nep-gth New Economics Papers
on Game Theory
Issue of 2017‒04‒09
24 papers chosen by
László Á. Kóczy
Magyar Tudományos Akadémia

  1. The asymptotic core, nucleolus and Shapley value of smooth market games with symmetric large players By Benyamin Shitovitz; Rubinchik, Anna
  2. Experimental investigations of binary threshold public good games By Spiller, Jörg; Bolle, Friedel
  3. On the Coalitional Stability of Monopoly Power in Differentiated Bertrand and Cournot Oligopolies By Aymeric Lardon
  4. Stability in Matching with Couples having Non-Responsive Preferences By Khare, Shashwat; Roy, Souvik
  5. Electing a parliament: an experimental study By Francesco De Sinopoli; Giovanna Iannantuoni; Maria Vittoria Levati; Ivan Soraperra
  6. On the Values for Bayesian Cooperative Games with Sidepayments By Andrés Salamanca Lugo
  7. Stabilizing unstable outcomes in prediction games By Brams, Steven; Kilgour, Marc
  8. Externalities in Economies with Endogenous Sharing Rules By Philippe Bich; Rida Laraki
  9. Multi winner Approval Voting: An Apportionment Approach By Brams, Steven J.; Kilgour, D. Marc; Potthoff, Richard F.
  10. A behavioral theory of equilibrium selection By Bolle, Friedel
  11. Mindreading and Endogenous Beliefs in Games By Lauren Larrouy; Guilhem Lecouteux
  12. Speculation rather than enterprise? Keynes’ beauty contest revisited in theory and experiment. By Kene Boun My; Camille Cornand; Rodolphe Dos Santos Ferreira
  13. Repeated bargaining By Shiran Rachmilevitch
  14. A Naïve Approach to Bidding By Paul Pezanis-Christou; Hang Wu
  15. An experimental investigation of rating-market regulation By Claudia Keser; Asri Özgümüs; Emmanuel Peterle; Martin Schmidt
  16. Agent base model in public goods game By Chen Yuyou
  17. Punishing greediness in Divide-the-dollar games By Shiran Rachmilevitch
  18. Tournaments By Dmitry Ryvkin; Mikhail Drugov
  19. Very Simple Markov-Perfect Industry Dynamics : Theory By Abbring, Jaap; Campbell, J.R.; Tilly, J.; Yang, N.
  20. Procurement Auctions with Uncertainty in Corruption By Shinya Horie
  21. Game-Theoretic Protection Against Networked SIS Epidemics by Human Decision-Makers By Ashish R. Hota; Shreyas Sundaram
  22. Using Personality Questionnaires in Experiments -- Limits and Potentials By Müller, Julia; Schwieren, Christiane
  23. Efficiency-wage competition: What happens as the number of players increases? By Guerrazzi, Marco
  24. How to choose a delegation for a peace conference? By Can, Burak; Csóka, Péter; Ergin, Emre

  1. By: Benyamin Shitovitz (University of Haifa, Department of Economics); Rubinchik, Anna (University of Amsterdam)
    Abstract: We examine the asymptotic nucleolus of a smooth and symmetric oligopoly with an atomless sector in a transferable utility (TU) market game. We provide sufficient conditions for the asymptotic core and the nucleolus to coincide with the unique TU competitive payoff distribution. This equivalence results from nucleolus of a finite TU market game belonging to its core, the core equivalence in a symmetric oligopoly with identical atoms and single-valuedness of the core in the limiting smooth game. In some cases (but not always), the asymptotic Shapley value is more favourable for the large traders than the nucleolus, in contrast to the monopoly case (Einy et al. in J Econ Theory 89(2):186–206, 1999), where the nucleolus allocation is larger than the Shapley value for the atom
    Keywords: Mixed games · Oligopoly · Asymptotic nucleolus · Asymptotic Shapley value
    JEL: C71 D40 D43
  2. By: Spiller, Jörg; Bolle, Friedel
    Abstract: In Binary Threshold Public Good (BTPG) games n players contribute or not to the production of a public good which is produced if and only if there are at least k contributors. The BTPG games with the highest (k=n) and the lowest (k=1) threshold are the Stag Hunt game and the Volunteer's Dilemma. There is a plethora of equilibria in BTPG games. We experimentally investigate 16 different symmetric and asymmetric BTPG games with n=4 and k=1,2,3,4 and test general theoretical attributes of equilibria and whether equilibrium play can apply at all. As theory predicts, neither magnitude effects nor a negative instead of a positive frame affect behavior which is contrary to the bulk of the experimental literature. In the Stag Hunt game, which is often used to discriminate between payoff dominance and risk dominance, risk dominance as a description of behavior is clearly rejected and payoff dominance is moderately supported. We show that no theory with homogeneous players can describe behavior.
