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on Game Theory |
| By: | Francisco Robles (Universitat de Barcelona) |
| Abstract: | We consider a market with only one seller and many buyers. The seller owns several indivisible objects on sale. Each buyer can receive many objects and has a gross-substitutes valuation for every package of objects. The gross-substitutes condition guarantees the non-emptiness of the core of the market (Ausubel and Milgrom, 2002). Moreover, the Vickrey outcome (Vickrey, 1961) of the market leads to a core payoff in which each buyer gets his maximum core payoff. The aim of this paper is to analyze the following mechanism. Simultaneously, each buyer requests a package by announcing how much he would pay for it. After all buyers' requests, the seller decides the final assignment of packages and the prices. If a buyer gets a package of objects, it must be his request or an allocation at least as good as his request. The subgame perfect equilibrium outcomes of the mechanism correspond to the Vickrey outcome of the market.. |
| Keywords: | assignment model, mechanism, implementation, Vickrey outcome. |
| JEL: | C71 C72 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:ewp:wpaper:353web&r=gth |
| By: | Somouaoga BONKOUNGOU |
| Abstract: | An early decision market is governed by rules that allow each student to apply to (at most) one college and require the student to attend this college if admitted. This market is ubiquitous in college admissions in the United States. We model this market as an extensive-form game of perfect information and study a refinement of subgame perfect equilibrium (SPE) that induces undominated Nash equilibria in every subgame (SPUE). Our main result shows that this game can be used to define a decentralized matching mechanism that weakly Pareto dominates student-proposing deferred acceptance. |
| Keywords: | early decision, Pareto dominance, decentralized market, subgame perfect equilibrium, subgame perfect undominated Nash equilibrium, costly application |
| JEL: | C78 C72 C73 I29 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montec:11-2016&r=gth |
| By: | Stéphane Gonzalez (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Université Jean Monnet - Saint-Etienne); Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics) |
| Abstract: | In cooperative games, the core is one of the most popular solution concept since it ensures coalitional rationality. For non-balanced games however, the core is empty, and other solution concepts have to be found. We propose the use of general solutions, that is, to distribute the total worth of the game among groups rather than among individuals. In particular, the k-additive core proposed by Grabisch and Miranda is a general solution preserving coalitional rationality which distributes among coalitions of size at most k, and is never empty for k ≥ 2. The extended core of Bejan and Gomez can also be viewed as a general solution, since it implies to give an amount to the grand coalition. The k-additive core being an unbounded set and therefore difficult to use in practice, we propose a subset of it called the minimal negotiation set. The idea is to select elements of the k-additive core mimimizing the total amount given to coalitions of size greater than 1. Thus the minimum negotiation set naturally reduces to the core for balanced games. We study this set, giving properties and axiomatizations, as well as its relation to the extended core of Bejan and Gomez. We give a method of computing the minimum bargaining set, and lastly indicate how to eventually get classical solutions from general ones. |
| Keywords: | general solution,core,balancedness,cooperative game |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01235625&r=gth |
| By: | Blake Allison (Department of Economics, Emory University); Adib Bagh (Department of Economics and Mathematics, University of Kentucky); Jason Lepore (Department of Economics, California Polytechnic State University) |
| Abstract: | We provide a sufficient condition for a game with discontinuous payoffs to be weakly reciprocally upper semi-continuous in mixed strategies. This condition is imposed on the individual payoffs and not on their sum, and it can be readily verified in a large class of games even when the sum of payoffs in such games is not upper semi-continuous. We apply our result to establish the existence of mixed strategy equilibria in probabilistic voting competitions when candidates have heterogenous beliefs about the distribution of the voters. |
| Keywords: | Better reply security, extended games, Weak reciprocal upper semi-continuity, Nash equilibria, Probabilistic voting models. |
| JEL: | C63 C72 D72 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:cpl:wpaper:1608&r=gth |
| By: | Rui Zhang (Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, USA); Quanyan Zhu (Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, USA) |
