nep-gth New Economics Papers
on Game Theory
Issue of 2020‒07‒13
seventeen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. A Game-Theoretical Model of the Landscape Theory By Le Breton, Michel; Shapoval, Alexander; Weber, Shlomo
  2. On the Internal and External Stability of Coalitions and Application to Group Purchasing Organizations By Dongshuang Hou; Aymeric Lardon; Hao Sun
  3. k -additive upper approximation of TU-games By Michel Grabisch; Agnieszka Rusinowska
  4. Projection of Private Values in Auctions By Tristan Gagnon-Bartsch; Marco Pagnozzi; Antonio Rosato
  5. Brokerage By Choi, S.; Goyal, S.; Moisan, F.
  6. An Optimal Distributionally Robust Auction By Alex Suzdaltsev
  7. Gridlock, leverage, and policy bundling By Barton E. Lee
  8. Pricing Pollution By Torben K. Mideksa
  9. Competitive equilibria in Shapley-Scarf markets with couples By Fatma Aslan; Jean Lainé
  10. Individual weighted excess and least square values By Xia Zhang; Rene van den Brink; Arantza Estevez-Fernandez; Hao Sun
  11. Affirmative Action, Shifting Competition, and Human Capital Accumulation: A Comparative Static Analysis of Investment Contests By Christopher Cotton; Brent R. Hickman; Joseph P. Price
  12. Network Topology and Market Structure By Chen, Ying-Ju; Zenou, Yves; Zhou, Junjie
  13. The Conservation Multiplier By Bård Harstad
  14. Lying and Mistrust in the Continuous Deception Game By Tobias Beck
  15. Search, Information and Prices By Bergemann, Dirk; Brooks, Benjamin A; Morris, Stephen
  16. Tax Competition in Presence of Profit Shifting. By Steeve Mongrain; David Oh; Tanguy van Ypersele
  17. Interacting collective action problems in the commons By Nicolas Querou

  1. By: Le Breton, Michel; Shapoval, Alexander; Weber, Shlomo
    Abstract: In this paper we examine a game-theoretical generalization of the landscape theory introduced by Axelrod and Bennett (1993). In their two-bloc setting each player ranks the blocs on the basis of the sum of her individual evaluations of members of the group. We extend the Axelrod-Bennett setting by allowing an arbitrary number of blocs and expanding the set of possible deviations to include multi-country gradual deviations. We show that a Pareto optimal landscape equilibrium which is immune to profitable gradual deviations always exists. We also indicate that while a landscape equilibrium is a stronger concept than Nash equilibrium in pure strategies, it is weaker than strong Nash equilibrium.
    Keywords: Landscape theory; landscape equilibrium; blocs; gradual deviation; potential functions; hedonic games.
    Date: 2020–06
  2. By: Dongshuang Hou (Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China); Aymeric Lardon (Univ Lyon, UJM Saint-Etienne, GATE UMR 5824, F-42023 Saint Etienne, France); Hao Sun (Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China)
    Abstract: Two new notions of stability of coalitions, based on the idea of exclusion or integration of players depending on how they affect allocations, are introduced for cooperative transferable utility games. The first one, called internal stability, requires that no coalition member would find that her departure from the coalition would improve her allocation or those of all her partners. The second one, called external stability, requires that coalitions members do not wish to recruit a new partner willing to join the coalition, since her arrival would hurt some of them. As an application of these two notions, we study the stability of Group Purchasing Organizations using the Shapley value to allocate costs between buyers. Our main results suggest that, when all buyers are initially alone, while small buyers will form internally and externally stable Group Purchasing Organizations to benefit from the best price discount, big buyers will be mutually exclusive and may cooperate with only small buyers.
    Keywords: Internal and external stability, Group purchasing organization, Cost allocation, Shapley value
    JEL: C71 D61 D62
    Date: 2020
  3. By: Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)
    Abstract: We study the problem of an upper approximation of a TU-game by a-additive game under the constraint that both games yield the same Shapley value. The best approximation is obtained by minimizing the sum of excesses with respect to the original game, which yields an LP problem. We show that for any game with at most 4 players all vertices of the polyhedron of feasible solutions are optimal, and we give an explicit formula of the value of the LP problem for a particular class of games.
