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on Game Theory |
| By: | Ismail M.S. (GSBE) |
| Abstract: | In this note, we introduce a new sufficient condition, called sign-quasiconcavity, on the existence of a pure equilibrium in two-person symmetric zerosum games, which generalizes both generalized ordinal potentials Monderer and Shapley, 1996 and quasiconcavity Duerschet al., 2012. |
| Keywords: | Noncooperative Games; |
| JEL: | C72 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2014035&r=gth |
| By: | Aymeric Lardon (University of Nice Sophia Antipolis, France; GREDEG CNRS) |
| Abstract: | In this article we study Bertrand oligopoly TU-games with transferable technologies under the Alpha and Beta-approaches (Aumann 1959). Although the convexity property does not always hold, we show that it is satisfied when firms' marginal costs are not too heterogeneous. Furthermore, we prove that the core of any game can be partially characterized by associating a Bertrand oligopoly TU-game derived from the most efficient technology. Such a game turns to be an efficient convex cover (Rulnick and Shapley 1997) of the original one. This result implies that the core is non-empty and contains a subset of payoff vectors with a symmetric geometric structure easy to compute. |
| Keywords: | Bertrand oligopoly TU-games, Transferable technologies, Core, Convexity property |
| JEL: | C71 D43 |
| Date: | 2014–11 |
| URL: | http://d.repec.org/n?u=RePEc:gre:wpaper:2014-33&r=gth |
| By: | Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris) |
| Abstract: | We study linear properties of TU-games, revisiting well-known issues like interaction transforms, the inverse Shapley value problem and the concept of semivalues and least square values. 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, etc.). In particular, we present a simple solution to the inverse problem in its general form: Given a linear value Φ and a game v, find all games v′ such that Φ(v) = Φ(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. We furthermore develop a general theory of allocations with a quadratic optimality criterion under linear constraints, obtaining results of Charnes et al., and Ruiz et al., and others as special cases. We prove that this class of allocations coincides exactly with the class of all linear values. |
| Keywords: | Cooperation system; cooperative game; basis; transform; inverse problem; potential; linear value; semivalue |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-00971393&r=gth |
| By: | Michele Lombardi (University of Glasgow); Yoshihara Naoki (Institute of Economic Research, Hitotsubashi University) |
| Abstract: | We study Nash implementation by natural price-quantity mechanisms in pure exchange economies with free-disposal (Saijo et al., 1996, 1999) where agents have weak/strong intrinsic preferences for honesty (Dutta and Sen, 2012). Firstly, the Walrasian rule is shown to be non-implementable where all agents have weak (but not strong) intrinsic preferences for honesty. Secondly, the class of efficient allocation rules that are implementable is identified provided that at least one agent has strong intrinsic preferences for honesty. Lastly, the Walrasian rule is shown to belong to that class. |
| Keywords: | Natural implementation, Nash equilibrium, exchange economies, intrinsic preferences for honesty. |
| JEL: | C72 D71 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:ums:papers:2014-09&r=gth |
| By: | Giménez Gómez, José M. (José Manuel); Subiza, Begoña; Peris, Josep E. |
| Abstract: | A minimum cost spanning tree (mcst) problem analyzes the way to efficiently connect individuals to a source when they are located at different places. Once the efficient tree is obtained, the question on how allocating the total cost among the involved agents defines, in a natural way, a confliicting claims situation. For instance, we may consider the endowment as the total cost of the network, whereas for each individual her claim is the maximum amount she will be allocated, that is, her connection cost to the source. Obviously, we have a confliicting claims problem, so we can apply claims rules in order to obtain an allocation of the total cost. Nevertheless, the allocation obtained by using claims rules might not satisfy some appealing properties (in particular, it does not belong to the core of the associated cooperative game). We will define other natural claims problems that appear if we analyze the maximum and minimum amount that an individual should pay in order to support the minimum cost tree. Keywords: Minimum cost spanning tree problem, Claims problem, Core JEL classification: C71, D63, D71. |
| Keywords: | Jocs cooperatius, Economia del benestar, Elecció social, 33 - Economia, |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:urv:wpaper:2072/242273&r=gth |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Peter Sudhölter (University of Southern Denmark - Department of Business and Economics and COHERE) |
| Abstract: | We generalize the characterizations of the positive core and the positive prekernel to TU games with precedence constraints and show that the positive core is characterized by non-emptiness (NE), boundedness (BOUND), covariance under strategic equivalence, closedness (CLOS), the reduced game property (RGP), the reconfirmation property (RCP) for suitably generalized Davis-Maschler reduced games, and the possibility of nondiscrimination. The bounded positive core, i.e., the union of all bounded faces of the positive core, is characterized similarly. Just RCP has to be replaced by a suitable weaker axiom, a weak version of CRGP (the converse RGP) has to be added, and CLOS can be deleted. For classical games the prenucleolus is the unique further solution that satisfies the axioms, but for games with precedence constraints it violates NE as well as the prekernel. The positive prekernel, however, is axiomatized by NE, anonymity, reasonableness, the weak RGP, CRGP, and weak unanimity for two-person games (WUTPG), and the bounded positive prekernel is axiomatized similarly by requiring WUTPG only for classical two-person games and adding BOUND. |
