nep-gth New Economics Papers
on Game Theory
Issue of 2018‒01‒29
twenty-one papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. The discrete Kuhn-Tucker theorem and its application to auctions By Yokote, Koji
  2. Application of the discrete separation theorem to auctions By Yokote, Koji
  3. Weighted Shapley levels values By Besner, Manfred
  4. Matrix representation of TU-games for Linear Efficient and Symmetric values By Maimo, Clovis Wendji
  5. Symmetric vs asymmetric equilibria and stochastic stability in a dynamic game of legislative lobbying By Raouf Boucekkine; Fabien Prieur; Benteng Zou
  6. Characterizing Assumption of Rationality by Incomplete Information By Shuige Liu
  7. Natural Instability of Equilibrium Prices By Dmitry Levando; Maxim Sakharov
  8. Stackelberg Games of Water Extraction By Alain Jean-Marie; Mabel Tidball; Fernando Ordóñez; Victor Bucarey López
  9. Le Mécanisme Optimal de Vote au Sein du Conseil des Représentants d'un Système Fédéral By Michel Le Breton; Dominique Lepelley; Antonin Macé; Vincent Merlin
  10. Meaningful Learning in Weighted Voting Games: An Experiment By Eric Guerci; Nobuyuki Hanaki; Naoki Watanabe
  11. The family of ideal values for cooperative games By Wenna Wang; Hao Sun; Rene (J.R.) van den Brink; Genjiu Xu
  12. Games of Incomplete Information and Myopic Equilibria By R. Simon; S. Spiez; H. Torunczyk
  13. Contests for public goods By Heine, Florian
  14. A piecewise smooth model of evolutionary game for residential mobility and segregation By Laura Gardini; Davide Radi
  15. Was Zidane honest or well-informed? How UEFA barely avoided a serious scandal By Csató, László
  16. Norms in bargaining: evidence from government formation in Spain By Thomas Fujiwara; Carlos Sanz
  17. Collusive Benchmark Rates Fixing By Nuria Boot; Timo Klein; Maarten Pieter Schinkel
  18. Bid Shading and Bidder Surplus in the U.S. Treasury Auction System By Ali Hortaçsu; Jakub Kastl; Allen Zhang
  19. Linear voting rules By Hans Peter Grüner; Thomas Tröger
  20. Taxes and Turnout By Felix Bierbrauer; Aleh Tsyvinski; Nicolas D. Werquin
  21. On supply function competition in a mixed oligopoly By Gutiérrez-Hita, Carlos; Vicente-Pérez, José

  1. By: Yokote, Koji
    Abstract: Using a notion of convexity in discrete convex analysis, we introduce a discrete analogue of the Kuhn-Tucker theorem. We apply it to an auction model and show that existing iterative auctions can be viewed as the process of finding a saddle point of the Lagrange function.
    Keywords: Auctions; Discrete convex analysis; Kuhn-Tucker theorem
    JEL: C78 D44
    Date: 2018–01–10
  2. By: Yokote, Koji
    Abstract: The separation theorem in discrete convex analysis states that two disjoint discrete convex sets can be separated by a hyperplane with a 0-1 normal vector. We apply this theorem to an auction model and provide a unified approach to existing results. When p is not an equilibrium price vector, i.e., aggregate demand and aggregate supply are disjoint, the separation theorem indicates the existence of excess demand/supply. This observation yields a refined analysis of a characterization of competitive price vectors by Gul and Stacchetti (2000). Adjusting the prices of items in excess demand/supply corresponds to Ausubel's (2006) auction.
    Keywords: Discrete convex analysis, Separation theorem, Hall's theorem, Auction
    JEL: C78 D44
    Date: 2017–11–23
  3. By: Besner, Manfred
    Abstract: This paper presents a collection of four different classes of weighted Shapley levels values. All classes contain generalisations of the weighted Shapley values to cooperative games with a level structure. The first class is an upgrade of the weighted Shapley levels value in Gómez-Rúa and Vidal-Puga (2011), who use the size of components as weights. The following classes contain payoff vectors from the Harsanyi set. Hence they satisfy the dummy axiom, in contrary to the values in the first class in general. The second class contains extensions of the McLean weighted coalition structure values (Dragan, 1992; Levy and McLean, 1989; McLean, 1991). The first two classes satisfy the level game property (the payoff to all players of a component sum up to the payoff to the component in a game where components are the players) and the last two classes meet a null player out property. As a special case, the first three classes include the Shapley levels value and the last class contains a new extension of the Shapley value.
