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on Game Theory |
| By: | Mikel Álvarez-Mozos (Universitat de Barcelona, Spain); René van den Brink (VU University Amsterdam, the Netherlands); Gerard van der Laan (VU University Amsterdam, the Netherlands); Oriol Tejada (ETH Zürich, Switzerland) |
| Abstract: | Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict players’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties that relate a player’s payoff to the payoffs of other players located in specific positions in the structure relative to that player. To define each of these solutions, we consider a certain mapping that transforms any hierarchical structure into a levels structure, and then we apply the standard generalization of the Shapley Value to the class of games with levels structure. The transformations that map the set of hierarchical structures to the set of levels structures are also studied from an axiomatic viewpoint by means of properties that relate a player’s position in both types of structure. |
| Keywords: | TU-game; hierarchical structure; levels structure; Shapley Value; axiomatization |
| JEL: | C71 |
| Date: | 2015–06–02 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150072&r=gth |
| By: | Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | We study linear properties of TU-games, revisiting well-known issues like interaction transforms, the inverse Shapley value problem and potentials. We embed TU-games into the model of cooperation systems and influence patterns, which allows us to introduce linear operators on games in a natural way. We focus on transforms, which are linear invertible maps, relate them to bases and investigate many examples (Möbius transform, interaction transform, Walsh transform and Fourier analysis etc.). In particular, we present a simple solution to the inverse problem in its general form: Given a linear value ? and a game v, find all games v' such that ?(v) = ?(v' ). Generalizing Hart and Mas-Colell's concept of a potential, we introduce general potentials and show that every linear value is induced by an appropriate potential |
| Keywords: | Cooperation system; cooperative game; basis; Fourier analysis; inverse problem; potential; transform |
| JEL: | C71 |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:14010r&r=gth |
| By: | Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | The problem of least square approximation for set functions by set functions satisfying specified linear equality or inequality constraints is considered. The problem has important applications in the field of pseudo-Boolean functions, decision making and in cooperative game theory, where approximation by additive set functions yields so-called least square values. In fact, it is seem that every linear value for cooperative games arises from least square approximation. We provide a general approach and problem overview. In particular, we derive explicit formulas for solutions under mild constraints, which include and extend previous results in the literature |
| Keywords: | least square approximation; cooperative game; pseudo-Boolean function; least square value; Shapley value; probabilistic value |
| JEL: | C71 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:15047&r=gth |
| By: | van den Brink, R.; van der Laan, G.; Herings, P.J.J. (Tilburg University, School of Economics and Management); Talman, Dolf (Tilburg University, School of Economics and Management) |
| Abstract: | In the literature, various models of games with restricted cooperation can be found. In those models, instead of allowing for all subsets of the set of players to form, it is assumed that the set of feasible coalitions is a subset of the power set of the set of players. In this paper, we consider such sets of feasible coalitions that follow from a permission structure on the set of players, in which players need permission to cooperate with other players.We assume the permission structure to be an oriented tree. This means that there is one player at the top of the permission structure, and for every other player, there is a unique directed path from the top player to this player.<br/>We introduce a new solution for these games based on the idea of the Average Tree value for cycle-free communication graph games.We provide two axiomatizations for this new value and compare it with the conjunctive permission value. |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiutis:97042492-4b03-4e72-b88d-dc79f80e3e0b&r=gth |
| By: | Metzger, Lars P. |
| Abstract: | This paper studies a contest in which players with unobservable types may form an alliance in a pre-stage of the game to join their forces and compete for a prize. We characterize the pure strategy equilibria of this game of incomplete information. We show that if the formation of an alliance is voluntary, players do not reveal private information in the process of alliance formation in any equilibrium. In this case there exists a pooling equilibrium without alliances with a unique effort choice in the contest and there exist equilibria in which all types prefer to form an alliance. If the formation of an alliance can be enforced by one player with positive probability there exists an equilibrium in which only the low types prefer to form an alliance. |