    Keywords: Binary Threshold Public Goods,framing,equilibrium selection,payoff dominance,risk dominance,efficiency,experiment
    JEL: C72 D72 H41
    Date: 2017
  3. By: Aymeric Lardon (Université Côte d'Azur, France; GREDEG CNRS)
    Abstract: In this article we revisit the classic comparison between Bertrand and Cournot competition in the presence of a cartel of firms that faces outsiders acting individually. This competition setting enables to deal with both non-cooperative and cooperative oligopoly games. We concentrate on industries consisting of symmetrically differentiated products where firms operate at a constant and identical marginal cost. First, while the standard Bertrand-Cournot rankings still hold for Nash equilibrium prices, we show that the results may be altered for Nash equilibrium quantities and profits.Second, we define cooperative Bertrand and Cournot oligopoly games with transferable utility on the basis of their non-cooperative foundation. We establish that the core of a cooperative Cournot oligopoly game is strictly included in the core of a cooperative Bertrand oligopoly game when the number of firms is lower or equal to 25. Otherwise the cores cannot be compared. Moreover, we focus on the aggregate-monotonic core, a subset of the core, that has the advantage to select point solutions satisfying both core selection and aggregate monotonicity properties. We succeed in comparing the aggregate-monotonic cores between Bertrand and Cournot competition regardless of the number of firms.
    Keywords: Bertrand, Cournot, Differentiated oligopoly, Cartel, Nash equilibrium, Core, Aggregate-monotonic core
    JEL: C71 D43
    Date: 2017–03
  4. By: Khare, Shashwat (Quantitative Economics); Roy, Souvik (QE / Mathematical economics and game the)
    Abstract: The paper studies matching markets where institutions are matched with possibly more than one individual. The matching market contains some couples who view the pair of jobs as complements. We specify that the couples have a "weak'' preference to be matched together. We first assume that the institutions have common preference over all the individuals. We then characterize under which weak preferences of couples a stable matching exists. We then impose further conditions on the common preference of institutions over the individuals and prove existence of stable matching for unrestricted couple preferences. Finally, we establish a result on stability by relaxing the condition on common preference of institutions over individuals and assuming different preferences for different institutions.
    Keywords: two-sided matching, stability, weak responsiveness
    JEL: C78 D47
    Date: 2017
  5. By: Francesco De Sinopoli (Department of Economics (University of Verona)); Giovanna Iannantuoni (University of Milano-Bicocca); Maria Vittoria Levati (Department of Economics (University of Verona)); Ivan Soraperra (Department of Economics (University of Verona))
    Abstract: We use laboratory experiments to explore what electoral outcomes emerge and how voters behave in a setting in which the electorate must determine the number of seats that two parties obtain in the parliament. Previous experimental work has mainly focused on winner-take-all elections and voting over fixed agendas, and has not studied elections where participants decide on the composition of a parliament. We consider two electoral systems, multidistrict majoritarian and single district proportional. Relying on De Sinopoli et al.'s (2013) model of a parliamentary election, we obtain a unique perfect equilibrium outcome under both systems and exploit this uniqueness to gauge, and compare, the predictive value of the equilibrium concept in the two systems. The experimental results are broadly supportive of the theory and reveal that electoral outcomes and individual votes are more often in line with the equilibrium in the proportional than in the majoritarian system.
