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on Game Theory |
| By: | Francisco Robles (Facultat d'Economia i Empresa; Universitat de Barcelona (UB)); Marina Núñez (Facultat d'Economia i Empresa; Universitat de Barcelona (UB)) |
| Abstract: | We consider one-seller assignment markets with multi-unit demands and prove that the associated game is buyers-submodular. Therefore the core is non-empty and it has a lattice structure which contains the allocation where every buyer receives his marginal contribution. We prove that in this kind of market, every pairwise-stable outcome is associated to a competitive equilibrium and vice versa. We study conditions under which the buyers-optimal and the seller-optimal core allocations are competitive equilibrium payoff vectors. Moreover, we characterize the markets for which the core coincidences with the set of competitive equilibria payoff vectors. When agents behave strategically, we introduce a procedure that implements the buyers-optimal core allocation as the unique subgame perfect Nash equilibrium outcome. |
| Keywords: | Many-to-many assignment markets, Core, Pairwise-stability, Competitive equilibrium. |
| JEL: | C71 C78 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:ewp:wpaper:316web&r=gth |
| By: | Csóka, Péter; Pintér, Miklós |
| Abstract: | Measuring and allocating risk properly are crucial for performance evaluation and internal capital allocation of portfolios held by banks, insurance companies, investment funds and other entities subject to financial risk. We show that by using coherent measures of risk it is impossible to allocate risk satisfying simultaneously the natural requirements of Core Compatibility, Equal Treatment Property and Strong Monotonicity. To obtain the result we characterize the Shapley value on the class of totally balanced games and also on the class of exact games. |
| Keywords: | Coherent Measures of Risk, Risk Allocation Games, Totally Balanced Games, Exact Games, Shapley value, Core |
| JEL: | C71 G10 |
| Date: | 2014–07–23 |
| URL: | http://d.repec.org/n?u=RePEc:cvh:coecwp:2014/12&r=gth |
| By: | Balog, Dóra; Bátyi, Tamás László; Csóka, Péter; Pintér, Miklós |
| Abstract: | In finance risk capital allocation raises important questions both from theoretical and practical points of view. How to share risk of a portfolio among its subportfolios? How to reserve capital in order to hedge existing risk and how to assign this to different business units? We use an axiomatic approach to examine risk capital allocation, that is we call for fundamental properties of the methods. Our starting point is Csóka and Pintér (2011) who show by generalizing Young (1985)'s axiomatization of the Shapley value that the requirements of Core Compatibility, Equal Treatment Property and Strong Monotonicity are irreconcilable given that risk is quantified by a coherent measure of risk. In this paper we look at these requirements using analytic and simulations tools. We examine allocation methods used in practice and also ones which are theoretically interesting. Our main result is that the problem raised by Csóka and Pintér (2011) is indeed relevant in practical applications, that is it is not only a theoretical problem. We also believe that through the characterizations of the examined methods our paper can serve as a useful guide for practitioners. |
| Keywords: | Coherent Measures of Risk, Risk Capital Allocation, Shapley value, Core, Simulation |
| JEL: | C71 G10 |
| Date: | 2014–07–23 |
| URL: | http://d.repec.org/n?u=RePEc:cvh:coecwp:2014/13&r=gth |
| By: | Salvador Barberà; Dolors Berga; Bernardo Moreno |
| Abstract: | We observe that three salient solutions to matching, division and house allocation problems are not only (partially) strategy-proof, but (partially) group strategy-proof as well, in appropriate domains of definition. That is the case for the Gale-Shapley mechanism, the uniform rule and the top trading cycle solution, respectively. We embed these three types of problems into a general framework. We then notice that the three rules, as well as many others, do share a common set of properties, which together imply their (partial) group strategy-proofness. This proves that the equivalence between individual and group strategy-proofness in all these cases is not a fortuitous event, but results from the structure of the functions under consideration. |
| Keywords: | matching, division, house allocation, strategy-proofness, group strategy-proofness, group monotonicity, non-bossiness |
| JEL: | C78 D71 D78 |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:773&r=gth |
| By: | Gaurab Aryal; Ronald Stauber |
| Abstract: | Kuhn's Theorem shows that extensive games with perfect recall can equivalently be analyzed using mixed or behavioral strategies, as long as players are expected utility maximizers. This note constructs an example that illustrate the limits of Kuhn's Theorem in an environment with ambiguity averse players who use maxmin decision rule and full Bayesian updating. |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1408.1022&r=gth |
| By: | Pintér, Miklós |
| Abstract: | Meier (2012) gave a "mathematical logic foundation" of the purely measurable universal type space (Heifetz and Samet, 1998). The mathematical logic foundation, however, discloses an inconsistency in the type space literature: a finitary language is used for the belief hierarchies and an infinitary language is used for the beliefs. In this paper we propose an epistemic model to fix the inconsistency above. We show that in this new model the universal knowledgebelief space exists, is complete and encompasses all belief hierarchies. Moreover, by examples we demonstrate that in this model the players can agree to disagree Aumann (1976)'s result does not hold, and Aumann and Brandenburger (1995)'s conditions are not sufficient for Nash equilibrium. However, we show that if we substitute selfevidence (Osborne and Rubinstein, 1994) for common knowledge, then we get at that both Aumann (1976)'s and Aumann and Brandenburger (1995)'s results hold. |
| Keywords: | Incomplete information game, Agreeing to disagree, Nash equilibrium, Epistemic game theory, Knowledge-belief space, Belief hierarchy, Common knowledge, Self-evidence, Nash equilibrium |
