nep-gth New Economics Papers
on Game Theory
Issue of 2020‒06‒15
24 papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Poisson-Cournot Games By Francesco De Sinopoli; Christopher Kunstler; Claudia Meroni; Carlos Pimienta
  2. A Complete Characterization of Infinitely Repeated Two-Player Games having Computable Strategies with no Computable Best Response under Limit-of-Means Payoff By Jakub Dargaj; Jakob Grue Simonsen
  3. Biodiversity, Shapley value and phylogenetic trees: some remarks By Hubert Stahn
  4. The Equivalence of the Minimal Dominant Set and the Myopic Stable Set for Coalition Function Form Games By Herings, P. Jean-Jacques; Kóczy, László Ã .
  5. Instability of Defection in the Prisoner's Dilemma: Best Experienced Payoff Dynamics Analysis By Srinivas Arigapudi; Yuval Heller; Igal Milchtaich
  6. Preemption with a Second-Mover Advantage By Smirnov, Vladimir; Wait, Andrew
  7. Undiscounted Bandit Games By Godfrey Keller; Sven Rady
  8. Efficient Bilateral Trade with Interdependent Values: The Use of Two-Stage Mechanisms By Kunimoto, Takashi; Zhang, Cuiling
  9. Zero-Intelligence vs. Human Agents: An Experimental Analysis of the Efficiency of Double Auctions and Over-the-Counter Markets of Varying Sizes By Giuseppe Attanasi; Samuele Centorrino; Elena Manzoni
  10. Is a dynamic approach of tax games relevant? By Nora Paulus; Patrice Pierreti; Benteng Zou
  11. A dynamic theory of spatial externalities By Raouf Boucekkine; Giorgio Fabbri; Salvatore Federico; Fausto Gozzi
  12. On Sustainable Equilibria By Srihari Govindan; Rida Laraki; Lucas Pahl
  13. Renegotiation and Coordination with Private Values By Yuval Heller; Christoph Kuzmics
  14. A dynamic analysis of nash equilibria in search models with fiat money By Federico Bonetto; Maurizio Iacopetta
  15. Forward utilities and Mean-field games under relative performance concerns By Goncalo dos Reis; Vadim Platonov
  16. The War of Rare Earth Elements: A Dynamic Game Approach By Luisito Bertinelli; Stéphane Poncin; Benteng Zou
  17. A Dynamic Theory of Regulatory Capture By Alessandro De Chiara; Marco A. Schwarz
  18. Entry games for the airline industry By Bontemps, Christian; Menezes Bezerra Sampaio, Raquel
  19. Information Validates the Prior: A Theorem on Bayesian Updating and Applications By Navin Kartik; Frances Lee; Wing Suen
  20. Lie detection: A strategic analysis of the Verifiability Approach By Konstantinos Ioannidis; Theo Offerman; Randolph Sloof
  21. Functional Decision Theory in an Evolutionary Environment By Noah Topper
  22. Permit markets with political and market distortions By Alex Dickson; Iain A Mackenzie
  23. Information Disclosure in Elections with Sequential Costly Participation By Dmitriy Vorobyev
  24. Funding Public Projects: A Case for the Nash Product Rule By Florian Brandl; Felix Brandt; Dominik Peters; Christian Stricker; Warut Suksompong

  1. By: Francesco De Sinopoli (Department of Economics, University of Verona); Christopher Kunstler (Institute of Energy and Climate Research, FZ Julich); Claudia Meroni (Department of Economics, University of Verona); Carlos Pimienta (School of Economics, UNSW Business School, UNSW)
    Abstract: We construct a Cournot model in which firms have uncertainty about the total number of firms in the industry. We model such an uncertainty as a Poisson game and we characterize the set of equilibria after deriving some novel properties of the Poisson distribution. When the marginal cost is zero, the number of equilibria increases with the expected number of firms ( n) and for n ≥ 3 every equilibrium exhibits overproduction relative to the model with deterministic population size. Overproduction is robust to sufficiently small marginal costs, however, for a fixed marginal cost, the set of equilibria approaches the equilibrium quantity of the deterministic model as n goes to infinity.