    Keywords: Cooperative game; Level structure; (Weighted) Shapley (levels) value; Weighted proportionality; Harsanyi set; Dividends
    JEL: C7 C71
    Date: 2017–11–28
  4. By: Maimo, Clovis Wendji
    Abstract: The aim of this article is to present a new tool for assessing TU-game based on a matrix representation. We focus on TU-games with coalition structures and provide a general matrix form of TU-game. We shed light on some useful properties of the matrix representation of TU-game and the general form obtained is applied to describe the representation for some classical TU-game. The facilities provided by such a representation are used to characterize subclasses of Linear Efficient and Symmetric (LES) values.
    Keywords: Cooperative games ; Matrix ; LES value
    JEL: C69 C71 D63
    Date: 2017–01–01
  5. By: Raouf Boucekkine (Aix-Marseille University); Fabien Prieur (Paris-X Nanterre University); Benteng Zou (CREA, Université du Luxembourg)
    Abstract: We study a 2-players stochastic dynamic symmetric lobbying differential game. Players have opposite interests; at any date, each player invests in lobbying ac- tivities to alter the legislation in her own benefit. The payoffs are quadratic and uncertainty is driven by a Wiener process. We prove that while a symmetric Markov Perfect Equilibrium (MPE) always exists, an asymmetric MPE only emerges when uncertainty is large enough. In the latter case, the legislative state converges to a stationary invariant distribution. Interestingly enough, the implications for the rent dissipation problem are much more involved than in the deterministic coun- terpart: the symmetric MPE still yields a limited social cost while the asymmetric may yield significant losses. We also characterize the most likely asymptotic state, in particular regarding the level of uncertainty.
    Keywords: Political lobbying, symmetric versus asymmetric equilibrium, stochastic differential games, stochastic stability, social cost of lobbying
    JEL: D72 C73
    Date: 2018
  6. By: Shuige Liu
    Abstract: We characterize common assumption of rationality of 2-person games within an incomplete information framework. We use the lexicographic model with incomplete information and show that a belief hierarchy expresses common assumption of rationality within a complete information framework if and only if there is a belief hierarchy within the corresponding incomplete information framework that expresses common full belief in caution, rationality, every good choice is supported, and prior belief in the original utility functions.
    Date: 2018–01
  7. By: Dmitry Levando (National Research University Higher School of Economics, Moscow, Russia); Maxim Sakharov (Bauman Mstu, Moscow, Russia)
    Abstract: We develop a theory of market fluctuations caused by strategic trade with complete information and without outside shocks. The constructed general equilibrium duopoly is a strategic market game with infinite strategies and multiple mixed strategies equilibria. First order conditions (FOC) of the game are the ill-posed problems (Hadamard, 1909), but every equilibrium mixed strategy can be only approximated. This imposes restrictions on convergence of common beliefs of players about actions of each other, existence of rational expectations and a price discovery property of the market, although the market is informationally efficient (Fama, 1970). We suggest a modification of Tikhonov regularization to construct pseudo-solutions. All endogenous variables of the model are exposed to unremovable instabilities, ‘natural instabilities’, specific to parameters of a chosen approximation. Our result is also related to existence of common knowledge, sun-spot equilibrium, and noise trade.
