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on Game Theory |
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Issue of 2011‒07‒27
seventeen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Dieter Balkenborg; Josef Hofbauer; Christoph Kuzmics (Institute of Mathematical Economics, Bielefeld University) |
| Abstract: | We call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it has (1) a product structure, is (2) upper semi-continuous, (3) always includes a best reply to any mixed strategy profile, and is (4) convex- and closed-valued. For each generalized best reply correspondence we define a generalized best reply dynamics as a differential inclusion based on it. We call a face of the set of mixed strategy profiles a minimally asymptotically stable face (MASF) if it is asymptotically stable under some such dynamics and no subface of it is asymptotically stable under any such dynamics. The set of such correspondences (and dynamics) is endowed with the partial order of point-wise set-inclusion and, under a mild condition on the normal form of the game at hand, forms a complete lattice with meets based on point-wise intersections. The refined best reply correspondence is then defined as the smallest element of the set of all generalized best reply correspondences. We ultimately find that every Kalai and Samet's (1984) persistent retract, which coincide with Basu and Weibull's (1991) CURB sets based, however, on the refined best reply correspondence, contains a MASF. Conversely, every MASF must be a Voorneveld's (2004) prep set, again, however, based on the refined best reply correspondence.. |
| Keywords: | Evolutionary game theory, best response dynamics, CURB sets, persistent retracts, asymptotic stability, Nash equilibrium refinements, learning |
| JEL: | C62 C72 C73 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:451&r=gth |
| By: | Messaoud Deghdak (Laboratoire de Mathématiques Appliquées et Modélisation - Université de Mentouri); Monique Florenzano (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional strategy spaces in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berge's strong equilibrium correspondence and prove that most of Berge's strong games are essential. |
| Keywords: | Nash equilibrium, strong Berge equilibrium, fixed point, essential games. |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:11039&r=gth |
| By: | David Csercsik (Process Control Research Group - Computer and Automation Institute, Hungarian Academy of Sciences); Laszlo A. Koczy (Institute of Economics - Hungarian Academy of Sciences) |
| Abstract: | An electrical transmission network consists of producers, consumers and the power lines connecting them. We build an ideal (lossless) DC load flow model as a cooperative game over a graph with the producers and consumers located at the nodes, each described by a maximum supply or desired demand and the power lines represented by the edges, each with a given power transmission capacity and admittance value describing its ability to transmit electricity. Today's transmission networks are highly interconnected, but organisationally partitioned into several subnetworks, the so-called balancing groups with balanced production and consumption. We study the game of balancing group formation and show that the game contains widespread externalities that can be both negative and positive. We study the stability of the transportation network using the recursive core. While the game is clearly cohesive, we demonstrate that it is not necessarily superadditive. We argue that subadditivity may be a barrier to achieve full cooperation. Finally the model is extended to allow for the extension of the underlying transmission network. |
| Keywords: | Energy transmission networks, Cooperative game theory, Partition function form games, Externalities |
| JEL: | C71 L14 L94 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1125&r=gth |
| By: | Omer Biran (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX) |
| Abstract: | We consider a second price auction between bidders with independently and identically distributed valuations, where a losing bidder suffers a negative direct externality. Considering ex-ante commitments to form bidding rings we study the question of core stability of the grand coalition, namely: is there a subset of bidders that prefers forming a small bidding ring rather than participating in the grand cartel? We show that in the presence of direct externalities between bidders the grand coalition is not necessarily core stable, as opposed to the zero externality case, where the stability of the grand coalition is a known result. Finally, we study collusion in auctions as a mechanism design problem, insisting on the difficulty to compare ex-ante and interim commitments. In particular, we show that there are situations in which bidders prefer colluding before privately learning their types. |
| Keywords: | Auctions;collusion;externalities;Bayesian games;core; partition function game;mechanism design |
| Date: | 2011–07–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00608008&r=gth |
| By: | Jean-François Laslier (Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X); Bernard Walliser (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris) |
| Abstract: | The paper studies a specific reinforcement learning rule in two-player games when each player faces a unidimensional strategy set. The essential feature of the rule is that a player keeps on incrementing her strategy in the same direction if and only if her utility increases. The paper concentrates on games on the square [0; 1] x [0; 1] with bilinear payoff functions such as the mixed extensions of 2 x 2 games. It studies the behavior of the system in the interior as well as on the borders of the strategy space. It precisely exhibits the trajectories of the system and the asymptotic states for symmetric, zero-sum, and twin games. |
| Date: | 2011–07–19 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00609501&r=gth |
| By: | Olivier l’Haridon (Greg-HEC, Institut Universitaire de France and University Paris Sorbonne.); Franck Malherbet (Université de Rouen, CECO – Ecole Polytechnique, IZA and fRDB.); Sébastien Pérez-Duarte (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany.) |