    Keywords: Cournot competition, Population uncertainty, Poisson games, Poisson distribution
    JEL: C72 D43 L13
    Date: 2020–05
  2. By: Jakub Dargaj; Jakob Grue Simonsen
    Abstract: It is well-known that for infinitely repeated games, there are computable strategies that have best responses, but no computable best responses. These results were originally proved for either specific games (e.g., Prisoner's dilemma), or for classes of games satisfying certain conditions not known to be both necessary and sufficient. We derive a complete characterization in the form of simple necessary and sufficient conditions for the existence of a computable strategy without a computable best response under limit-of-means payoff. We further refine the characterization by requiring the strategy profiles to be Nash equilibria or subgame-perfect equilibria, and we show how the characterizations entail that it is efficiently decidable whether an infinitely repeated game has a computable strategy without a computable best response.
    Date: 2020–05
  3. By: Hubert Stahn (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)
    Abstract: This paper explores the main differences between the Shapley values of a set of taxa introduced by Haake et al. (J Math Biol 56:479–497, 2007. and Fuchs and Jin (J Math Biol 71:1133–1147, 2015., the latter having been found identical to the Fair Proportion index (Redding and Mooers in Conserv Biol 20:1670–1678, 2006. In line with Shapley (in: Kuhn, Tucker (eds) Contributions to to the theory of games, volume II, annals of mathematics studies 28, Princeton University Press, Princeton, 1953), we identify the cooperative game basis for each of these two classes of phylogenetic games and use them (i) to construct simple formulas for these two Shapley values and (ii) to compare these different approaches. Using the set of weights of a phylogenetic tree as a parameter space, we then discuss the conditions under which these two values coincide and, if they are not the same, revisit Hartmann's (J Math Biol 67:1163–1170, 2013. convergence result. An example illustrates our main argument. Finally, we compare the species ranking induced by these two values. Considering the Kendall and the Spearman rank correlation coefficient, simulations show that these rankings are strongly correlated. These results are consistent with Wicke and Fischer (J Theor Biol 430:207–214, 2017., who reach similar conclusions with a different simulation method.
    Keywords: Fair Proportion index,Biodiversity,Phylogenetic trees,Shapley value
    Date: 2020–02
  4. By: Herings, P. Jean-Jacques (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics); Kóczy, László Ã .
    Abstract: In cooperative games, the coalition structure core is, despite its potential emptiness, one of the most popular solutions. While it is a fundamentally static concept, the consideration of a sequential extension of the underlying dominance correspondence gave rise to a selection of non-empty generalizations. Among these, the payoff-equivalence minimal dominant set and the myopic stable set are defined by a similar set of conditions. We identify some problems with the payoff-equivalence minimal dominant set and propose an appropriate reformulation called the minimal dominant set. We show that replacing asymptotic external stability by sequential weak dominance leaves the myopic stable set unaffected. The myopic stable set is therefore equivalent to the minimal dominant set.
    JEL: C71
    Date: 2020–06–09
  5. By: Srinivas Arigapudi; Yuval Heller; Igal Milchtaich
    Abstract: We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable in the prisoner`s dilemma. By contrast, when k > 1 we show that there exists a globally stable state in which agents cooperate with probability between 28% and 50%. Next, we characterize stability of strict equilibria in general games. Our results demonstrate that the empirically plausible case of k > 1 can yield qualitatively different predictions than the case of k = 1 that is commonly studied in the literature.
    Date: 2020–05
  6. By: Smirnov, Vladimir; Wait, Andrew
    Abstract: We examine innovation in a market-entry timing game with complete information and observable actions when there is a second-mover advantage. Allowing for heterogenous payoffs between players, and for both leader's and follower's payoff functions to be multi-peaked and non-monotonic, we find that there are at most two pure-strategy subgame perfect equilibria. Sometimes these resemble familiar second-mover advantage equilibria from the literature. However, we show that despite there being a follower advantage at all times, there can be a preemption equilibrium with inefficient early entry. In fact, immediate entry is possible in a continuous analogue of the centipede game. These results are related to the observed premature entry and product launches in various markets.
    Keywords: timing games, second-mover advantage, preemption.