| Abstract: | Der vorliegende Aufsatz untersucht ein Modell, in welchem Agenten mit unbeobachtbaren Typen ihre Kräfte in Allianzen vereinen können, bevor sie in einen Wettstreit um eine Ressource eintreten. Wir beschreiben die Gleichgewichte in reinen Strategien dieses Spiels unter unvollständiger Information. Für den Fall des freiwilligen Eintritts in eine Allianz zeigen wir, dass die Spieler in keinem Gleichgewicht private Information während der Bildung der Allianz offenbaren. In diesem Fall existiert ein vereinigendes Gleichgewicht ohne Allianz, in dem die Spieler eine eindeutige, typen-abhängige Investition im Wettstreit wählen. Es existieren auch vereinigende Gleichgewichte, in welchen es alle Spieler-Typen strikt bevorzugen, in eine Allianz einzutreten. Falls eine Allianz seitens eines Spielers mit positiver Wahrscheinlichkeit erzwungen werden kann, existiert ein trennendes Gleichgewicht, in welchem nur die schwachen Spieler-Typen in die Allianz eintreten wollen. |
| Keywords: | alliance formation,contest,incomplete information,free-riding,signalling |
| JEL: | C72 D72 D74 D82 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:rwirep:544&r=gth |
| By: | Aaron Kamm (Faculty of Economics and Business, University of Amsterdam, the Netherlands); Harold Houba (Faculty of Economics and Business Administration, VU University Amsterdam, the Netherlands) |
| Abstract: | This paper reports results from a laboratory experiment studying the role of asymmetries, both in payoffs and recognition probabilities, in a model of strategic bargaining with Condorcet cycles. Overall, we find only limited support for the equilibrium predictions. The main deviations from theory are: a) Subjects under-exploit their bargaining power by being more accommodating in their acceptance decision than predicted; b) subjects’ change in behavior in reaction to asymmetric recognition probabilities exhibits systematic deviations from theory. This suggests that subjects do not fully grasp the subtle effects asymmetries have on bargaining power, especially when the asymmetries relate to recognition probabilities. |
| Keywords: | Bargaining; Condorcet Paradox; Experiments; Voting; Committees |
| JEL: | C73 C78 C91 C92 D72 |
| Date: | 2015–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150071&r=gth |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | The paper studies the vector space of set functions on a finite set X, which can be alternatively seen as pseudo-Boolean functions, and including as a special cases games. We present several bases (unanimity games, Walsh and parity functions) and make an emphasis on the Fourier transform. Then we establish the basic duality between bases and invertible linear transform (e.g., the Möbius transform, the Fourier transform and interaction transforms). We apply it to solve the well-known inverse problem in cooperative game theory (find all games with same Shapley value), and to find various equivalent expressions of the Choquet integral |
| Keywords: | set function; basis; Walsh function; Fourier transform; game |
| JEL: | C71 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:15048&r=gth |
| By: | Franke, Jörg; Leininger, Wolfgang; Wasser, Cédric |
| Abstract: | We characterize revenue maximizing head starts for all-pay auctions and lottery contests with many heterogeneous players. We show that under optimal head starts all-pay auctions revenue-dominate lottery contests for any degree of heterogeneity among players. Moreover, all-pay auctions with optimal head starts induce higher revenue than any multiplicatively biased all-pay auction or lottery contest. While head starts are more effective than multiplicative biases in all-pay auctions, they are less effective than multiplicative biases in lottery contests. |
| Abstract: | Wir charakterisieren die erlösmaximierende Gewährung eines "Vorsprungs" für heterogene Spieler in All-Pay Auktionen und stochastischen Wettstreiten. Wir zeigen, dass der optimale Gebrauch von Vorteilsgewährung durch Einräumen eines Vorsprungs in All-Pay Auktionen immer; d.h. für jeden Grad von Heterogenität unter den Wettstreitern zu höheren Erlösen führt als bei stochastischen Wettstreiten. Darüber hinaus ist Vorsprungsgewährung in All-Pay Auktionen ein effektiveres Mittel zur Erlösmaximierung als das multiplikative Gewichten von Einsätzen. Optimale Vorsprungsgewährung führt in All-Pay Auktionen zu höheren Erlösen als optimales Gewichten, in stochastischen Wettstreiten ist es jedoch umgekehrt. |
| Keywords: | all-pay auction,lottery contest,head start,revenue dominance |
| JEL: | C72 D72 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:rwirep:524&r=gth |
| By: | Leininger, Wolfgang; Moghadam, Hamed M. |
| Abstract: | It is a very well-known result that in terms of evolutionary stability the long-run outcome of a Cournot oligopoly market with finitely many firms approaches the perfectly competitive Walrasian market outcome (Vega-Redondo, 1997). However, in this paper we show that an asymmetric structure in the cost functions of firms may change the long-run outcome. Contrary to Tanaka (1999) we show that the evolutionarily stable price in an asymmetric Cournot oligopoly needs not equal the marginal cost, it may rather equal a weighted average of (different) marginal cost. We apply a symmetrization technique in order to transform the game with asymmetric firms into a symmetric oligopoly game and then extend Schaffer's definition (1988) of a finite population ESS (FPESS) to this setup. Moreover, we show that the FPESS in this game represents a stochastically stable state of an evolutionary process of imitation with experimentation. |