| Abstract: | Cyber insurance is a valuable approach to mitigate further the cyber risk and its loss in addition to the deployment of technological cyber defense solutions such as intrusion detection systems and firewalls. An effective cyber insurance policy can reduce the number of successful cyber attacks by incentivizing the adoption of preventative measures and the implementation of best practices of the users. To study cyber insurance in a holistic manner, we first establish a bi-level game-theoretic model that nests a zero-sum game in a moral-hazard type of principal-agent game to capture complex interactions between a user, an attacker, and the insurer. The game framework provides an integrative view of the cyber insurance and enables a systematic design of incentive compatible and attack-aware insurance policy. The framework is further extended to study a network of users and their risk interdependencies. We completely characterize the equilibrium solutions of the bi-level game. Our analytical results provide a fundamental limit on insurability, predict the Peltzman effect, and reveal the principles of zero operating profit and the linear insurance policy of the insurer. We provide analytical results and numerical experiments to corroborate the analytical results and demonstrate the network effects as a result of the strategic interactions among three types of players. |
| Keywords: | Cyber Insurance, Network Security, Moral Hazard, Information Asymmetry, Network Effects, Security Games, Mechanism Design |
| JEL: | G22 D80 D86 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:net:wpaper:1618&r=gth |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Benjamin Brooks (Dept. of Economics, University of Chicago); Stephen Morris (Dept. of Economics, Princeton University) |
| Abstract: | We explore the impact of private information in sealed-bid first-price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning-bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning bids and for the informationally robust comparison of alternative bidding mechanisms. |
| Keywords: | First price auction, Information structure, Bayes correlated equilibrium, Private values, Interdependent values, Common values, Revenue, Surplus, Welfare bounds, Reserve price |
| JEL: | C72 D44 D82 D83 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2018r3&r=gth |
| By: | Ata Atay (Universitat de Barcelona) |
| Abstract: | Solymosi and Raghavan (2001) characterize the stability of the core of the assignment game by means of a property of the valuation matrix. They show that the core of an assignment game is a von Neumann-Morgenstern stable set if and only if its valuation matrix has a dominant diagonal. Their proof makes use of some graph-theoretical tools, while the present proof relies on the notion of buyer-seller exact representative in Núñez and Rafels (2002). |
| Keywords: | Assignment game, core, stability, von Neumann-Morgenstern stable set. |
| JEL: | C71 C78 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:ewp:wpaper:350web&r=gth |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - 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. |
| Abstract: | Nous étudions l'espace vectoriel des fonctions d'ensemble sur un espace fini X, qui peuvent être vues aussi comme des fonctions pseudo-booléennes, et incluent comme cas particulier les jeux. Nous présentons plusieurs bases (jeux unanimes, fonctions de Walsh, fonctions de parité) ainsi que la transformée de Fourier. Nous établissons la dualité fondamentale entre les bases et les transformées linéaires et inversibles (e.g., la transformée de Möbius, de Fourier et les transformées en interaction). Nous l'appliquons pour résoudre le problème inverse bien connu de la théorie des jeux coopératifs (trouver tous les jeux ayant la même valeur de Shapley), et pour trouver différentes expressions équivalentes pour l'intégrale de Choquet. |
| Keywords: | set function,basis,Walsh function,Fourier transform,game,fonction d'ensemble,base,fonction de Walsh,transformée de Fourier,jeu |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01169287&r=gth |
| By: | Christian Basteck; Marco Mantovani; ; |
| Abstract: | We take school admission mechanisms to the lab to test whether the widely-used manipulable Boston-mechanism disadvantages students of lower cognitive ability and whether this leads to ability segregation across schools. Results show this is the case: lower ability participants receive lower payoffs and are over-represented at the worst school. Under the strategy-proof Deferred Acceptance mechanism, payoff differences are reduced, and ability distributions across schools harmonized. Hence, we find support for the argument that a strategy-proof mechanisms “levels the playing-field”. Finally, we document a trade-off between equity and efficiency in that average payoffs are larger under Boston than under Deferred Acceptance. |
| JEL: | C78 C91 D82 I24 |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2016-037&r=gth |
| By: | Peter Mitic (Santander UK); Bertrand K. Hassani (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Santander UK) |
| Abstract: | The Shapley method is applied to capital allocation in the context of a simple business model, where many business units supported by services. In this model the services are capable of either reducing the capital payable by the business units, or the opposite. A simple model of evaluating the value of coalitions is proposed, with a modification if a service is a member of the coalition. A closed form formula for the Shapley allocation to all players is derived, thus eliminating combinatorial problems. |
| Keywords: | Capital value,Game theory,Service,Diversification,Allocation,Shapley,Operational Risk |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01179057&r=gth |
| By: | Auerswald, Heike; Schmidt, Carsten; Thum, Marcel; Torsvik, Gaute |