    Date: 2020–05
  7. By: Godfrey Keller; Sven Rady
    Abstract: We analyze undiscounted continuous-time games of strategic experimentation with two-armed bandits. The risky arm generates payoffs according to a Lévy process with an unknown average payoff per unit of time which nature draws from an arbitrary finite set. Observing all actions and realized payoffs, plus a free background signal, players use Markov strategies with the common posterior belief about the unknown parameter as the state variable. We show that the unique symmetric Markov perfect equilibrium can be computed in a simple closed form involving only the payoff of the safe arm, the expected current payoff of the risky arm, and the expected full-information payoff, given the current belief. In particular, the equilibrium does not depend on the precise specification of the payoff-generating processes.
    Keywords: Strategic Experimentation, Bayesian Two-Armed Bandit, Strong Long-Run Average Criterion, Markov Perfect Equilibrium, HJB Equation, Viscosity Solution
    JEL: C73 D83
    Date: 2020–05
  8. By: Kunimoto, Takashi (School of Economics, Singapore Management University); Zhang, Cuiling (School of Economics, Singapore Management University)
    Abstract: As efficient, voluntary bilateral trades are generally not incentive compatible in an interdependent-value environment (Fieseler, Kittsteiner, Moldovanu (2003) and Gresik (1991)), we seek for more positive results by employing two-stage mechanisms (Mezzetti (2004)). We say that a two-stage mechanism satisfies incentive compatibility if the truth-telling in both stages constitutes an equilibrium strategy.First, we show by means of a stylized example that the generalized two-stage Groves mechanism never guarantees voluntary trade, while it satisfies efficiency and incentive compatibility. In a general environment, we next propose Assumption 1 under which there exists a two-stage incentive compatible mechanism implementing an efficient, voluntary trade. Third, within the same example, we confirm that our Assumption 1 is very weak because it holds as long as the buyer’s degree of interdependence of preferences is not too high relative to the seller’s counterpart. Finally, we show by the same example that if Assumption 1 is violated, our proposed two-stage mechanism fails to achieve voluntary trade.
    Keywords: Bilateral trade; interdependent values; two-stage mechanisms
    JEL: C72 D78 D82
    Date: 2020–05–01
  9. By: Giuseppe Attanasi (University of Côte d’Azur, Nice); Samuele Centorrino (Stony Brook University); Elena Manzoni (Department of Economics (University of Verona))
    Abstract: We study two well-known electronic markets: an over-the-counter (OTC) market, in which each agent looks for the best counterpart through bilateral negotiations, and a double auc- tion (DA) market, in which traders post their quotes publicly. We focus on the DA-OTC efficiency gap and show how it varies with different market sizes (10, 20, 40, and 80 traders). We compare experimental results from a sample of 6,400 undergraduate students in Economics with zero-intelligent (ZI) agent-based simulations. Simulations with ZI traders show that the traded quantity (with respect to the efficient one) increases with market size under both DA and OTC. Experimental results with human traders confirm the same tendency under DA, while the share of periods in which the traded quantity is higher (lower) than the efficient one decreases (increases) with market size under OTC, ultimately leading to a DA-OTC efficiency gap increasing with market size. We rationalize these results by putting forward a novel game-theoretical model of OTC market as a repeated bargaining procedure under incomplete information on buyers’ valuations and sellers’ costs, showing how efficiency decreases slightly with size due to two counteracting effects: acceptance rates in earlier periods decrease with size, and earlier offers increase, but not always enough to compensate the decrease in acceptance rates.
    Keywords: Market Design, Classroom Experiment, Agent-based Modelling, Game-theoretic Modelling.
    JEL: C70 C91 C92 D41 D47
    Date: 2020–03
  10. By: Nora Paulus (CREA, Université du Luxembourg); Patrice Pierreti (CREA, Université du Luxembourg); Benteng Zou (CREA, Université du Luxembourg)
    Abstract: In this paper we argue that static models provide an incomplete analysis of interjurisdictional tax competition. According to Wilson (1987) a static tax competition model might predict the long-run outcomes of government decision making in a dynamic setting. We show that this conjecture is only true when policymakers commit to a tax path at the start of the game without future updates (open-loop behavior), with the proviso that they are time-indifferent and/or capital is perfectly mobile. Static models however never predict future outcomes when policymarkers continuously update their tax rates (Markovian behavior). In particular, we address the following aspects. How do long-run outcomes in a dynamic setting change relative to static games? How does social welfare change accordingly? If policymakers have the choice, which strategical behavior (Markovian or open-loop) should they adopt? In light of this, which one confers the highest social advantage?