    Keywords: Strategic market games, ill-posed problems, common knowledge, rational expectations, efficient market, price fluctuations
    JEL: C68 C61 C72 D59 E31 E32 G14
    Date: 2018
  8. By: Alain Jean-Marie (NEO - Network Engineering and Operations - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique, UCA - Université Côte d'Azur); Mabel Tidball (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UM3 - Université Paul-Valéry - Montpellier 3 - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - INRA Montpellier - Institut national de la recherche agronomique [Montpellier] - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier); Fernando Ordóñez (DII - Departamento de Ingenieria Industrial [Santiago] - USACH - Universidad de Santiago de Chile [Santiago]); Victor Bucarey López (DII - Departamento de Ingenieria Industrial [Santiago] - USACH - Universidad de Santiago de Chile [Santiago])
    Abstract: We consider a discrete time, infinite horizon dynamic game of groundwater extraction. A Water Agency charges an extraction cost to water users, and controls the marginal extraction cost so that it depends linearly on total water extraction (through a parameter n) and on rainfall (through parameter m). The water users are selfish and myopic, and the goal of the agency is to give them incentives them so as to, at the same time, improve their total welfare and improve the long-term level of the resource. We look at this problem in several situations for a linear-quadratic model. In the first situation, the parameters n and m are considered to be fixed over time, and the Agency selects the value that maximizes the total discounted welfare of agents. We analyze this solution, from the economic and environmental point of view, as a function of model parameters, including the discount factor that is used. A first result shows that when Water Agency is patient (discount factor tends to 1) optimal marginal extraction cost asks for strategic interactions between agents. In a second situation, we look at the dynamic Stackelberg game where the Agency decides at each time what cost parameter they must announce in order to maximize the welfare function. We present the sensitivity analysis of the solution for a small time horizon, and present a numerical scheme for the infinite-horizon problem.
    Date: 2017–07–13
  9. By: Michel Le Breton (TSE - Toulouse School of Economics - Toulouse School of Economics); Dominique Lepelley (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de la Réunion - IAE - Institut d'Administration des Entreprises - UR - Université de la Réunion); Antonin Macé (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - CNRS - Centre National de la Recherche Scientifique - ECM - Ecole Centrale de Marseille); Vincent Merlin (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - CNRS - Centre National de la Recherche Scientifique)
    Date: 2017–03
  10. By: Eric Guerci (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis - UCA - Université Côte d'Azur - CNRS - Centre National de la Recherche Scientifique - UCA - Université Côte d'Azur); Nobuyuki Hanaki (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis - UCA - Université Côte d'Azur - CNRS - Centre National de la Recherche Scientifique - UCA - Université Côte d'Azur); Naoki Watanabe (Faculty of Engineering, Information and Systems, University of Tsukuba - University of Tsukuba)
    Abstract: By employing binary committee choice problems, this paper investigates how varying or eliminating feedback about payoffs affects: (1) subjects' learning about the underlying relationship between their nominal voting weights and their expected payoffs in weighted voting games; and (2) the transfer of acquired learning from one committee choice problem to a similar but different problem. In the experiment, subjects choose to join one of two committees (weighted voting games) and obtain a payoff stochastically determined by a voting theory. We found that: (i) subjects learned to choose the committee that generates a higher expected payoff even without feedback about the payoffs they received; and (ii) there was statistically significant evidence of ``meaningful learning'' (transfer of learning) only for the treatment with no payoff-related feedback. This finding calls for re-thinking existing models of learning to incorporate some type of introspection.
    Keywords: experiment,voting game,learning,two-armed bandit problem
    Date: 2017–02–02
  11. By: Wenna Wang (Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, P.R. China); Hao Sun (Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, P.R. China); Rene (J.R.) van den Brink (Department of Econometrics and Operations Research, VU University, Amsterdam, The Netherlands); Genjiu Xu (Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, P.R. China)
    Abstract: In view of the nature of pursuing profit, a selfish coefficient function is employed to describe the degrees of selfishness of players in different coalitions, which is the desired rate of return to the worth of coalitions. This function brings in the concept of individual expected reward to every player. Built on different selfish coefficient functions, the family of ideal values can be obtained by minimizing deviations from the individual expected rewards. Then we show the relationships between the family of ideal values and two other classical families of values: the procedural values and the least square values. For any selfish coefficient function m, the m-ideal value is characterized by efficiency, linearity, m-equal-expectation player property and nullifying player m-punishment property. We also provide an interpretation of a dynamic process for the m-ideal value. As two dual cases in the family of ideal values, the center-of-gravity of imputation-set value (CIS value) and the equal allocation of nonseparable costs value (EANS value) are raised from new axiomatic angles.
