reciprocal networks, characterized by transitive relative importance of players also features this property, as by a rescaling of the action space the interaction becomes reciprocal. Additionally, we show that networks rescalable to exhibit weak externalities always have a single Nash equilibrium, and by the theory of best-response potential games we show convergence for this class as well. Finally, we show that this class includes directed acyclic networks. |
| Date: | 2019–11–06 |
| URL: | http://d.repec.org/n?u=RePEc:ceu:econwp:2019_3&r=all |
| By: | Abhinash Borah (Department of Economics, Ashoka University); Christopher Kops (Heidelberg University) |
| Abstract: | We address the oft-repeated criticism that the demands which the rational choice approach makes on the knowledge and cognition of a decision maker (DM) are way beyond the capabilities of typical human intelligence. Our key ï¬ nding is that it may be possible to arrive at this ideal of rationality by means of cognitively less demanding, heuristic-based ecological reasoning that draws on information about others’ choices in the DM’s environment. Formally, we propose a choice procedure under which, in any choice problem, the DM, ï¬ rst, uses this information to shortlist a set of alternatives. The DM does this shortlisting by a mental process of categorization whereby she draws similarities with certain societal members—the ingroup—and distinctions from others—the outgroup—and considers those alternatives that are similar (dissimilar) to ingroup (outgroup) members’ choices. Then, she chooses from this shortlisted set by applying her preferences, which may be incomplete owing to limitations of knowledge. We show that if a certain homophily condition connecting the DM’s preferences with her ingroup-outgroup categorization holds, then the procedure never leads the DM to making bad choices. If, in addition, a certain shortlisting consistency condition holds vis-a-vis non-comparable alternatives under the DM’s preferences, then the procedure results in rational choices. |
| Keywords: | Rational choice, ecological rationality, ingroup-outgroup categorization, fast and frugal heuristics, homophily |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:07&r=all |
| By: | Abhinash Borah (Department of Economics, Ashoka University) |
| Abstract: | We address a common criticism directed towards models of expressive voting that they are ad hoc in nature. To that end, we propose a foundation for expressive behavior that is based on a novel theory of social preferences under risk. Under our proposal, expressive considerations in behavior arise from the particular way in which risky social prospects are assessed by decision makers who want to interpret their choices as moral. To illustrate the scope of our framework, we use it to address some key questions in the literature on expressive voting: why, for expressive considerations, might voters vote against their self-interest in large elections and why might such elections exhibit a moral bias (Feddersen et al. 2009). Speciï¬ cally, we consider an electoral set-up with two alternatives and explain why, when the size of the electorate is large, voters may want to vote for the alternative they deem morally superior even if this alternative happens to be strictly less preferred, in an all-inclusive sense, than the other. |
| Keywords: | expressive voting, morals, social preferences, decisions under risk, voting against self-interest, moral bias of large elections |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:08&r=all |