    Keywords: Dynamic Tax Competition, Differential Games, Markovian Nash Equilibrium, Open-loop Strategy
    JEL: C73 F21 H21 H87
    Date: 2019
  11. By: Raouf Boucekkine (Aix-Marseille Univ, CNRS, EHESS, Ecole Centrale, AMSE & IMERA, Marseille, France); Giorgio Fabbri (Univ. Grenoble Alpes, CNRS, INRA, Grenoble INP, GAEL, 38000 Grenoble); Salvatore Federico (Universita degli Studi di Siena, Dipartimento di Economia Politica e Statistica, Siena, Italy); Fausto Gozzi (Dipartimento di Economia e Finanza, LUISS Guido Carli, Rome, Italy)
    Abstract: In this paper, we revisit the theory of spatial externalities. In particular, we depart in several respects from the important literature studying the fundamental pollution free riding problem uncovered in the associated empirical works. First, instead of assuming ad hoc pollution diffusion schemes across space, we consider a realistic spatiotemporal law of motion for air and water pollution (diffusion and advection). Second, we tackle spatiotemporal non-cooperative (and cooperative) differential games. Precisely, we consider a circle partitioned into several states where a local authority decides autonomously about its investment, production and depollution strategies over time knowing that investment/production generates pollution, and pollution is transboundary. The time horizon is infinite. Third, we allow for a rich set of geographic heterogeneities across states while the literature assumes identical states. We solve analytically the induced non-cooperative differential game under decentralization and fully characterize the resulting long-term spatial distributions. We further provide with full exploration of the free riding problem, reflected in the so-called border effects. In particular, net pollution flows diffuse at an increasing rate as we approach the borders, with strong asymmetries under advection, and structural breaks show up at the borders. We also build a formal case in which a larger number of states goes with the exacerbation of pollution externalities. Finally, we explore how geographic discrepancies affect the shape of the border effects.
    Keywords: spatial externalities, environmental federalism, transboundary pollution, differential games in continuous time and space, infinite dimensional optimal control problems
    JEL: Q53 R12 O13 C72 C61 O44
    Date: 2020–05
  12. By: Srihari Govindan; Rida Laraki; Lucas Pahl
    Abstract: Following the ideas laid out in Myerson (1996), Hofbauer (2000) defined an equilibrium of a game as sustainable if it can be made the unique equilibrium of a game obtained by deleting a subset of the strategies that are inferior replies to it, and then adding others. Hofbauer also formalized Myerson's conjecture about the relationship between the sustainability of an equilibrium and its index: for a generic class of games, an equilibrium is sustainable iff its index is +1. Von Schemde and von Stengel (2008) proved this conjecture for bimatrix games. This paper shows that the conjecture is true for all finite games. More precisely, we prove that an isolated equilibrium of a given game has index +1 if and only if it can be made unique in a larger game obtained by adding finitely many inferior reply strategies.
    Date: 2020–05
  13. By: Yuval Heller; Christoph Kuzmics
    Abstract: We define and characterize the set of renegotiation-proof equilibria of coordination games with pre-play communication in which players have private preferences over the feasible coordinated outcomes. Renegotiation-proof equilibria provide a narrow selection from the large set of qualitatively diverse Bayesian Nash equilibria in such games. They are such that players never mis-coordinate, play their jointly preferred outcome whenever there is one, and communicate only the ordinal part of their preferences. Moreover, they are robust to changes in players beliefs, interim Pareto efficient, and evolutionarily stable.
    Date: 2020–05
  14. By: Federico Bonetto; Maurizio Iacopetta (Observatoire français des conjonctures économiques)
    Abstract: We analyze the rise in the acceptability fiat money in a Kiyotaki–Wright economy by developing a method that can determine dynamic Nash equilibria for a class of search models with genuine heterogeneous agents. We also address open issues regarding the stability properties of pure strategy equilibria and the presence of multiple equilibria, numerical experiments illustrate the liquidity conditions that favor the transition from partial to full acceptance of fiat money, and the effects of inflationary shocks on production, liquidity, and trade.
