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on Game Theory |
| By: | Claudius Gros |
| Abstract: | In physics, the wavefunctions of bosonic particles collapse when the system undergoes a Bose-Einstein condensation. In game theory, the strategy of an agent describes the probability to engage in a certain course of action. Strategies are expected to differ in competitive situations, namely when there is a penalty to do the same as somebody else. We study what happens when agents are interested how they fare not only in absolute terms, but also relative to others. This preference, denoted envy, is shown to induce the emergence of distinct social classes via a collective strategy condensation transition. Members of the lower class pursue identical strategies, in analogy to the Bose-Einstein condensation, with the upper class remaining individualistic. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.03421&r= |
| By: | Florian Navarro (GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement) |
| Abstract: | This article presents an axiomatic characterization of the Aumann-Drèze value (1974) for cooperative games with coalition structures. We build an associated game that extends the original associated game presented by Hamiache (2001) to cooperative games with coalition structures. We use a similar approach to the one used in Hamiache and Navarro (2020). This new associated game is expressed through a matrix form. We show that the series of successive associated games is convergent and that its limit is an inessential game. This allows us to propose a characterization of the Aumann-Drèze value that relies on associated consistency, inessential game and continuity axioms. Hence, this paper strengthens the results of Hamiache (2001) and Hamiache and Navarro (2020) considering that if these axioms are viewed as desirable, we are now able to provide a unique value for three different types of problems : the Shapley value on standard games (Hamiache 2001), the Hamiache-Navarro value on games with graphs (Hamiache and Navarro 2020) and the Aumann-Drèze value for games with coalition structures. |
| Keywords: | associated consistency,coalition structures,cooperative games,game theory,shapley value,aumann-drèze value |
| Date: | 2022–05–25 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03678064&r= |
| By: | Claus-Jochen Haake (Paderborn University); Thomas Streck (Paderborn University) |
| Abstract: | We study the consequences of modeling asymmetric bargaining power in two-person bargaining problems. For this, we compare application of an asymmetric version of a bargaining solution to a corresponding modification of the disagreement point. It turns out that the distortion between these two methods crucially depends on the bargaining solution concept. While for the Kalai-Smorodinsky solution weaker players benefit from modifying the disagreement point, the situation is reversed for the Nash bargaining solution. There, weaker players are better off in the asymmetric bargaining solution. When comparing application of the asymmetric versions of the Nash and the Kalai-Smorodinsky solutions, we demonstrate that there is an upper bound for the weight of a player, so that he is better off with the Nash bargaining solution. This threshold is ultimately determined by the relative utilitarian bargaining solution. From a mechanism design perspective, our results provide valuable information for a social planner, when implementing a bargaining solution for unequally powerful players. |
| Keywords: | Asymmetric bargaining power, Nash bargaining solution, Kalai-Smorodinsky bargaining solution |
| JEL: | C78 D63 |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:ciepap:148&r= |
| By: | Frédéric Koessler (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Marie Laclau (GREGHEC - Groupement de Recherche et d'Etudes en Gestion - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique); Jerôme Renault (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Tristan Tomala (Unknown) |
| Abstract: | We analyze information design games between two designers with opposite preferences and a single agent. Before the agent makes a decision, designers repeatedly disclose public information about persistent state parameters. Disclosure continues until no designer wishes to reveal further information. We consider environments with general constraints on feasible information disclosure policies. Our main results characterize equilibrium payoffs and strategies of this long information design game and compare them with the equilibrium outcomes of games where designers move only at a single predetermined period. When information disclosure policies are unconstrained, we show that at equilibrium in the long game, information is revealed right away in a single period; otherwise, the number of periods in which information is disclosed might be unbounded. As an application, we study a competition in product demonstration and show that more information is revealed if each designer could disclose information at a pre-determined period. The format that provides the buyer with most information is the sequential game where the last mover is the ex-ante favorite seller. |