| Abstract: | Challenges in global politics like climate change, maritime piracy and fighting highly contagious diseases concern global public goods. The related policy decisions are mostly made by teams. In contrast, economic models of global public goods typically assume a single rational decision-maker. We use a laboratory experiment to compare team decisions to decisions of individuals in a finitely repeated public good game with and without a costly punishment option. Teams of three participants coordinate on decisions either by majority or unanimity rule. We find that in absence of a punishment option teams contribute more to the public good than individuals. With a punishment option subsequently to the contribution decision team treatments exhibit a less frequent use of anti-social punishment and lower levels of social as well as anti-social punishment. Extreme preferences for punishment are eliminated by the majority decision rule. Overall, team decisions are closer to the social optimum and teams yield higher net payoffs when compared to individuals. |
| Keywords: | Public Good,Group Decision-Making,Punishment,Experiment,Öffentliche Güter,Entscheidungsverhalten in Gruppen,Bestrafung,Experiment |
| JEL: | C72 C92 H41 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:tudcep:0216&r=gth |
| By: | Lorenzo Cerda Planas (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics) |
| Abstract: | The aim of this paper is twofold. Starting from the population dynamics literature, which usually finds the resulting distribution of a trait in a population, according to some parents' preferences, I answer the inverted question: Which preference function would yield into a given trait distribution? I solve this using a continuous trait, instead of finite types of agents. Using this result, I connect this transmission theory of social traits with the well-known results of Dictator Game (DG) experiments. I use a specific definition of a Kantian trait applied to DG results, and determine the distribution of this trait that is commonly found in these experiments. With these two ingredients, I show that homo-œconomicus parents have a greater' dislike' or disutility of having offspring with different traits from them compared to their Kantian counterparts. This could be a result of myopic empathy being stronger in homo-œconomicus parents, driving this dislike of difference. |
| Keywords: | population dynamics,Kantian morale,evolutionary equilibrium |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01163937&r=gth |
| By: | Stéphane Zuber (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics) |
| Abstract: | This paper studies the extension of Harsanyi's theorem (Harsanyi, 1995) in a framework involving uncertainty. It seeks to extend the aggregation result to a wide class of Monotonic Bernoullian and Archimedean preferences (Cerreia-Vioglio et al., 2011) that subsumes many models of choice under uncertainty proposed in the literature. An impossibility result is obtained, unless we are in the specific framework where all individuals and the decision-maker are subjective expected utility maximizers sharing the same beliefs. This implies that non-expected utility preferences cannot be aggregated consistently. |
| Keywords: | Subjective expected utility,Harsanyi's theorem,Pareto principle,Monotonic Bernoullian and Archimedean preferences |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01224145&r=gth |
| 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 (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique, Department of Economics, Ecole Polytechnique - Polytechnique - X - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Endogenous sharing rules was introduced by Simon and Zame to model payoff indeterminacy in discontinuous games. Their main result concerns the existence of a solution, i.e., a mixed Nash equilibrium and an associated sharing rule. This note extends their result to abstract economies where, by definition, players are restricted to pure strategies, and provide an interpretation of Simon and Zame's model in terms of preference incompleteness. |
| Abstract: | La notion de règle de partage endogène (« Endogenous sharing rules ») a été introduite par Simon et Zame (Econometrica 1990) afin de modéliser la possible indétermination des paiements dans les jeux stratégiques discontinus. Leur résultat principal est l'existence d'une solution, c'est à dire qu'un équilibre de Nash mixte et d'une règle de partage associée. Dans cette note, l'on étend leur résultat au cas d'une économie abstraite, où, par définition, les joueurs doivent choisir des stratégies pures, et l'on fournit une interprétation du modèle Simon et Zame en terme de préférences incomplètes. |
| Keywords: | abstract economies,endogenous sharing rules,competitive equilibrium,incomplete and discontinuous preferences,better-reply security,économie abstraite,règle de partage endogène,équilibre compétitif,préférences discontinues et incomplètes |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01179102&r=gth |
| By: | Stéphane Gonzalez (Université Jean Monnet - Saint-Etienne, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics) |
| Abstract: | We consider in this paper solutions for TU-games where it is not assumed that the grand coalition is necessarily the final state of cooperation. Partitions of the grand coalition, or balanced collections together with a system of balancing weights interpreted as a time allocation vector are considered as possible states of cooperation. The former case corresponds to the c-core, while the latter corresponds to the aspiration core or d-core, where in both case, the best configuration (called a maximising collection) is sought. We study maximising collections and characterize them with autonomous coalitions, that is, coalitions for which any solution of the d-core yields a payment for that coalition equal to its worth. In particular we show that the collection of autonomous coalitions is balanced, and that one cannot have at the same time a single possible payment (core element) and a single possible configuration. We also introduce the notion of inescapable coalitions, that is, those present in every maximising collection. We characterize the class of games for which the sets of autonomous coalitions, vital coalitions (in the sense of Shellshear and Sudhölter), and inescapable coalitions coincide, and prove that the set of games having a unique maximising coalition is dense in the set of games. |