    Keywords: Voting, Majority election, Proportional election, Experiment
    JEL: C72 D72
    Date: 2016–07
  6. By: Andrés Salamanca Lugo (TSE - Toulouse School of Economics - Toulouse School of Economics)
    Abstract: In this paper we study several value like solution concepts for cooperative games with incomplete information and sidepayments. In our model, sidepayments are required to be incentive compatible, thus utility is not fully transferable (as it would be in the complete information case). Restricting attention to games with orthogonal coalitions, which do not involve strategic externalities, we show that Myerson's (1984a) extension of the Shapley NTU value and Salamanca's (2016) extension of the Harsanyi NTU value coincide. Allowing for arbitrary informational and strategic externalities, we show that the ex-ante evaluation of Myerson's (1984a) value equals Kalai and Kalai's (2013) cooperative-competitive value in two-player games with verifiable types.
    Keywords: Cooperative games, incomplete information, sidepayments
    Date: 2017–02–15
  7. By: Brams, Steven; Kilgour, Marc
    Abstract: Assume in a 2-person game that one player, Predictor (P), does not have a dominant strategy but can predict with probability p > 1/2 the strategy choice of an opponent, Predictee (Q). Q chooses a strategy that maximizes her expected payoff, given that she knows p—but not P’s prediction—and that P will act according to his prediction. In all 2 2 strict ordinal games in which there is a unique Pareto-inferior Nash equilibrium (Class I) or no pure-strategy equilibrium (Class II), and which also has a Pareto-optimal non-Nash “cooperative outcome,” P can induce this outcome if p is sufficiently high. This scenario helps to explain the observed outcomes of a Class I game modeling the 1962 Cuban missile crisis between the United States and the Soviet Union, and a Class II game modeling the 2015 conflict between Iran and Israel over Iran’s possible development of nuclear weapons.
    Keywords: Noncooperative games, prediction, Nash equilibrium, 1962 Cuban missile crisis, 2015 Iran-Israel conflict
    JEL: C72 C78 D81
    Date: 2017–03
  8. By: Philippe Bich (PSE - Paris School of Economics, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Rida Laraki (Ecole Polytechnique [Palaiseau])
    Abstract: Endogenous sharing rules were introduced by Simon and Zame [16] to model payoff indeterminacy in discontinuous games. They prove the existence in every compact strategic game of a mixed Nash equilibrium and an associated sharing rule. We extend their result to economies with externalities [1] where, by definition, players are restricted to pure strategies. We also provide a new interpretation of payoff indeterminacy in Simon and Zame's model in terms of preference incompleteness.
    Keywords: Economies, Generalized Games, Endogenous Sharing Rules, Wal-,rasian Equilibrium, Incomplete and Discontinuous Preferences, Better Reply Security,JEL Classification: C02, C62, C72, D50
    Date: 2017
  9. By: Brams, Steven J.; Kilgour, D. Marc; Potthoff, Richard F.
    Abstract: We extend approval voting so as to elect multiple candidates, who may be either individuals or members of a political party, in rough proportion to their approval in the electorate. We analyze two divisor methods of apportionment, first proposed by Jefferson and Webster, that iteratively depreciate the approval votes of voters who have one or more of their approved candidates already elected. We compare the usual sequential version of these methods with a nonsequential version, which is computationally complex but feasible for many elections. Whereas Webster apportionments tend to be more representative of the electorate than those of Jefferson, the latter, whose equally spaced vote thresholds for winning seats duplicate those of cumulative voting in 2-party elections, is even-handed or balanced.
    Keywords: Approval voting, apportionment methods, multiple winners, proportional representation, cumulative voting
    JEL: C6 C63 C7 C72 C8 D6 D63 D7 D71 D72
    Date: 2017–03–26
  10. By: Bolle, Friedel
    Abstract: Theories about unique equilibrium selection are often rejected in experimental investigations. We drop the idea of selecting a single prominent equilibrium but suggest the coexistence of different beliefs about "appropriate" equilibrium or non-equilibrium play. Our main selection criterion is efficiency applied to all or only to "fair" equilibria. This assumption is applied to 16 Binary Threshold Public Good games where at least k of four homogeneous or heterogeneous players have to incur fixed costs in order to produce a public good. The case k=4 is the Stag Hunt game which is most often used to test equilibrium selection. Our finite mixture model applies with the same parameters (shares of populations, altruism parameters) to the four thresholds k=1,2,3,4. The estimated shares of populations are similar in four treatments with identical or different cost/benefit ratios of the players. Our results for k=4 clearly contradict selection by Risk Dominance and Global Games. In the two (almost) symmetric treatments the Harsanyi/Selten selection explains 40% of the decisions.