    Date: 2020–07
  4. By: Tristan Gagnon-Bartsch (Harvard University); Marco Pagnozzi (Università di Napoli Federico II and CSEF); Antonio Rosato (University of Technology Sydney)
    Abstract: We explore how taste projection – the tendency to overestimate how similar others’ tastes are to one’s own – affects bidding in auctions. Taste-projecting bidders underestimate the dispersion in valuations and exaggerate the intensity of competition. Consequently, they overbid in firstprice auctions – irrespective of whether values are independent, correlated, or (a)symmetrically distributed – but not in second-price auctions. Hence, first-price auctions raise more revenue. Moreover, the optimal reserve price in first-price auctions is lower than the rational benchmark, and decreasing in the extent of projection and the number of bidders. With an uncertain common-value component, projecting bidders draw distorted inferences about others’ information. This misinference is stronger in second-price and English auctions, reducing their allocative efficiency compared to first-price auctions.
    Keywords: Auctions; Projection Bias; False-Consensus Effect; Overbidding.
    JEL: D03 D44 D82 D83
    Date: 2020–06–24
  5. By: Choi, S.; Goyal, S.; Moisan, F.
    Abstract: Dominant intermediaries are a defining feature of the modern economy. This paper studies the mechanisms that give rise to trading networks with a dominant intermediary. Trades between actors require a direct link or a path that involves intermediaries. Links are costly. Efficiency therefore pushes towards connected networks with few links: this set includes the hub-spoke network, the cycle network and their variants. The hub-spoke network exhibits extreme inequality, while the cycle network yields equal payoffs for all traders. We conduct a large scale experiment on link formation among traders; the game takes place in continuous time and allows for asynchronous choices. The main finding is that the pricing protocol - the rule dividing the surplus between traders and intermediaries - determines which of these two networks arises.
    JEL: C92 D83 D85 Z13
    Date: 2020–01–20
  6. By: Alex Suzdaltsev
    Abstract: An indivisible object may be sold to one of $n$ agents who know their valuations of the object. The seller would like to use a revenue-maximizing mechanism but her knowledge of the valuations' distribution is scarce: she knows only the means (which may be different) and an upper bound for valuations. Valuations may be correlated. Using a constructive approach based on duality, we prove that a mechanism that maximizes the worst-case expected revenue among all deterministic dominant-strategy incentive compatible, ex post individually rational mechanisms takes the following form: (1) the bidders submit bids $b_i$; (2) for each bidder, a linear score $s_i=\beta_ib_i-\alpha_i$ is calculated where $\alpha_i$, $\beta_i$ are fixed parameters; (3) the object is awarded to the agent with the highest score, provided it's nonnegative; (4) the winning bidder pays the minimal amount he would need to bid to still win in the auction. The set of optimal mechanisms includes other mechanisms but all those have to be close to the optimal linear score auction in a certain sense. When means are high, all optimal mechanisms share the linearity property. Second-price auction without a reserve is an optimal mechanism when the number of symmetric bidders is sufficiently high.
    Date: 2020–06
  7. By: Barton E. Lee (School of Economics, UNSW Sydney)
    Abstract: We consider a dynamic model of bargaining where alternatives to the status-quo arrive stochastically during the bargaining process, the proposer can bundle multiple alternatives into a single proposal, and a forward-looking voter elects the agendasetter. We show that the prevailing wisdom that policy bundling reduces gridlock — by facilitating compromise across different policy areas — is incomplete. Policy bundling can also increase gridlock: a player may veto or delay a bipartisan alternative, which is unanimously preferred to the status-quo, so that in the future they can bundle this same alternative with a divisive alternative that otherwise would not pass. Gridlock of this form is more likely to occur during periods of economic stability and suggests that traditional measures of legislator ideology will overstate polarization. From the voter’s perspective, we show that gridlock occurs at an inefficiently high frequency. This state of “excess gridlock” is driven by the voter being forward-looking and lacking commitment power to punish players that veto.
    Keywords: Gridlock, bargaining, policy bundling
    JEL: D72 D78
    Date: 2020–06
  8. By: Torben K. Mideksa
    Abstract: I examine a policy-making game among countries that must choose both a policy instrument (e.g., a tax or a quota) and its intensity (i.e., the tax rate or the quota level) to price pollution. When countries price pollution non-cooperatively, they not only set the intensity inefficiently, they are also likely to adopt Pigouvian fees, despite quotas being better from a welfare perspective. Adopting a Pigouvian fee to address a multi-country externality generates a risk externality, and non-cooperatively chosen quotas can generate higher social welfare than maximum social welfare Pigouvian fees can deliver.