| Abstract: | In this article, we use a stylized model of the labor market to investigate the effects of three alternative and well-known bargaining solutions. We apply the Nash, the Egalitarian and the Kalai-Smorodinsky bargaining solutions in the small firm's matching model of unemployment. To the best of our knowledge, this is the first attempt to implement and systematically compare these solutions in search-matching economies. Our results are twofold. First from the theoretical and methodological viewpoint, we extend a somewhat flexible search-matching economy to alternative bargaining solutions. In particular, we prove that the Egalitarian and the Kalai-Smorodinsky solutions are easily implementable within search-matching economies. Second, our results show that even though the traditional results of bargaining theory apply in this context, they are generally qualitatively different from the standard results, and the differences are quantitatively weaker than expected. This is of particular relevance in comparison with the results established in the earlier literature. JEL Classification: C71, C78, J20, J60. |
| Keywords: | Search and matching models, Bargaining theory, Nash, Egalitarian, Kalai-Smorodinsky. |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20111359&r=gth |
| By: | Xu, Yongsheng; Yoshihara, Naoki |
| Abstract: | This paper studies the Nash solution to nonconvex bargaining problems. The Nash solution in such a context is typically multi-valued. We introduce a procedure to exclude some options recommended by the Nash solution. The procedure is based on the idea of the Kalai-Smorodinsky solution which has the same informational requirement on individual utilities as the Nash solution does and has an equity consideration as well. We then use this procedure to introduce two new solutions to nonconvex bargaining problems and study them axiomatically. |
| JEL: | C71 C78 D6 D7 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:hit:ccesdp:42&r=gth |
| By: | Dora Balog (Department of Finance Corvinus University of Budapest) |
| Abstract: | Capital allocation is used for many purposes in financial institutions and for this purpose several methods are known. The aim of this paper is to review possible methods (we present six of them) and to help financial companies to choose between the methods. There are some properties that an allocation method should satisfy: full allocation, core compatibility, riskless allocation, symmetry and suitability for performance measurement (compatibility with Return on Risk Adjusted Capital calculation). If we think about practical application we should also consider simplicity of the methods. First we examine the methods from the point of view if they are satisfying core compatibility. We test this with simulation where we add to the existing literature that we test core compatibility with different assumptions on returns: on normal and t-distributed returns and also on returns generated from a copula. We find that if we measure risk by a coherent risk measure, the Expected Shortfall there are two methods satisfying core compatibility: the Euler method (that always fulfills the criteria) and cost gap method (obeys it around in about 99%). As Euler method is very easy to calculate even for many players while cost gap method becomes very complicated as the number of the players increases we examine further the properties of Euler method. We find that it fulfills all the above given criteria but symmetry and as aforementioned it is also very easy to calculate. Therefore we believe that the method might be suggested for practical applications. |
| Keywords: | Capital Allocation, Coherent Measures of Risk, Core, Simulation |
| JEL: | C60 C70 G20 |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1126&r=gth |
| By: | Pierre Cardaliaguet (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX); Rida Laraki (Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X); Sylvain Sorin (Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X, Université Pierre et Marie curie - Combinatoire et Optimisation IMJ, CNRS 7586) |
| Abstract: | We consider the asymptotic value of two person zero sum repeated games with general evaluations of the stream of stage payoffs. We show existence for incomplete information games, splitting games and absorbing games. The technique of proof consists in embedding the discrete repeated game into a continuous time one and to use viscosity solution tools. |
| Date: | 2011–07–19 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00609476&r=gth |
| By: | Ron Peretz |
| Abstract: | Two agents independently choose mixed m-recall strategies that take actions in finite action spaces A1 and A2. The strategies induce a random play, a1,a2,..., where at assumes values in A1 X A2. An M-recall observer observes the play. The goal of the agents is to make the observer believe that the play is similar to a sequence of i.i.d. random actions whose distribution is Q \in \Delta(A1 X A2). For nearly every t, the following event should occur with probability close to one: "the distribution of a_{t+M} given at a_t,..,a_{t+M} is close to Q." We provide a sufficient and necessary condition on m, M, and Q under which this goal can be achieved (for large m). This work is a step in the direction of establishing a folk theorem for repeated games with bounded recall. It tries to tackle the difficulty in computing the individually rational levels (IRL) in the bounded recall setting. Our result implies, for example, that in some games the IRL in the bounded recall game is bounded away below the IRL in the stage game, even when all the players have the same recall capacity. |
| Date: | 2011–07–21 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp579&r=gth |
| By: | Vranceanu, Radu (ESSEC Business School); Besancenot, Damien (Université Paris 13) |
| Abstract: | This paper brings experimental evidence on investors’ behavior subject to an "illiquidity" constraint, where the success of a risky project depends on the participation of a minimum number of investors. The experiment is set up as a frameless coordination game that replicates the investment context. Results confirm the insidious nature of the illiquidity risk: as long as a first illiquidity default does not occur, investors do not seem able to fully internalize it. After several defaults, agents manage to coordinate on a default probability above which they refuse to participate to the project. This default probability is lower than the default probability of the first illiquidity default. |