    Keywords: equilibrium selection,Binary Threshold Public Goods,payoff dominance,risk dominance,Global Games,efficiency,experiment
    JEL: C51 C57 C72 D72 H41
    Date: 2017
  11. By: Lauren Larrouy (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis - CNRS - Centre National de la Recherche Scientifique); Guilhem Lecouteux (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis - CNRS - Centre National de la Recherche Scientifique)
    Abstract: We argue that a Bayesian explanation of strategic choices in games requires introducing a psychological theory of belief formation. We highlight that beliefs in epistemic game theory are derived from the actual choice of the players, and cannot therefore explain why Bayesian rational players should play the strategy they actually chose. We introduce the players’ capacity of mindreading in a game theoretical framework with the simulation theory, and characterise the beliefs that Bayes rational players could endogenously form in games. We show in particular that those beliefs need not be ratifiable, and therefore that rational players can form action-dependent beliefs.
    Keywords: action-dependent beliefs, simulation, prior beliefs, mindreading, choice under uncertainty
    Date: 2017–02–16
  12. By: Kene Boun My; Camille Cornand; Rodolphe Dos Santos Ferreira
    Abstract: In Keynes’ beauty contest, agents make evaluations reflecting both an expected fundamental value and the conventional value expected to be set by the market. They thus respond to fundamental and coordination motives, respectively, the prevalence of either being set exogenously. Our contribution is twofold. First, we propose a valuation game in which agents strategically choose how to weight each motive. This game emphasises how public information leads agents to favour the coordination motive. Second, we test the game through a laboratory experiment. Subjects tend to conform to theoretical predictions, except when fundamental uncertainty is low relative to strategic uncertainty.
    Keywords: dispersed information, public information, beauty contest, coordination, experiment.
    JEL: D84 C92 E12
    Date: 2017
  13. By: Shiran Rachmilevitch (University of Haifa, Department of Economics)
    Abstract: Two symmetric players bargain over an in nite stream of pies. There is one exogenously given pie in every period, whose size is stochastic, and the pies are iid. Play can be in a tabula rasa mode or dispute mode. When it is in the former, Nature selects a proposer and a responder with equal probabilities, and a proposal is made by the proposer regarding the division of the present pie. If there is agreement then it is implemented and play moves on to the next period, where it is again in tabula rasa. If there is rejection then dispute starts, which means that the players start to bargain over the disputed pie according to Rubinstein's (1982) protocol. As long as the disputed pie is Rubinstein- bargained over, all the new pies that arrive are not available for consumption (they disappear right after they materialize). Once a dispute settles, the game shifts back to tabula rasa. I characterize the game's unique stationary subgame perfect equilibrium
    Keywords: Bargaining; Repeated games.
    JEL: D70 D74
  14. By: Paul Pezanis-Christou (School of Economics, University of Adelaide); Hang Wu (Centre for Behavioural Economics, National University of Singapore)
    Abstract: We propose a novel approach to the modelling of bidding behavior in pay-your-bid auctions that builds on the presumption that bidders are mostly concerned with losing an auction if they happen to have the highest signal. Our models assume risk neutrality, no profit maximization and no belief about competitors' behavior. They may entail overbidding in first-price and all-pay auctions and we discuss conditions for the revenue equivalence of standard pay-your-bid auctions to hold. We fit the models to the data of first-price auction experiments and find that they do at least as well as VickreyÂ’s benchmark model for risk neutral bidders. Assuming probability misperception or impulse weighting (when relevant) improves their goodness-of-fit and leads to very similar revenue predictions. An analysis of individuals' heterogeneous behavioral traits suggests that impulse weighting is a more consistent rationale for the observed behavior than a power form of probability misperception.
    Keywords: first-price auctions, all-pay auctions, impulse balance equilibrium, overbidding, bounded rationality, probability distortion, regret, experiments.