| Keywords: | Bayesian persuasion,concavification,convexification,information,design,Mertens–Zamir solution,product demonstration,splitting games,Statistical experiments,stochastic games. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:pseptp:hal-03700394&r= |
| By: | David Lowing (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | A gas distribution network connects consumers to a source in gas. It is managed by a network operator, whose task incurs various costs, some of which may not be attributable to a particular consumer. Assuming that the operator wishes to recover these costs by charging for its services, the problem is then to determine how much each consumer should pay. In other words, how should these costs be shared among consumers. In this paper, we address this problem and propose cost sharing rules that depend on the network and the demands of the consumers. To that end, we adopt a normative approach and resort to three principles: (i) the independence of higher demands principle, (ii) the connection principle and (iii) the uniformity principle. Applying (i) and (ii), we derive the Connection rule and applying (i) and (iii), we derive the Uniform rule. It appears that (ii) and (iii) are incompatible. In order to make a trade-off between these two principles, we propose the Mixed rules, which compromise between the Connection rule and the Uniform rule. For each cost sharing rule, an axiomatic characterization is provided. Then, we show that the Connection rule coincides with the multi-choice Shapley value of a specific multi-choice game derived from the network and the demands of the consumers. Moreover, the Connection rule is in the Core of this specific multi-choice game. Similarly, we show that the Uniform rule coincides with the multi-choice Equal division value and the Mixed rules coincide with the multi-choice Egalitarian Shapley values. |
| Keywords: | Gas distribution network,Cost sharing rules,Axiomatization,Multi-choice games |
| Date: | 2022–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03680156&r= |
| By: | Frédéric Koessler (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Marie Laclau (HEC Paris - Ecole des Hautes Etudes Commerciales, GREGHEC - Groupement de Recherche et d'Etudes en Gestion - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique); Jérôme Renault (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Tristan Tomala (HEC Paris - Ecole des Hautes Etudes Commerciales, GREGHEC - Groupement de Recherche et d'Etudes en Gestion - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | This paper studies zero-sum splitting games with finite sets of states. Players dynamically choose a pair of martingales {pt,qt}t, in order to control a terminal payoff u(p∞,q∞). A first part introduces the notion of "Mertens–Zamir transform" of a real-valued matrix and use it to approximate the solution of the Mertens–Zamir system for continuous functions on the square [0,1]2. A second part considers the general case of finite splitting games with arbitrary correspondences containing the Dirac mass on the current state: building on Laraki and Renault (Math Oper Res 45:1237–1257, 2020), we show that the value exists by constructing non Markovian ε-optimal strategies and we characterize it as the unique concave-convex function satisfying two new conditions. |
| Keywords: | Splitting games,Mertens-Zamir system,Repeated games with incomplete information,Bayesian persuasion,Information design |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:hal:pseptp:halshs-03672222&r= |
| By: | Francisco Cabo (Universitad de Valladolid); Alain Jean-Marie (UM - Université de Montpellier); Mabel Tidball (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement) |
| Abstract: | Consumption satisfaction depends on other factors apart from the inherent characteristic of commodities. Among them, positional concerns are central in behavioural economics. Individuals enjoy returns from the ranking occupied by the consumed item. In public good, agents obtain satisfaction from their relative contribution. We analyse how positional preferences for voluntary contribution to a public good favour players' contributions and could lead to social welfare improvements. A two-player public good game is analysed, first a one-shot game and later a simple dynamic game with inertia. Homogeneous and non-homogeneous individuals are considered and particular attention is given to the transition path. |
| Keywords: | Public good,positional concerns,inertia,static and dynamic game. JEL code: H41,D91,C72,C73 |
| Date: | 2022–04–22 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpceem:hal-03649283&r= |
| By: | Onur A. Koska (University of Canterbury); Frank Stähler |
| Abstract: | This paper discusses the role of secret versus public reserve prices when bidders’ valuations depend positively on the seller’s private signal. A public reserve price is announced before the auction starts, and a secret reserve price is disclosed after the highest bid has been reached. The public reserve price regime may warrant a distortion as a good seller type may have to increase the reserve price beyond payoff-maximization in order to be able to credibly signal her type. We introduce and determine a rational signaling equilibrium which adds two domination-based conditions to the belief structure of a weak perfect Bayesian equilibrium. We show that a secret (public) reserve price design qualifies as an equilibrium if the distortion is large (small). |