| JEL: | C70 C72 D80 D82 D83 |
| Date: | 2014–04–18 |
| URL: | http://d.repec.org/n?u=RePEc:cvh:coecwp:2014/02&r=gth |
| By: | Schotter, Andrew; Trevino, Isabel |
| Abstract: | This paper investigates the usefulness of non-choice data, namely response times, as a predictor of threshold behavior in a simple global game experiment. Our results indicate that the signal associated to the highest or second highest response time at the beginning of the experiment are both unbiased estimates of the threshold employed by subjects at the end of the experiment. This predictive ability is lost when we move to the third or higher response times. Moreover, the response time predictions are better predictors of observed behavior than the equilibrium predictions of the game. They are also robust, in the sense that they characterize behavior in an out-of-treatment exercise where we use the strategy method to elicit thresholds. This paper is the first to point out the predictive power of response times in a strategic situation. -- |
| Keywords: | response time,threshold strategies,global games |
| JEL: | C71 C9 D03 D89 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbeoc:spii2014305&r=gth |
| By: | Puppe, Clemens; Tasnádi, Attila |
| Abstract: | In a framework with two parties, deterministic voter preferences and a type of geographical constraints, we propose a set of simple axioms and show that they jointly characterize the districting rule that maximizes the number of districts one party can win, given the distribution of individual votes (the "optimal gerrymandering rule"). As a corollary, we obtain that no districting rule can satisfy our axioms and treat parties symmetrically. |
| Keywords: | districting, gerrymandering |
| JEL: | D72 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:cvh:coecwp:2014/01&r=gth |
| By: | Shachat, Jason; Geng, Sen; Peng, Yujia; Zhong, Huizhen |
| Abstract: | We conduct experiments with adolescent participants on repeated fixed play in three different zero-sum games which have mixed strategy minimax solutions. Further, we collect subject information on cognitive abilities and participation rates in competitive activities. We find the adolescents' correspondences with and deviations from minimax play largely consistent with previously and widely studied adult populations. Further, we find strategic sophistication in terms of implementation of the mixed minimax strategy as well as earnings are not correlated with cognitive ability nor previous experience in competitive situations. |
| Keywords: | Minimax; experimental game; adolescent; cognitive abilities |
| JEL: | C72 C93 D03 |
| Date: | 2014–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:57710&r=gth |
| By: | Ramon Jesus Flores Diaz; Elisenda Molina Ferragut; Juan Tejada |
| Abstract: | This paper is centered in the valuation of the centrality of groups following aproblem-specific approach (Friedkin, 1991). Assuming a TU-game that reflects theinterests which motivate the interactions among individuals in a network, we extend thegame theoretic centrality measure of Gomez et al. (2003) to the case of groups, anddefine the game theoretic group centrality of a group as the variation of its value orpower due to their social relations. We rely on the Shapley group value (Flores et al.,2014) for measuring the value of a group in a game without any restriction, and weintroduce the Myerson group value in order to measure the value when the socialstructure is considered |
| Keywords: | Centrality, Social capital, Shapley group value, Myerson value |
| Date: | 2014–07 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws142215&r=gth |
| By: | Jordi Brandts; Christina Rott; Carles Solà |
| Abstract: | We conduct a laboratory experiment to study how, after a history of decay, cooperation in a repeated voluntary contribution game can be revived in an enduring way. Simply starting the repeated game over - a simple fresh start - leads to an initial increase of cooperation, but to a subsequent new decay. Motivated by cooperation decay in organizations we study the potential of three interventions of triggering higher and sustained cooperation taking place at the same time as a restart. Surprisingly, we find that the detailed explanation of the causes of the decay in cooperation from Fischbacher and Gaechter (2010) combined with an advice on how to prevent decay do not have an effect beyond that of just starting over. In contrast, a one-way free form communication message sent by the leader to the followers strongly revives cooperation. Repeated free form communication by the leader further strengthens the reviving effect on cooperation. Combining the two previous interventions does not outperform the pure effect of communication. Our content analysis reveals that leader communication is more people oriented and less formal than the expert advice. |
| Keywords: | leadership, cooperation, communication |
| JEL: | C71 C73 C92 D83 J63 L20 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:775&r=gth |
| By: | Sheremeta, Roman |
| Abstract: | The standard theoretical description of rent-seeking contests is that of rational individuals or groups engaging in socially inefficient behavior by exerting costly effort. Experimental studies find that the actual efforts of participants are significantly higher than predicted in the models based on rational behavior and that over-dissipation of rents (or overbidding or over-expenditure of resources) can occur. Although over-dissipation cannot be explained by the standard rational-behavior theory, it can be explained by incorporating behavioral dimensions into the standard model, such as (1) the utility of winning, (2) relative payoff maximization, (3) bounded rationality, and (4) judgmental biases. These explanations are not exhaustive but provide a coherent picture of important behavioral dimensions to be considered when studying rent-seeking behavior in theory and in practice. |
| Keywords: | rent-seeking, contests, experiments, overbidding, over-dissipation |
| JEL: | C72 C91 C92 D72 D74 |
| Date: | 2014–08–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:57751&r=gth |