    JEL: C44 C72 D44 L2
    Date: 2017–03
  15. By: Claudia Keser (University of Göttingen); Asri Özgümüs (University of Göttingen); Emmanuel Peterle (Université Bourgogne Franche-Comté, CRESE); Martin Schmidt (Karlsruhe Institute of Technology (KIT))
    Abstract: We introduce a simple game-theoretical model that captures the main aspects of the repeated interaction between an issuer and a credit-rating agency. It involves up-front payments of issuer fees and direct publication of requested ratings. Due to pecuniary injuries for untruthful ratings, the credit-rating agency should always report truthfully in the subgame perfect equilibrium. Knowing this, the issuer should never request a rating. Conducting laboratory experiments, we find that behavior significantly deviates from the equilibrium prediction in favor of a cooperative solution: issuers frequently do request ratings, which is often reciprocated with untruthful good ratings.
    Keywords: Game theory, laboratory experiments, rating agencies, regulation
    JEL: C70 C9 G01
    Date: 2017–03
  16. By: Chen Yuyou
    Abstract: Build some model to describe types of different social preference. Explore all composition of social preference in public game, and find some of them will disobey the dynamics of free riding. Base on the public goods game, we build five types social preference agents, and simulate this agents play public goods game.The dynamics of free riding in public game play key role at the most. And it suggests that selfishness is inevitable. Only in the case that agents in one group are altruism, the contribution will not decline. With the numbers of agents in one group increasing, much more composition can be distinguished as advantageous to improve public welfare. The belief formation mechanism make no sense in repeat game.
    Keywords: China, Agent-based modeling, Agent-based modeling
    Date: 2015–07–01
  17. By: Shiran Rachmilevitch (University of Haifa, Department of Economics)
    Abstract: Brams and Taylor (1994) presented a version of the Divide-the-dollar game (DD), which they call DD1. DD1 su ers from the following drawback: when each player demands approximately the entire dollar, then if the least greedy player is unique, then this player obtains approximately the entire dollar even if he is only slightly less greedy than the other players. I introduce a parametrized family of 2-person DD games whose endpoints" (the games that correspond to the extreme points of the parameter space) are (1) a variant of DD1, and (2) a game that completely overcomes the greediness-related problem. I also study an n-person generalization of this family. Finally, I show that the modeling choice between discrete and continuous bids may have far-reaching implications in DD games
    Keywords: Bargaining games; Divide-the-dollar; Fair division
  18. By: Dmitry Ryvkin (Florida State University); Mikhail Drugov (New Economic School and CEPR)
    Abstract: We derive robust comparative statics for general rank-order tournaments with additive and multiplicative noise. For unimodal distributions of noise, we show that individual equilibrium effort is unimodal in the number of players when it is deterministic. For a stochastic number of players, the unimodality is preserved for changes in the number of players in the sense of first-order stochastic dominance under an additional log-supermodularity restriction. Aggregate equilibrium effort can be increasing, decreasing or nonmonotone in the number of players. Equilibrium effort decreases as noise becomes more dispersed, in the sense of dispersive order or appropriately defined entropy.
    Keywords: tournament, comparative statics, stochastic number of players, unimodality, log-supermodularity, entropy
    JEL: C72 D72 D82
    Date: 2017–03
  19. By: Abbring, Jaap (Tilburg University, Center For Economic Research); Campbell, J.R.; Tilly, J.; Yang, N. (Tilburg University, Center For Economic Research)
    Abstract: This paper develops a simple model of firm entry, competition, and exit in oligopolistic markets. It features toughness of competition, sunk entry costs, and market-level demand and cost shocks, but assumes that firms' expected payoffs are identical when entry and survival decisions are made. We prove that this model has an essentially unique symmetric Markov-perfect equilibrium, and we provide an algorithm for its computation. Because this algorithm only requires finding the fixed points of a finite sequence of contraction mappings, it is guaranteed to converge quickly.
    Keywords: demand uncertainty; dynamic oligopoly; firm entry and exit; sunk costs; toughness of competition
    JEL: L13 C25 C73
    Date: 2017
  20. By: Shinya Horie (Graduate School of Economics, Kobe University)
    Abstract: This paper considers a situation in which a corrupt government official does not commit to using the common corruption scheme called right of first refusal in a procurement auction. Under the right of first refusal, the contractors (or bidders) participate in a sequential auction, and there is no inefficiency in project allocation. However, in cases in which the scheme is not practiced, both contractors participate in a simultaneous auction, and the disadvantaged contractor bids more aggressively than the advantaged contractor. I found that such uncertainty regarding the practice of corruption schemes can lead to inefficiency, even when the corruption scheme itself is not practiced.