| Keywords: | TU games; restricted cooperation; game with precedence constraints; positive core; bounded core; positive prekernel; prenucleolus |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01020282&r=gth |
| By: | Hafalir, Isa E.; Hakimov, Rustamdjan; Kübler, Dorothea; Kurino, Morimitsu |
| Abstract: | We theoretically and experimentally study a college admissions problem in which colleges accept students by ranking students' efforts in entrance exams. Students hold private information regarding their ability level that affects the cost of their efforts. We assume that student preferences are homogeneous over colleges. By modeling college admissions as contests, we solve and compare the equilibria of "centralized college admissions" (CCA) in which students apply to all colleges, and "decentralized college admissions" (DCA) in which students can only apply to one college. We show that lower ability students prefer DCA whereas higher ability students prefer CCA. The main qualitative predictions of the theory are supported by the experimental data, yet we find a number of behavioral differences between the mechanisms that render DCA less attractive than CCA compared to the equilibrium benchmark. |
| Keywords: | college admissions,incomplete information,student welfare,contests,all-pay auctions,experiment |
| JEL: | C78 D78 I21 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbmbh:spii2014208&r=gth |
| By: | Sayantan Ghosal; Simone Tonin |
| Abstract: | In this paper, we extend the non-cooperative analysis of oligopoly to exchange economies with innitely many commodities by using strategic market games. This setting can be in- terpreted as a model of oligopoly with dierentiated commodities by using the Hotelling line. We prove the existence of an \active" Cournot-Nash equilibrium and show that, when traders are replicated, the price vector and the allocation converge to the Wal- ras equilibrium. We examine how the notion of oligopoly extends to our setting with a coutable innity of commodities by distinguishing between asymptotic oligopolists and asymptotic price-takers. We illustrate these notions via a number of examples. |
| JEL: | C72 D43 D50 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:gla:glaewp:2014_15&r=gth |
| By: | Ahmet Ozkardas (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne) |
| Abstract: | We present a non-cooperative union-firm wage bargaining model in which the union must choose between strike and holdout if a proposed wage contract is rejected. The innovative element that our model brings to the existing literature on wage bargaining, concerns the parties' preferences which are not expressed by constant discount rates, but by sequences of discount factors varying in time. First, we determine subgame perfect equilibria if the strike decision of the union is exogenous. We analyze the case when the union is committed to strike in each disagreement period, the case when the union is committed to strike only when its own offer is rejected, and the case of the never strike exogenous decision. A comparison of the results is provided, among the cases of the exogenous strike decisions. Next, we consider the general model with no assumption on the commitment to strike. We find subgame perfect equilibria in which the strategies supporting the equilibria in the exogenous cases are combined with the minimum-wage strategies, provided that the firm is not less patient than the union. If the firm is more impatient than the union, then the firm is better off by playing the no-concession strategy. We find a subgame perfect equilibrium for this case. |
| Keywords: | union - firm bargaining ; alternating offers ; varying discount rates ; subgame perfect equilibrium |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-00975533&r=gth |
| By: | Sylvain Béal (CRESE, Université de Franche-Comté); Eric Rémila (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne); Philippe Solal (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne) |
| Abstract: | In this article, we provide a new basis for the kernel of the Shapley value (Shapley, 1953), which is used to construct a new axiom of invariance, and to provide a new axiomatic characterization of the Shapley value. This characterization only invokes marginalistic principles, and does not rely on classical axioms such as symmetry, efficiency or linearity. Moreover, our approach reveals a new instructive role played by veto players. |
| Keywords: | Veto players, Addition invariance, Basis, Kernel, Shapley value. |
| JEL: | C71 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2014-03&r=gth |
| By: | Peleg B.; Peters H.J.M. (GSBE) |
| Abstract: | We show that feasible elimination procedures Peleg, 1978 can be used to select k from m alternatives. An important advantage of this method is the core property no coalition can guarantee an outcome that is preferred by all its members. We also provide an axiomatic characterization for the case k1, using the conditions of anonymity, Maskin monotonicity, and independent blocking. Finally, we show for any k that outcomes of feasible elimination procedures can be computed in polynomial time, by showing that the problem is computationally equivalent to finding a maximal matching in a bipartite graph. |
| Keywords: | Game Theory and Bargaining Theory: General; Social Choice; Clubs; Committees; Associations; |
| JEL: | C70 D71 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2014033&r=gth |
| By: | Nicolas Jacquemet (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, BETA - Bureau d'économie théorique et appliquée - CNRS : UMR7522 - Université de Strasbourg - Université Nancy II); Adam Zylbersztejn (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne) |