| Keywords: | cooperative game,core,balancedness,c-core,aspiration core,coalition formation,autonomous coalitions JEL Classification: C71 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01235632&r=gth |
| By: | Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - 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. |
| Abstract: | On considère le problème de l'approximation au sens des moindres carrés des fonctions d'ensemble par des fonctions d'ensemble satisfaisant des contraintes linéaires d'égalité ou d'inégalité. Le problème a des applications importantes dans le domaine des fonctions pseudo-Booléennes, la décision et la théorie des jeux coopératifs, où l'approximation par des jeux additifs mène à la notion de valeur aux moindres carrés. En fait, on voit que toute valeur linéaire pour les jeux coopératifs vient d'un problème d'approximation par les moindres carrés. Nous proposons une approche générale du problème. En particulier, nous obtenons des formules explicites pour les solutions sous des hypothèses faibles, qui incluent et étendent des résultats précédents de la littérature. |
| Keywords: | probabilistic value,least square value,Shapley value,least square approximation,cooperative game,pseudo-Boolean function,approximation par les moindres carrés,jeu coopératif,fonction pseudo-booléenne,valeur aux moindre carrés,valeur de Shapley,valeur probabiliste |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01169281&r=gth |
| By: | José María Alonso-Meijide (Universidade de Santiago de Compostela); Mikel Alvarez-Mozos (Universitat de Barcelona); María Gloria Fiestras-Janeiro (Universidade de Vigo); Andrés Jiménez-Losada (Universitad de Sevilla) |
| Abstract: | In this paper we investigate some structural properties of the order on the set of embedded coalitions outlined in de Clippel and Serrano (2008). Besides, we characterize the scalars associated to the basis they proposed of the vector space of partition function form games. |
| Keywords: | embedded coalitions, lattice, partition function form games. |
| JEL: | C71 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:ewp:wpaper:349web&r=gth |
| By: | Christian Basteck; Marco Mantovani; ; |
| Abstract: | Unsophisticated applicants can be at a disadvantage under manipulable and hence strategically demanding school choice mechanisms. Disclosing information on applications in previous admission periods makes it easier to asses the chances of being admitted at a particular school, and hence may level the playing field between applicants who differ in their cognitive ability. We test this conjecture experimentally for the widely used Boston mechanism. Results show that, absent this information, there exist a substantial gap between subjects of higher and lower cognitive ability, resulting in significant differences in payoffs, and ability segregation across schools. The treatment is effective in improving applicants’ strategic performance. However, because both lower and higher ability subjects improve when they have information about past demands, the gap between the two groups shrinks only marginally, and the instrument fails at levelling the playing field. |
| JEL: | C78 C91 D82 I24 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2016-036&r=gth |
| By: | Daniel Goetz (Princeton University, Department of Economics, Fisher Hall, Princeton, NJ, 08540) |
| Abstract: | I measure how mergers in the market for broadband internet service affect short-run welfare. Mergers between internet service providers (ISPs) with non-overlapping markets may decrease welfare by increasing ISP bargaining leverage against content providers. However, study of this welfare channel has been stymied by a lack of data on interconnection fees between content and internet service providers. I estimate an industry model of demand, plan choice, pricing and interconnection bargaining using data on plan prices, consumer choice sets and bargaining delays between major U.S ISPs and the leading purveyor of streaming video content, Netflix. Intuitively, if delaying agreement over interconnection degrades quality of service to subscribers, then the opportunity cost of lost subscriptions identifies the fee. To map disagreement times and ISP competition into interconnection fees, I develop a multilateral dynamic bargaining model with asymmetric information. ISPs make take-it-or-leave it offers to learn about Netflix's benefit from interconnection, while simultaneously competing for subscribers who value Netflix quality of service. I structurally estimate the model and recover fixed interconnection fees ranging from 44 to 69 million USD. I find that a proposed merger between TimeWarner and Comcast that was challenged by the Federal Communications Commission would have slightly raised interconnection fees and bargaining length, reducing consumer welfare by 1.9 percent. |
| Keywords: | mergers; streaming video; dynamic games of incomplete information; two-sided markets; |
| JEL: | C7 L41 L96 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:net:wpaper:1607&r=gth |