    Keywords: Procurement Auctions; Corruption, Right of first refusal
    JEL: C72 D44 L14
    Date: 2017–03
  21. By: Ashish R. Hota; Shreyas Sundaram
    Abstract: We study decentralized protection strategies by human decision-makers against Susceptible-Infected-Susceptible (SIS) epidemics on networks. Specifically, we examine the impact of behavioral (mis)-perceptions of infection probabilities (captured by Prospect theory) on the Nash equilibrium strategies in two classes of games. In the first class of games, nodes choose their curing rates to minimize the steady-state infection probability under the degree-based mean-field approximation plus the cost of their selected curing rate. We establish the existence of pure Nash equilibria under both risk neutral and behavioral decision-makers. When the per-unit cost of curing rate is sufficiently high, we show that risk neutral players choose the curing rate to be zero at the equilibrium, while curing rate is nonzero under behavioral decision-making for any finite cost. In the second class of games, the nodes choose whether or not to vaccinate themselves. We establish the existence of unique threshold equilibria where nodes with degrees larger than a certain threshold vaccinate. When the vaccination cost is sufficiently high, fewer behavioral players vaccinate compared to risk neutral players, and vice versa. Finally, we provide a rigorous comparison of the equilibrium thresholds under behavioral and risk neutral players in networks with power-law degree distributions.
    Date: 2017–03
  22. By: Müller, Julia; Schwieren, Christiane
    Abstract: Growing interest in using personality variables in economic research has led to the question whether personality as measured by psychology is useful to predict economic behavior. It is undoubted that personality can influence large-scale economic outcomes. Whether personality variables can also be used to understand micro-behavior in economic games is, however, less clear. We discuss the reasons for and against this assumption. In the framework of our own experiment, we test whether and which personality factors are useful in predicting behavior in the Trust Game. We can also use the Trust Game to understand how personality measures fare relatively in predicting behavior when situational constraints are strong or weak. This approach can help economists to better understand what to expect from the inclusion of personality variables in their models and experiments, and where further research might be useful and needed.
    Keywords: Personality, Big Five, Five Factor Model, Incentives, Experiment, Trust Game
    JEL: C72 C91 D03
    Date: 2017–04–05
  23. By: Guerrazzi, Marco
    Abstract: In this paper, I explore the consequences of extending the number of firms in an efficiency-wage competition framework. In this setting, I show that the effort function shape is crucial in determining key features of the model economy. Specifically, with a concave (sigmoid) effort function, the wage and the employment levels prevailing in a symmetric Nash equilibrium are, respectively, lower (higher) and higher (lower), the higher the number of competing firms. Moreover, assuming that firms adjust their wages on the basis of lagged wage bids, the adoption of a concave (sigmoid) effort function reveals that the symmetric Nash equilibrium is unstable (stable) and the speed of divergence (convergence) is an increasing function of the number of firms. Furthermore, with a concave (sigmoid) effort function the full employment equilibrium is characterized by a monopsonistic exploitation of labour that increases (decreases) with the number of productive units required to sustain that allocation. Those findings have intriguing implications for the existence of involuntary unemployment as well as for policies aimed at increasing employment.
    Keywords: Efficiency-wage competition; Number of competitors; Effort function; Nash equilibrium; Monopsonistic exploitation
    JEL: C72 E12 E24 J41
    Date: 2017–03–27
  24. By: Can, Burak (General Economics 1 (Micro)); Csóka, Péter (corvinus university of budapest); Ergin, Emre (General Economics 1 (Micro))
    Abstract: This paper analyzes how to choose a delegation, a committee to represent a society such as in a peace conference. We propose normative conditions and seek optimal, consistent, neutral and non-manipulable ways to choose a delegation. We show that a novel class of threshold rules are characterized by these criteria. The rules impose that a delegation is chosen when its combined support in the society first reaches a particular percentage of the public opinion - depending on the size of the delegation. Conversely, minority opinions that are not reflected in the delegation should always be below a threshold, which follows a geometric series.
    Keywords: aggregation rules, committee selection, conflict management, Kemeny Distance, strategy-proofness
    JEL: C70 D71
    Date: 2017–04–06

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