| Keywords: | Auctions; Interdependent values; Optimal reserve prices; Rational signaling |
| JEL: | D44 |
| Date: | 2022–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:22/10&r= |
| By: | Eliaz, Kfir; Spiegler, Ran; Thysen, Heidi C. |
| Abstract: | We study strategic communication when the sender's multi-dimensional messages are given an interpretation by the sender himself or by a proxy. Interpreting messages involves the provision of some data about their statistical state-dependence. Interpretation can be selective: different kinds of data interpret different sets of message components. The receiver uses this data to decipher messages, yet he does not draw any inferences from the kind of data he is given. In this way, strategic interpretation of messages can influence the receiver's understanding of their equilibrium meaning. We show that in a two-action, two-state setting, the sender can attain his first-best payoff when the prior on one state exceeds a threshold that decays quickly with message dimensionality. We examine the result's robustness to the critique that our receiver does not attempt any inferences from selective interpretations. |
| Keywords: | bounded rationality; model misspecification; persuasion; Advanced Investigator grant no. 692995; 1779091 |
| JEL: | C72 D83 |
| Date: | 2021–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:108660&r= |
| By: | Sudhölter, Peter (Department of Economics); Grabisch, Michel (Paris School of Economics, Université Paris); Laplace Mermoud, Dylan (Paris School of Economics, Université Paris) |
| Abstract: | We describe algorithms and their implementations as computer programs derived from several theoretical results of the theory of cooperative transferable utility (TU) games. We show how to use Peleg’s well-known inductive method to explicitly compute all minimal balanced collections of coalitions. The described method is of independent interest and applied in the implementations of (a) the Bondareva-Shapley Theorem, which allows checking whether a TU game is balanced, i.e., has a non-empty core, and (b) a recent result of the second and third author that provides a sufficient and necessary condition for the stability of the core, which allows checking whether a balanced TU game has a core that is a von Neumann-Morgenstern stable set. |
| Keywords: | Core; stable set; minimal balanced collections; cooperative game. |
| JEL: | C44 C71 |
| Date: | 2022–06–08 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2022_004&r= |
| By: | Döpper, Hendrik; Sapi, Geza; Wey, Christian |
| Abstract: | This paper analyzes vertical integration incentives in a bilaterally duopolistic industry where input market outcomes are determined by bargaining. Vertical integration incentives are a combination of horizontal integration incentives up- and downstream and depend on the strength of substitutability or complementarity and the shape of the unit cost function. In contrast to the widely prevailing view in competition policy, vertical integration can under particular circumstances convey more bargaining power to the merged entity than a horizontal merger to monopoly. In a bidding game for an exogenously determined target firm, a vertical merger can dominate a horizontal one, while pre-emption does not occur. |
| Keywords: | Bargaining,Vertical Mergers,Shapley Value |
| JEL: | L13 L22 L42 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:dicedp:389&r= |
| By: | Stefano Dughera (UNITO - Università degli studi di Torino = University of Turin); Alain Marciano (MRE - Montpellier Recherche en Economie - UM - Université de Montpellier, UM - Université de Montpellier) |
| Abstract: | The Samaritan's Dilemma has largely been investigated, frequently by assuming that Samaritans help recipients out of altruism. Yet, Buchanan did not make any behavioral assumption regarding the Samaritan's motives. In this paper, we explicitly introduce this assumption in Buchanan's original model and analyze how this changes the nature of the game. We show that altruism alone does not explain the dilemma. A parameter that captures the disutility the Samaritan feels when helping someone who does not reciprocate her benevolence must be introduced to make sense of the different version of Buchanan's Samaritan's Dilemma. We also show that the Samaritan's dilemma is an evolutionary stable outcome, which confirms Buchanan's intuitions. Finally, a third important point put forward in the paper is that the more altruistic are the Samaritans, the less likely it is that they will show the kind of strategic courage envisaged by Buchanan, which is one of the most important traits Samaritans should display to avoid being trapped in a dilemma. |
| Keywords: | Buchanan,Samaritan's Dilemma,Altruism,Strategic Courage,Strategic Courage JEL Classification: B15 |
| Date: | 2022–06–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03684249&r= |
| By: | Nestor Gandelman (Universidad ORT Uruguay. Facultad de Administración y Ciencias Sociales. Departmento de Economía); Diego Lamé |