    Keywords: Acceptability of money; Perron; Search
    Date: 2019–10
  15. By: Goncalo dos Reis; Vadim Platonov
    Abstract: We introduce the concept of mean field games for agents using Forward utilities to study a family of portfolio management problems under relative performance concerns. Under asset specialization of the fund managers, we solve the forward-utility finite player game and the forward-utility mean-field game. We study best response and equilibrium strategies in the single common stock asset and the asset specialization with common noise. As an application, we draw on the core features of the forward utility paradigm and discuss a problem of time-consistent mean-field dynamic model selection in sequential time-horizons.
    Date: 2020–05
  16. By: Luisito Bertinelli (CREA, Université du Luxembourg); Stéphane Poncin (CREA, Université du Luxembourg); Benteng Zou (CREA, Université du Luxembourg)
    Abstract: Rare earth elements govern today’s high-tech world and are deemed to be essential for the attainment of sustainable development goals. Since the 1990s, these elements have been predominantly supplied by one single actor, China. However, due to the increasing global relevance of their availability, other countries are now encouraged to enter the market. The objective of this paper is to analyze the strategic interactions among (potential) suppliers. In particular, we are interested in (1) the optimal timing for a newcomer (e. g. the U.S.) to enter the market, (2) the incumbent’s (i. e. China’s) optimal behavior, and (3) the cost-efficiency of cooperative vs. competitive market relations. By setting up a continuous-time dynamic game model, we show that (1) the newcomer should postpone the production launch until its rare earth reserves coincide with those of the incumbent, (2) the incumbent should strive for a late market entry and therefore keep its monopolistic resource extraction at the lowest possible level, (3) compared to the payoffs under competition, cooperation leads to a Pareto improvement when started at an early stage. The findings of our model are particularly relevant for the rational strategic positioning of the two great powers, America and China.
    Keywords: rare earth elements, dynamic games, open-loop strategic Nash equilibria.
    JEL: C61 C7 Q3
    Date: 2019
  17. By: Alessandro De Chiara; Marco A. Schwarz
    Abstract: Firms have incentives to influence regulators' decisions. In a dynamic setting, we show that a firm may prefer to capture regulators through the promise of a lucrative future job opportunity (i.e., the revolving-door channel) than through a hidden payment (i.e., a bribe). This is because the revolving door publicly signals the firm's eagerness and commitment to reward friendly regulators, which facilitates collusive equilibria. Moreover, the revolving-door channel need not require an explicit agreement between the firm and the regulator, but may work implicitly giving rise to an industry norm. This renders ineffective standard anti-corruption practices, such as whistle-blowing protection policies. We highlight that closing the revolving door may give rise to other inefficiencies. Moreover, we show that cooling-off periods may make all players worse off if timed wrongly. Opening the revolving door conditional on the regulator's report may increase social welfare.
    Keywords: collusion, corruption, dynamic games, experts, regulation, regulatory capture, revolving door
    JEL: D82 J45 K23 L14 L51
    Date: 2020–12
  18. By: Bontemps, Christian; Menezes Bezerra Sampaio, Raquel
    Abstract: In this paper we review the literature on static entry games and show how they can be used to estimate the market structure of the airline industry. The econometrics challenges are presented, in particular the problem of multiple equilibria and some solutions used in the literature are exposed. We also show how these models, either in the complete information setting or in the incomplete information one, can be estimated from i.i.d. data on market presence and market characteristics. We illustrate it by estimating a static entry game with heterogeneous firms by Simulated Maximum Likelihood on European data for the year 2015.
    Keywords: entry, airlines, multiple equilibria, estimation, industrial organization.
    Date: 2020–05
  19. By: Navin Kartik; Frances Lee; Wing Suen
    Abstract: We develop a result on Bayesian updating, dubbed information validates the prior (IVP). Roughly, when two agents have different priors, each believes that a (Blackwell) more informative experiment will, on average, bring the other's posterior mean closer to his own prior mean. We apply the result in two contexts of games of asymmetric information: voluntary testing or certification, and costly signaling or falsification. IVP can be used to determine how an agent's behavior responds to additional exogenous or endogenous information. We discuss economic implications.