| Keywords: | Coordination game; Illiquidity risk; Threshold strategy; Experimental economics |
| JEL: | C72 C92 D81 G20 |
| Date: | 2011–07–13 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:essewp:dr-11007&r=gth |
| By: | Nicolas Jacquemet (Centre d'Economie de la Sorbonne - Paris School of Economics); Adam Zylbersztejn (Centre d'Economie de la Sorbonne) |
| Abstract: | In experiments based on the Beard and Beil (1994) game, second movers very often fail to select the decision that maximizes both players payoff. This note reports on a new experimental treatment, in which we neutralize the potential effect of inequality aversion on the likelihood of this behavior. We show this behavior is robust to this change, even after allowing for repetition-based learning. |
| Keywords: | Coordination failure, laboratory experiments, aversion to inequality. |
| JEL: | C72 D83 |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:11036&r=gth |
| By: | Toke Fosgaard (Institute of Food and Resource Economics, University of Copenhagen); Lars Gårn Hansen (Institute of Food and Resource Economics, University of Copenhagen); Erik Wengström (Department of Economics, University of Lund; Department of Economics, University of Copenhagen) |
| Abstract: | Earlier studies have found that a substantial part of the contributions in public good games can be explained by subjects misperceiving the game's incentives. Using a large-scale public good experiment, we show that subtle changes in how the game is framed substantially affect such misperceptions and that this explains major parts of framing effect on subjects' behavior. When controlling for the different levels of misperception between frames, the framing effect on subjects' cooperation preferences disappears. This suggests that merely changing how tax-, fine- or subsidy systems are framed, without reducing complexity, could reduce welfare loss from misperception of incentives. |
| Keywords: | Public goods, Cooperation, Misperception, Game form recognition, Framing effects, Internet experiment |
| JEL: | C90 H41 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:foi:wpaper:2011_11&r=gth |
| By: | Sophie Bade (Max Planck Institute for Research on Collective Goods, Bonn) |
| Abstract: | A version of the Second Fundamental Theorem of Welfare Economics that applies to a money-free environment, in which a set of indivisible goods needs to be matched to some set of agents, is established. In such environments, "trade" can be identied with the set of hierarchical exchange mechanisms dened by Papai (2000). Papai (2000)'s result – that any such mechanism yields Pareto-optimal allocations – can be interpreted as a version of the First Fundamental Theorem of Welfare Economics for the given environment. In this note, I show that for any Pareto-optimal allocation and any hierarchical exchange mechanism one can nd an initial allocation of ownership rights, such that the given Pareto-optimal allocation arises as a result of trade. |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:mpg:wpaper:2011_11&r=gth |
| By: | Girard, Victoire |
| Abstract: | We study the impact of inter-group relationships, with inter-group distance, on intra-group cooperation behavior for Indian rural households. This is an application to a real world case of some experimental results of the identity economics literature. This literature offers insight of channels through which inter-group relationships affect in-group actions, with identification to the in-group, and the resulting norm enforcement behavior. We proxy distance with differences of returns to attributes to one traditionally low status group (the Scheduled Castes, SC, standing for traditionally so-called untouchables), compared to the rest of the population (reference group). We then study the effect of this distance variable on in-group cooperation. In our data set, a cooperative behavior corresponds to the involvement in a collective action for water supply. Inter-group relationships appear to have the expected effect on intra-group cooperation for SC and households: the worst inter-group relationships, the more intra-group cooperation. -- |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:gdec11:32&r=gth |
| By: | Jouini, Elyès; Napp, Clotilde |
| Abstract: | In this paper, we show that behavioral features can be obtained at a group level when the individuals of the group are heterogeneous enough. More precisely, starting from a standard model of Pareto optimal allocations, with expected utility maximizers and exponential dis- counting, but allowing for heterogeneity among agentsíbeliefs and time preference rates, we show that the representative agent exhibits interesting behavioral properties. In particular, we obtain an inverse S-shaped probability distribution weighting function and hyperbolic discounting. We provide possible interpretation as well as applications for this result. |
| Keywords: | Hyperbolic Discounting; Behavioral Agent; Neurofinance; Representative Agent; Probability Weighting Function; |
| JEL: | D87 H43 D84 D81 G11 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ner:dauphi:urn:hdl:123456789/2319&r=gth |
| By: | Besancenot, Damien (Université paris 13); Huynh, Kim (Université Paris 2); Vranceanu, Radu (ESSEC Business School) |
| Abstract: | This paper provides a dynamic analysis of the market for academic publications. Given imperfect information about journals’editorial line, authors can sometimes target a wrong journal; in turn, the editor will desk-reject their paper. An equilibrium is de…ned as a situation where both editors and authors implement their optimal publication strategies, given the matching technology and the prevailing surplus sharing rule. The model can be solved for the equilibrium submission fee, desk rejection rate and ratio between the number of editors and the number of authors. |
| Keywords: | Academic journals; Desk-rejection; Publishing; Matching; Imperfect information |
| JEL: | A14 C78 |
| Date: | 2011–07–13 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:essewp:dr-11004&r=gth |