    Keywords: environmental policy, global pollution, international relations
    JEL: C72 D81 F50 H21 Q38 Q58
    Date: 2020
  9. By: Fatma Aslan (LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - CNAM - Conservatoire National des Arts et Métiers [CNAM]); Jean Lainé (Department of Economics, Bilgi University - Istanbul Bilgi University)
    Abstract: We investigate the existence and properties of competitive equilibrium in Shapley-Scarf markets involving an exogenous partition of individuals into couples. The presence of couples generates preference interdependencies which cause existence problems. For both cases of transferable and non-transferable income among partners, we establish properties for preferences that are sufficient for the existence of an equilibrium. Moreover, we show that these properties define a maximal preference domain.
    Date: 2020–08
  10. By: Xia Zhang (Vrije Universiteit Amsterdam); Rene van den Brink (Vrije Universiteit Amsterdam); Arantza Estevez-Fernandez (Vrije Universiteit Amsterdam); Hao Sun (Northwestern Polytechnical University)
    Abstract: This work deals with the weighted excesses of players in cooperative games which are obtained by summing up all the weighted excesses of all coalitions to which they belong. We first show that lexicographically minimizing the individual weighted excesses of players gives the same minimal weighted excess for every player. Moreover, we show that the associated payoff vector is the corresponding least square value. Second, we show that minimizing the variance of the players' weighted excesses on the preimputation set, again yields the corresponding least square value. Third, we show that these results give rise to lower and upper bounds for the core payoff vectors and, using these bounds, we define the weighted super core as a polyhedron that contains the core. It turns out that the least square values can be seen as a center of this weighted super core, giving a third new characterization of the least square values. Finally, these lower and upper bounds for the core inspire us to introduce a new solution for cooperative TU games that has a strong similarity with the Shapley value.
    Keywords: Individual weighted excess, Prenucleolus, Least square value, Weighted super core, Shapley value
    JEL: C71
    Date: 2020–06–20
  11. By: Christopher Cotton (Queen's University); Brent R. Hickman (Olin Business School, University of Washington); Joseph P. Price (Brigham Young University)
    Abstract: We develop a model in which many heterogeneous agents invest in human capital as they compete for better college admission slots or employment opportunities. The model provides theoretical predictions about how affirmative action or preferential treatment policies change the distribution of effort, human capital accumulation, and job/college slot allocations across different population groups. Our findings deliver two key insights. First, incentives to invest in human capital depends substantially on the strength of one's competition. Second, we find evidence of a counter-intuitive role for preferential treatment in promoting overall human capital development.
    Keywords: large contest, all-pay contest, all-pay auction, affirmative action, college admissions, field experiment, human capital
    JEL: J15 J24 C93 D82 D44
    Date: 2020–06
  12. By: Chen, Ying-Ju; Zenou, Yves; Zhou, Junjie
    Abstract: We develop a two-stage oligopolistic network competition model where, first, firms simultaneously determine their prices and, then, users connected through a network determine their product's consumption. We show that denser networks (network topology) reduce prices and that a higher number of firms (market structure) reduces prices only when competition is weak. However, the price for the most influential users can increase with the number of firms when competition is very fierce and when there are enough network externalities. We also show that increasing competition always leads to a lower firm's profit while increasing network density leads to a clockwise rotation of the profit curve as a function of the number of firms. Finally, we study the effect of network topology and market structure on price dispersion and determine the optimal network structure from the perspective of both firms and users.
    Keywords: competitive pricing; Entry; market structure; optimal network structure
    JEL: D43 D85 L13 L14
    Date: 2020–03
  13. By: Bård Harstad
    Abstract: Every government that controls an exhaustible resource must decide whether to exploit it or to conserve and thereby let the subsequent government decide whether to exploit or conserve. This paper develops a theory of this situation and shows when a small probability that some future government will exploit a resource leads to a domino effect with rapid exploitation. This effect leads to a multiplier that measures how a small change in parameters can have large effects. The multiplier is especially large if the government is powerful now but unlikely to be in power later. The multiplier also permits dramatic returns on lobby contributions contingent on exploitation -- or on compensations contingent on conservation -- when these offers are expected to continue. To best take advantage of the multiplier, I show how and when compensations should be offered to the president, the party in power, the general public, or to the lobby group.
    Keywords: dynamic games, exhaustible resources, deforestation, political economy, lobbying, conservation, PES, REDD+.