    Date: 2020–05
  20. By: Konstantinos Ioannidis (University of Amsterdam); Theo Offerman (University of Amsterdam); Randolph Sloof (University of Amsterdam)
    Abstract: The Verifiability Approach is a lie detection method based on the insight that truth-tellers provide precise details whereas liars sometimes remain vague to avoid being exposed. We provide a-game-theoretic analysis of a speaker who wants to be acquitted and an investigator who prefers to find out the truth. The investigator can verify the speaker’s statement at some cost; verification gets more reliable the more details are provided. If, after a falsified statement, the investigator convicts, an additional obstruction penalty is imposed. We derive all the equilibria of the game and thereby the conditions under which the investigator can infer additional information from the speaker's statement at face value. Strategic information revelation by the speaker and verification by the investigator then necessarily work in tandem. Improvements in reliability result in more valuable (strategic) information transmission, whereas a harsher obstruction penalty does not as soon as a lower limit is met.
    Keywords: Lie detection, Verifiability approach, Strategic information revelation
    JEL: K14 C72 D01 D82
    Date: 2020–06–06
  21. By: Noah Topper
    Abstract: Functional decision theory (FDT) is a fairly new mode of decision theory and a normative viewpoint on how an agent should maximize expected utility. The current standard in decision theory and computer science is causal decision theory (CDT), largely seen as superior to the main alternative evidential decision theory (EDT). These theories prescribe three distinct methods for maximizing utility. We explore how FDT differs from CDT and EDT, and what implications it has on the behavior of FDT agents and humans. It has been shown in previous research how FDT can outperform CDT and EDT. We additionally show FDT performing well on more classical game theory problems and argue for its extension to human problems to show that its potential for superiority is robust. We also make FDT more concrete by displaying it in an evolutionary environment, competing directly against other theories.
    Date: 2020–05
  22. By: Alex Dickson (Department of Economics, University of Strathclyde); Iain A Mackenzie (School of Economics, University of Queensland, Brisbane, Australia, 4072.)
    Abstract: This article investigates the cost effectiveness of cap-and-trade markets in the presence of both political and market distortions. We create a model where dominant firms have the ability to rent seek for a share of pollution permits as well as influence the market equilibrium with their choice of permit exchange because of market power. We derive the subgame-perfect equilibrium and show the interaction of these two distortions has consequences for the resulting allocative efficiency of the market. We find that if the dominant rent-seeking firms are all permit buyers (or a composition of buyers and sellers) then allocative efficiency is improved relative to the case without rent seeking; by contrast, if the dominant rent-seeking firms are all permit ellers then allocative efficiency reduces.
    Keywords: pollution market, market power, rent-seeking.
    JEL: E65 G12 G18 P16
    Date: 2020–01
  23. By: Dmitriy Vorobyev (Graduate School of Economics and Management, Ural Federal University, Yekaterinburg, Russia; CERGE-EI, a joint workplace of Charles University and the Economics Institute of the Czech Academy of Sciences, Prague, Czech Republic)
    Abstract: Electoral legislation varies across countries and within countries over time, and across different types of elections in terms of how it allows publication of intermediate election results including turnout and candidates’ vote shares during an election day. Using a pivotal costly voting model of elections in which voters have privately observed preferences between two candidates and act sequentially, I study how different rules for disclosing information about the actions of early voters affect the actions of later voters, and how they ultimately impact voter and candidate welfare. Comparing three rules observed in real life elections (no disclosure, turnout disclosure and vote count disclosure), I find that vote count disclosure dominates the other two rules in terms of voter welfare. I further show that each of the rules can provide a candidate with either the greatest or the least chance to win, depending on the candidate’s ex-ante support.
    Keywords: voting, participation, information disclosure
    JEL: D71 D72 D83
    Date: 2020–05
  24. By: Florian Brandl; Felix Brandt; Dominik Peters; Christian Stricker; Warut Suksompong
    Abstract: We study a mechanism design problem where a community of agents wishes to fund public projects via voluntary monetary contributions by the community members. This serves as a model for participatory budgeting without an exogenously available budget, as well as donor coordination when interpreting charities as public projects and donations as contributions. Our aim is to identify a mutually beneficial distribution of the individual contributions. In the preference aggregation problem that we study, agents report linear utility functions over projects together with the amount of their contributions, and the mechanism determines a socially optimal distribution of the money. We identify a specific mechanism---the Nash product rule---which picks the distribution that maximizes the product of the agents' utilities. This rule is Pareto efficient, and we prove that it satisfies attractive incentive properties: the Nash rule spends an agent's contribution only on projects the agent finds acceptable, and it provides strong participation incentives. We also discuss issues of strategyproofness and monotonicity.
    Date: 2020–05

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