    Keywords: Game theory; m-Individual expected reward; The family of ideal values; Dynamic process; CIS and EANS values
    JEL: C71
    Date: 2018–01–11
  12. By: R. Simon; S. Spiez; H. Torunczyk
    Abstract: A new concept of an equilibrium in games is introduced that solves an open question posed by A. Neyman.
    Date: 2017–11
  13. By: Heine, Florian (Tilburg University, School of Economics and Management)
    Abstract: In this dissertation I examine group contests for both endogenous and exogenous public goods. Three studies jointly illustrate that participants accede to a pernicious one-upping in order to outdo the competing party. This tendency to over-contribute in (group) contest games complements earlier studies. Taking extant contributions in that field into account I investigate the role of fundamental institutions, which have been characterised as vehicles to promote cooperation towards a more efficient strategy in cooperative games. The results of my studies, however, paint a grim picture of the role of these simple institutions – such as rewarding and punishment, free form text communication or wealth redistribution – in group contest games. Unequivocally, players use them to push groupmates to intensify the between-group contest and add insult to injury.
    Date: 2017
  14. By: Laura Gardini (Department of Economics, Society & Politics, Università di Urbino "Carlo Bo"); Davide Radi (Department of Economics and Management, University of Pisa)
    Abstract: The paper proposes an evolutionary version of a Schelling-type dynamic system to model the patterns of residential segregation when two groups of people are involved. The payoff functions of agents are the individual preferences for integration which are empirically grounded. Differently from Schelling's model, where the limited levels of tolerance are the driving force of segregation, in the current setup agents bene t from integration. Despite the di¤erences, the evolutionary model shows a dynamics of segregation that is qualitatively similar to the one of the classical Schelling's model: segregation is always a stable equilib- rium while equilibria of integration exist only for peculiar configurations of the payoff functions and their asymptotic stability is highly sensitive to parameter variations. Moreover, a rich variety of integrated dy- namic behaviors can be observed. In particular, the dynamics of the evolutionary game is regulated by a one-dimensional piecewise smooth map with two kink points that is rigorously analyzed using techniques recently developed for piecewise smooth dynamical systems. The investigation reveals that when a stable internal equilibrium exists, the bimodal shape of the map leads to several di¤erent kinds of bifurcations, smooth and border collision, in a complicated interplay. A social planner that aims to maximize integration can use our global analysis of the dynamics of the model to understand the possible achievements of social policies that manipulate peoples preferences for integration.
    Date: 2018
  15. By: Csató, László
    Abstract: UEFA Euro 1996 qualifying is known to violate strategy-proofness. It is proved that a team could be better off by exerting a lower effort: it might be optimal to concede some goals in order to achieve a better position among runners-up, and hence avoid a hazardous play-off. We show that it is not only an irrelevant scenario with a marginal probability since France had an incentive to kick two own goals on its last match against Israel.
    Keywords: OR in sport; UEFA Euro 1996; tournament ranking; strategy-proofness
    JEL: C44 D71
    Date: 2017–11–17
  16. By: Thomas Fujiwara (Princeton, CIFAR, and NBER); Carlos Sanz (Banco de España)
    Abstract: Theories of multilateral bargaining and coalition formation applied to legislatures predict that parties’ seat shares determine their bargaining power. We present findings that are difficult to reconcile with this prediction. We use data from 2,898 municipal Spanish elections in which two parties tie in the number of seats. The party with slightly more general election votes is substantially more likely to appoint the mayor (form the government). Since tied parties should, on average, have equal bargaining power, this identifies the effect of being the most voted due to a norm prescribing that “the most voted should form government.” The effect of being most voted is comparable in size to the effect of obtaining an additional seat. This norm binds behavior even when the second and third most voted parties can form a winning coalition that prefers the most voted not to appoint the mayor. Voters punish, in future elections, second most voted parties that appoint mayors, suggesting that they enforce the norm. We document a similar second-versus-third most voted effect and provide suggestive evidence of similar norms from 28 national European parliaments. A model where elections play a dual role (aggregating information and disciplining incumbents) and different equilibria (norms) can occur is consistent with our results and yields additional predictions.