| Abstract: | Einem bekannten und überraschenden Result zufolge ist das langfristige evolutionäre Gleichgewicht in einem endlichen Cournot-Opligopol durch die Allokation des vollkommenen Wettbewerbsgleichgewichts nach Walras (und nicht die des klassischen Cournot-Gleichgewichts) gekennzeichnet (Vega-Redondo, 1997). Diese Arbeit zeigt, dass dies nicht mehr zutrifft, wenn sich die Firmen asymmetrisch durch unterschiedliche Kostenfunktionen unterscheiden. Das Ergebnis wird durch die Analyse einer symmetrisierten Version des ursprünglich asymmetrischen Spiels erzeugt, in der das Lösungskonzept einer evolutionär stabilen Strategie für endliche Populationen (Schaffer, 1988) für diesen Modellrahmen adaptiert wird. Das Ergebnis widerspricht insbesondere einem Resultat von Tanaka (1999), der das "marginal cost pricing"-Resultat von Vega-Redondo für symmetrische Firmen auch auf einen asymmetrischen Fall übertragen hatte. Die vorliegende Arbeit kritisiert dessen Modell und sein Ergebnis und weist ein "average cost pricing"-Resultat als evolutionär stabile Oligopollösung nach. |
| Keywords: | Cournot oligopoly,asymmetry,finite population evolutionary stable strategy,stochastic stability |
| JEL: | C72 C73 D43 L13 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:rwirep:497&r=gth |
| By: | Wei Ma |
| Abstract: | This paper addresses the issue of how a given piece of information should be transmitted from a better-informed doctor to an ill-informed patient. The information to be transmitted is expressed as a probability distribution on a space of the patient’s possible health states. For a formal analysis of the issue we develop a two-person dynamic game, in which the doctor sends a sequence of messages to the patient to inform him of his health state, and the patient, after receiving each message, chooses an action in an attempt to improve upon his current health status. We study some standard properties of the equilibria of this game; in particular, we show that it has a subgame perfect equilibrium. |
| Keywords: | Information transmission, Dynamic game theory, Subgame perfect equilibrium |
| JEL: | D73 D83 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:rza:wpaper:519&r=gth |
| By: | Mido Chang (Florida International University); Sunha Kim (State University of New York at Buffalo); Namok Choi (University of Louisville) |
| Abstract: | The main purpose of the study was to examine the effects of student’s gaming behaviors and perceptions of games on the engagement in the mathematics classrooms. For the study, the research team recruited 299 sixth grade students from two schools located in rural areas of Virginia in the United States and collected data. For the analytical tool, we employed Structural Equation Modeling (SEM) to examine the relationship of gaming behaviors with the engagement mediated by perceptions of instructional games. We found that student’s mathematics engagement was associated with student’s perceptions of games and gaming behaviors. The game hours drew a significant path to student’s perceptions of game learning while the game frequencies had a significant path to student’s perceptions of game utility. The student’s perceptions made significant paths to mathematics engagement. This study provided empirical information on student’s mathematics engagement connecting student’s perceptions of game learning and games utility. |
| Keywords: | instructional games, gaming behavior, perception of gaming, engagement, middle grades |
| JEL: | I21 O39 |
| URL: | http://d.repec.org/n?u=RePEc:sek:itepro:2404065&r=gth |
| By: | Heike Hennig-Schmidt (University of Bonn); Gari Walkowitz (University of Cologne) |
| Abstract: | This paper aims to better understand negotiation behaviour between Germans and Chinese. We study intra- and inter-cultural bargaining in negotiations with asymmetric outside options. Our analysis is based on team decisions and verbal transcripts of video-recorded within- and between-team discussions. The data show the importance of aspiration formation in combination with equity concerns. Before the negotiation starts, all teams already have formulated goals that can be traced during the subsequent negotiation. Moreover, all first offers and demands and the majority of final outcomes represent equitable shares of the amount at stake. Teams often agree upon the 'Split the Difference' allocation, which represents a feasible and justifiable compromise. Chinese typically gather as much information on their counterparts as possible, anticipate and simulate their counterparts' behavior and make harmony an issue. German teams, however, put great emphasis on fairness issues and aim at efficient outcomes by reaching an acceptable payoff within reasonable time. |
| Keywords: | Bargaining, Negotiation, Culture, Aspirations, Equity, Experiment |
| JEL: | C7 F51 C92 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:cgr:cgsser:06-01&r=gth |