| Abstract: | We experimentally study an asymmetric coordination game with two Nash equilibria: one is Pareto-efficient, the other is Pareto-inefficient and involves a weakly dominated strategy. We assess whether information about the interaction partner helps eliminate the imperfect equilibrium. Our treatments involve three information-enhancing mechanisms: repetition and two kinds of individual signals: messages from partner or observation of his past choices. Repetition-based learning increases the frequencies of the most efficient outcome and the most costly strategic mismatch. Moreover, it is superseded by individual signals. Like previous empirical studies, we find that signals provide a screening of partners' intentions that reduces the frequency of coordination failures. Unlike these studies, we find that the transmission of information between partners, either via messages or observation, does not suffice to significantly increase the overall efficiency of outcomes. This happens mostly because information does not restrain the choice of the dominated action by senders. |
| Keywords: | coordination game; communication; cheap-talk; observation |
| Date: | 2013–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-00845123&r=gth |
| By: | Dechenaux, Emmanuel; Kovenock, Dan; Sheremeta, Roman |
| Abstract: | Many economic, political and social environments can be described as contests in which agents exert costly efforts while competing over the distribution of a scarce resource. These environments have been studied using Tullock contests, all-pay auctions and rank-order tournaments. This survey provides a comprehensive review of experimental research on these three canonical contests. First, we review studies investigating the basic structure of contests, including the number of players and prizes, spillovers and externalities, heterogeneity, risk and incomplete information. Second, we discuss dynamic contests and multi-battle contests. Then we review studies examining sabotage, feedback, bias, collusion, alliances, group contests and gender, as well as field experiments. Finally, we discuss applications of contests and suggest directions for future research. |
| Keywords: | contests, all-pay auctions, tournaments, experiments |
| JEL: | C7 C9 D7 H4 J4 J7 K4 L2 M5 |
| Date: | 2014–10–27 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:59714&r=gth |
| By: | Randall Martyr |
| Abstract: | This paper studies the connection between Dynkin games and optimal switching in continuous time and on a finite horizon. An auxiliary two-mode optimal switching problem is formulated which enables the derivation of the game's value under very mild assumptions. Under slightly stronger assumptions, the optimal switching formulation is used to prove the existence of a saddle point and a connection is made to the classical "Mokobodski's hypothesis". Results are illustrated by comparison to numerical solutions of three specific Dynkin games which have appeared in recent papers, including an example of a game option with payoff dependent on a jump-diffusion process. |
| Date: | 2014–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1411.4438&r=gth |
| By: | Ralph-C. Bayer (School of Economics, University of Adelaide) |
| Abstract: | This paper develops a quantal-response adaptive learning model which combines sellers’ bounded rationality with adaptive belief learning in order to explain price dispersion and dynamics in laboratory Bertrand markets with perfect information. In the model, sellers hold beliefs about their opponents’ strategies and play quantal best responses to these beliefs. After each period, sellers update their beliefs based on the information learned from previous play. Maximum likelihood estimation suggests that when sellers have full past price information, the learning model explains price dispersion within periods and the dynamics across periods. The fit is particularly good if one allows for sellers being risk averse. In contrast, Quantal Response Equilibrium does not organize the data well. |
| Keywords: | Price dispersion, Adaptive Learning, Bounded rationality, Quantal Response Equilibrium. |
| JEL: | C73 C91 D83 L13 |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2013-16&r=gth |
| By: | Gächter, Simon (University of Nottingham); Renner, Elke (University of Nottingham) |
| Abstract: | We investigate the link between leadership, beliefs and pro-social behavior. This link is interesting because field evidence suggests that people's behavior in domains like charitable giving, tax evasion, corporate culture and corruption is influenced by leaders (CEOs, politicians) and beliefs about others' behavior. Our framework is an experimental public goods game with a leader. We find that leaders strongly shape their followers' initial beliefs and contributions. In later rounds, followers put more weight on other followers' past behavior than on the leader's current action. This creates a path dependency the leader can hardly correct. We discuss the implications for understanding belief effects in naturally occurring situations. |
| Keywords: | leadership, beliefs, experiments, public goods, path dependency, public policy, management |
| JEL: | C72 C90 H41 Z13 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp8580&r=gth |
| By: | Ralph-C. Bayer (School of Economics, University of Adelaide) |
| Abstract: | This paper studies the effects of increasing the number of sellers on Quantal Response Equilibrium (QRE) prices in homogeneous product Bertrand oligopoly markets. We show that the two most commonly used choice functions (power and logistic) lead to qualitatively different comparative-static predictions with respect to the relationship between number of firms and prices. |
| Keywords: | Bertrand Oligopoly, Quantal Response Equilibrium, Comparative Statics |
| JEL: | C73 D83 L13 |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2013-15&r=gth |