    Keywords: keyword, bargaining, elections, government formation, political economy, regression discontinuity
    JEL: C7 D7 D9
    Date: 2017–11
  17. By: Nuria Boot (KU Leuven, DIW Berlin); Timo Klein (Amsterdam School of Economics, University of Amsterdam); Maarten Pieter Schinkel (Amsterdam School of Economics and ACLE, University of Amsterdam)
    Abstract: The fixing of the Libor and Euribor benchmark rates has proven vulnerable to manipulation. Individual rate-setters may have incentives to fraudulently distort their submissions. For the contributing banks to collectively agree on the direction in which to rig the rate, however, their interests need to be sufficiently aligned. In this paper we develop cartel theory to show how an interbank lending rates cartel can be sustained by preemptive portfolio changes. Exchange of information facilitates front running that allows members to reduce conflicts in their trading books. Designated banks then engage in eligible transactions rigging to justify their submissions. As the cartel is not able to always find stable cooperative submissions against occasional extreme exposure values, there is episodic recourse to non-cooperative quoting. Periods of heightened volatility in the rates may be indicative of cartelization. Recent reforms to broaden the class of transactions eligible for submission may reduce the level of manipulation, but can lead to more frequent collusive quoting.
    Keywords: Libor; Euribor; IRD; banking; cartel; insider trading
    JEL: E43 G14 G21 K21 L41
    Date: 2017–12–27
  18. By: Ali Hortaçsu; Jakub Kastl; Allen Zhang
    Abstract: We analyze bidding data from uniform price auctions of U.S. Treasury bills and notes between July 2009-October 2013. Primary dealers consistently bid higher yields compared to direct and indirect bidders. We estimate a structural model of bidding that takes into account informational asymmetries introduced by the bidding system employed by the U.S. Treasury. While primary dealers’ estimated willingness-to-pay is higher than direct and indirect bidders’, their ability to bid-shade is even higher, leading to higher yield/lower price bids. Total bidder surplus averaged to about 3 basis points across the sample period along with efficiency losses around 2 basis points.
    JEL: G12 L1
    Date: 2017–11
  19. By: Hans Peter Grüner; Thomas Tröger
    Abstract: How should a society choose between two social alternatives if participation in the decision process is voluntary and costly and monetary transfers are not feasible? Considering symmetric voters with private valuations, we show that it is utilitarian-optimal to use a linear voting rule: votes get alternativedependent weights, and a default obtains if the weighted sum of votes stays below some threshold. Standard quorum rules are not optimal. We develop a perturbation method to characterize equilibria in the case of small participation costs and show that leaving participation voluntary increases welfare for linear rules that are optimal under compulsory participation.
    Keywords: Network effects, two-sided markets, platform competition, competitive bottleneck, multihoming
    JEL: D43 L13 L86
    Date: 2018–01
  20. By: Felix Bierbrauer; Aleh Tsyvinski; Nicolas D. Werquin
    Abstract: We develop a model of political competition with endogenous turnout and endogenous platforms. Parties face a trade-off between maximizing their base and getting their supporters out to vote. We study the implications of this framework for non-linear income taxation. In equilibrium, both parties propose the same tax policy. This equilibrium policy is a weighted combination of two terms, one reflecting the parties’ payoff from mobilizing their own supporters, one reflecting the payoff from demobilizing the supporters of the other party. The key determinant of the equilibrium policy is the distribution of the voters’ party attachments rather than their propensity to swing vote. Our analysis also provides a novel explanation for why even left-leaning parties may not propose high taxes on the rich.
    JEL: D72 D82 H21
    Date: 2017–12
  21. By: Gutiérrez-Hita, Carlos; Vicente-Pérez, José
    Abstract: In this paper we present a mixed duopoly model of supply function competition under uncertainty with product differentiation. We find that, regardless the nature of product heterogeneity, the best response of the private firm always arises as strategic complement. Contrary to this, state-owned firm's best response arises either as strategic complement or substitute depending on the product heterogeneity. As a result of the ex post realization of the demand uncertainty, different equilibria are reached.
    Keywords: Supply Function Equilibria; Mixed oligopoly; Differentiated products.
    JEL: D43 H42 L13
    Date: 2018–01–07

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