| Abstract: | Using a standard trust game, we elicit trust and reciprocity measures in a representative sample of adult players in Montevideo, the capital city of Uruguay, a country that exhibits relatively better levels of tolerance towards migrants than other Latin American countries. We find no statistically significant differences in trust levels of Uruguayans towards countrymen versus migrants. In reciprocity, we find only marginally significant differences attributable to the nationality of the players. |
| Keywords: | Trust, Reciprocity, Experimental games, Migrations |
| JEL: | C9 J15 |
| Date: | 2021–09 |
| URL: | http://d.repec.org/n?u=RePEc:avs:wpaper:128&r= |
| By: | Bara Kim (Department of Mathematics, Korea University, South Korea); Seung Han Yoo (Department of Economics, Korea University, South Korea) |
| Abstract: | This paper studies an informed mechanism designer problem in which the principal's private information is a number of agents. We define mechanical equivalence such that it holds if each agent's and the principal's perspectives are consistent in the sense that a conversion problem for a grand mechanism is resolved - each agent's expected payment taking into account the principal's private information can be incorporated into the principal's revenue. With mechanical equivalence and, additionally, the principal's expected payoff linearity, there is a single threshold for the optimal grand mechanism if a sub-mechanism cannot depend on the principal's private information. Interestingly, the main result shows that if a sub-mechanism can also depend on his private information, the optimal grand mechanism is characterized by double thresholds such that the principal does not announce the number of agents if it is in the middle range. We further extend the signal structure to include rich signal sets. |
| Keywords: | informed principal, mechanism, population uncertainty, mechanical equivalence |
| JEL: | C72 D44 D82 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:iek:wpaper:2204&r= |
| By: | Ryan Kor; Junjie Zhou |
| Abstract: | We study a planner's optimal interventions in both the standalone marginal utilities of players on a network and weights on the links that connect players. The welfare-maximizing joint intervention exhibits the following properties: (a) when the planner's budget is moderate (so that optimal interventions are interior), the change in weight on any link connecting a pair of players is proportional to the product of eigen-centralities of the pair; (b) when the budget is sufficiently large, the optimal network takes a simple form: It is either a complete network under strategic complements or a complete balanced bipartite network under strategic substitutes. We show that the welfare effect of joint intervention is shaped by the principal eigenvalue, while the distributional effect is captured by the dispersion of the corresponding eigenvalues, i.e., the eigen-centralities. Comparing joint intervention in our setting with single intervention solely on the standalone marginal utilities, as studied by Galeotti et al. (2020), we find that joint intervention always yields a higher aggregate welfare, but may lead to greater inequality, which highlights a possible trade-off between the welfare and distributional impacts of joint intervention. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.03863&r= |
| By: | Thomas Daske; Christoph March |
| Abstract: | This study explores mechanism design with allocation-based social preferences. Agents’ social preferences and private payoffs are all subject to asymmetric information. We assume quasi-linear utility and independent types. We show how the asymmetry of information about agents’ social preferences can be operationalized to satisfy agents’ participation constraints. Our main result is a possibility result for groups of at least three agents: If endowments are sufficiently large, any such group can resolve any given allocation problem with an ex-post budget-balanced mechanism that is Bayesian incentive-compatible, interim individually rational, and ex-post Pareto-efficient. |
| Keywords: | mechanism design, social preferences, Bayesian implementation, participation constraints, participation stimulation |
| JEL: | C72 C78 D62 D82 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9784&r= |
| By: | Guido Merzoni; Federico Trombetta |
| Abstract: | This paper proposes the first game theoretical model of technocratic governments, i.e. cases where a non political technocrat is put in charge by political parties. Based on the literature on post-electoral politics and agenda setting, we show conditions for the existence of a technocratic government equilibrium, where both parties agree to delegate the agenda setting power to technocrats, committed to maximize social welfare. Such an equilibrium exists only if the technocrats have a superior competence with respect to the majority party/coalition, or if the country is in a sufficiently important economic crisis. Furthermore, it is more likely to exist in countries with unstable parliament (i.e. one where the governing coalition is not always able to impose its will) and where parties care about the common value dimension, vis-a-vis the ideological one. Finally, we show that polarization increases the set of parameters where the technocratic government equilibrium exists, when parliament is unstable. |
| JEL: | C78 D72 D73 D78 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:dis:wpaper:dis2204&r= |