    JEL: D72 C73 Q57 O13
    Date: 2020
  14. By: Tobias Beck (University of Kassel)
    Abstract: I present a novel experimental design to measure lying and mistrust as continuous variables on an individual level. My experiment is a sender-receiver game framed as an investment game. It features two players: firstly, an advisor with complete information (i.e., the sender) who is incentivized to lie about the true value of an optimal investment and, secondly, an investor with incomplete information (i.e., the receiver) who is incentivized to invest optimally and therefore must rely on the alleged optimum reported by the advisor. The extents of lying and mistrust are both measured on continuous scales. This allows observing more differentiated behavior and therefore enables testing of more sophisticated theoretical predictions. I find that the senders lie by overstating the true value of the optimum to an average extent of about 148%, while the receivers suspect them to do so by only 56%. The senders seldomly lie to the fullest possible extent as they correctly expect the receivers to disproportionally mistrust lies of such a high extent. This indicates that people make strategic considerations about their potential to manipulate others when lying. In line with this, I discover that lying and mistrusting behavior can be predicted by first-order beliefs about the other player. Consistent with previous studies, my findings support the conjecture that lying costs increase with the extent of lying. In addition, I provide evidence for some endogenous preference for trust. Both players’ behaviors and beliefs are consistent over time. Moreover, my ex ante classification of both players’ strategy sets is consistent with their ex post self-assessment of their own behavior within the experiment.
    Keywords: Lies, Honesty, Mistrust, Deception Game, Investments, Asymmetric information, Experimental Design
    JEL: C91 D01 D82
    Date: 2020
  15. By: Bergemann, Dirk; Brooks, Benjamin A; Morris, Stephen
    Abstract: Consider a market with many identical firms offering a homogeneous good. A consumer obtains price quotes from a subset of firms and buys from the firm offering the lowest price. The "price count" is the number of firms from which the consumer obtains a quote. For any given ex ante distribution of the price count, we obtain a tight upper bound (under first-order stochastic dominance) on the equilibrium distribution of sale prices. The bound holds across all models of firms' common-prior higher-order beliefs about the price count, including the extreme cases of complete information (firms know the price count exactly) and no information (firms only know the ex ante distribution of the price count). A qualitative implication of our results is that even a small ex ante probability that the price count is one can lead to dramatic increases in the expected price. The bound also applies in a wide class of models where the price count distribution is endogenized, including models of simultaneous and sequential consumer search.
    Keywords: "Law of One Price"; Bayes correlated equilibrium; Bertrand Competition; information structure; price competition; Price Count; Price Quote; search
    JEL: D41 D42 D43 D83
    Date: 2020–03
  16. By: Steeve Mongrain (Simon Fraser University); David Oh (Canada Mortgage and Housing Corporation); Tanguy van Ypersele (Aix-Marseille Univ., CNRS, EHESS, Central Marseille, AMSE, Marseille)
    Abstract: The popular view is that governments should crack down on tax avoidance by multinational firms. In this paper, we analyze how anti-profit-shifting policies influence fiscal competition. Governments commit to profit shifting control effort and then set taxes on capital. Equilibrium tax rates are determined by the elasticities of the two components: profit shifting and capital mobility. Anti-profit-shifting policies decrease the elasticity of the first but increase the elasticity of the second, so that the impact of these policies on the equilibrium of the tax game is ambiguous. We show that there are cases in which laxer policies increase all equilibrium tax rates and that the country announcing laxer profit shifting policies may gain. It appears that there is not always a pure strategy equilibrium in such a fiscal competition game. We construct a mixed strategy equilibrium when the pure strategy equilibrium does not exist.
    Keywords: Tax competition; Profit shifting; International taxation; Capital mobility
    JEL: H87 H25 H26 F38 F23
    Date: 2020–06
  17. By: Nicolas Querou (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - INRA - Institut National de la Recherche Agronomique - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier, CNRS - Centre National de la Recherche Scientifique)
    Abstract: We consider a setting where agents are subject to two types of collective action problems, any group user's individual extraction inducing an externality on others in the same group (intra-group problem), while aggregate extraction in one group induces an externality on each agent in other groups (intergroup problem). One illustrative example of such a setting corresponds to a case where a common-pool resource is jointly extracted in local areas, which are managed by separate groups of individuals extracting the resource in their respective location. The interplay between both types of externality is shown to affect the results obtained in classical models of common-pool resources. We show how the fundamentals affect the individual strategies and welfare compared to the benchmark commons problems. Finally, different initiatives (local cooperation, inter-area agreements) are analyzed to assess whether they may alleviate the problems, and to understand the conditions under which they do so.
    Keywords: common-pool resource,collective action,externalities
    Date: 2020–06–05

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