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on Game Theory |
| By: | Jean Guillaume Forand (Department of Economics, University of Waterloo); Metin Uyanik (School of Economics, University of Queensland) |
| Abstract: | We provide two new proofs of the Bondareva-Shapley theorem, which states that the core of a transferable utility cooperative is nonempty if and only if the game is balanced. Both proofs exploit the fixed points of self-maps of the set of imputations, applying elementary existence arguments typically associated with noncooperative games to cooperative games. |
| JEL: | C71 C62 |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:wat:wpaper:1706&r=gth |
| By: | Beckmann, Klaus B. (Helmut Schmidt University, Hamburg) |
| Abstract: | The present paper proposes a myopic, boundedly rational heuristic for individual decision-making in differential game settings. I demonstrate that this type of behaviour converges to Nash equilibrium in infinitely repeated stage games without a state variable if the stage game is strategically symmetric. Two examples are used to illustrate the application of the heuristic in differential games. |
| Keywords: | differential games; simulation; bounded rationality |
| JEL: | C72 |
| Date: | 2017–12–19 |
| URL: | http://d.repec.org/n?u=RePEc:ris:vhsuwp:2017_178&r=gth |
| By: | Alexandre Skoda (Centre d'Economie de la Sorbonne) |
| Abstract: | We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum partition. This minimum partition Pmin is induced by the deletion of the minimum weight edges. We provide five necessary conditions on the graph edge-weights to have inheritance of convexity from the underlying game to the restricted game associated with Pmin. Then, we establish that these conditions are also sufficient for a weaker condition, called F-convexity, obtained by restriction of convexity to connected subsets. Moreover, we prove that inheritance of convexity for Myerson restricted game associated with a given graph G is equivalent to inheritance of F-convexity for the Pmin-restricted game associated with a particular weighted graph G' built from G by adding a dominating vertex, and with only two different edge-weights. Then, we prove that G is cycle-complete if and only if a specific condition on adjacent cycles is satisfied on G' |
| Keywords: | communication networks; cooperative game; convex game; restricted game; partitions |
| JEL: | C71 C61 |
| Date: | 2017–08 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:17049&r=gth |
| By: | Ulrich Faigle (Mathematisches Institut, Universität zu Köln); Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint matrices and hence a spectral representation. As a result, cooperation systems, decision systems and quantum systems all become visible as manifestations of special interaction systems. The treatment of the theory is purely mathematical and does not require any special knowledge of physics. It is shown how standard notions in cooperative game theory arise naturally in this context. In particular, Fourier transformation of cooperative games becomes meaningful. Moreover, quantum games fall into framework. Finally, a theory of Markov evolution of interaction states is presented that generalizes classical homogeneous Markov chains to the present context |
| Keywords: | cooperative game; decision system; evolution; Fourier transform; interaction system; measurement; quantum game |
| JEL: | C71 |
| Date: | 2017–06 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:17046&r=gth |
| By: | Britta Hoyer (Paderborn University); Nadja Stroh-Maraun (Paderborn University) |
| Abstract: | In actual school choice applications the theoretical underpinnings of the Boston School Choice Mechanism (BM) (complete information and rationality of the agents) are often not given. We analyze the actual behavior of agents in such a matching mechanism, using data from the matching mechanism currently used in a clearinghouse at a faculty of Business Administration and Economics at a German university, where a variant of the BM is used, and supplement this data with data generated in a survey among students who participated in the clearinghouse. We find that under the current mechanism over 70% of students act strategically. Controlling for students' limited information, we find that they do act rationally in their decision to act strategically. While students thus seem to react to the incentives to act strategically under the BM, they do not seem to be able to use this to their own advantage. However, those students acting in line with their beliefs manage a significantly better personal outcome than those who do not. We also run simulations by using a variant of the deferred acceptance algorithm, adapted to our situation, to show that the use of a different algorithm may be to the students' advantage. |
| Keywords: | Matching, Application of the Boston Mechanism, School Choice, Strategic Behavior, Incomplete Information |
| JEL: | C78 D82 |
| Date: | 2017–12 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:ciepap:110&r=gth |
| By: | Alexandre Skoda (Centre d'Economie de la Sorbonne) |
| Abstract: | We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum partition. This minimum partition Pmin is induced by the deletion of the minimum weight edges. We provide a characterization of the graphs satisfying inheritance of convexity from the underlying game to the restricted game associated with P min. |
| Keywords: | communication networks; cooperative game; convex game; restricted game; partitions |
| JEL: | C71 C61 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:17051&r=gth |
| By: | Triossi, Matteo; Romero-Medina, Antonio |
| Abstract: | We study the existence of group strategy-proof stable rules in many to-many matching markets. We show that when firms have acyclical preferences over workers the set of stable matchings is a singleton, and the worker-optimal stable mechanism is a stable and group strategy-proof rule for firms and workers. Furthermore, acyclicity is the minimal condition guaranteeing the existence of stable and strategy-proof mechanisms in many-to-many matching markets. |
| Keywords: | Singleton core; Two-sided Group Strategy-proofness; Stability; Acyclicity; Many-to-many markets |
| JEL: | D78 D71 C78 C71 |
| Date: | 2017–12–18 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:26081&r=gth |
| By: | ALVAREZ-MOZOS, Mikel; EHLERS, Lars |
| Abstract: | In most economic applications, externalities prevail: the worth of a coalition depends on how the other players are organized. We show that there is a unique natural way of extending the nucleolus from (coalitional) games without externalities to games with externalities. This is in contrast to the Shapley value and the core for which many different extensions have been proposed. |
| Keywords: | Externalities; partition function; nucleolus, reduced game |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montde:2017-04&r=gth |
| By: | Alexandre Skoda (UP1 - Université Panthéon-Sorbonne, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the sub-components corresponding to a minimum partition. This minimum partition P min is induced by the deletion of the minimum weight edges. We provide five necessary conditions on the graph edge-weights to have inheritance of convexity from the underlying game to the restricted game associated with P min. Then, we establish that these conditions are also sufficient for a weaker condition, called F-convexity, obtained by restriction of convexity to connected subsets. Moreover, we prove that inheritance of convexity for Myerson restricted game associated with a given graph G is equivalent to inheritance of F-convexity for the P min-restricted game associated with a particular weighted graph G ′ built from G by adding a dominating vertex, and with only two different edge-weights. Then, we prove that G is cycle-complete if and only if a specific condition on adjacent cycles is satisfied on G ′ . |
| Keywords: | partitions,communication networks,cooperative game,convex game,restricted game |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01617023&r=gth |
| By: | Cristina Bicchieri; Alessandro Sontuoso (Philosophy, Politics and Economics, University of Pennsylvania) |
| Abstract: | This is a draft of a chapter in a planned book on behavioral game theory. Social norms and social preferences have increasingly become an integral part of the economics discourse. After disentangling the two notions, this paper focuses on social norms, which we stipulate as group-specific solutions to strategic problems. More precisely, we define social norms as behavioral regularities emerging in mixed-motive games, as a result of preferences for conformity conditional on an endogenous set of beliefs and expectations. To that end, we review models that explicitly feature normative expectations, as well as models that account for category-specific prescriptions. We finally survey some relevant experimental evidence. |
| Keywords: | social norms, social preferences, social dilemmas |
| JEL: | C72 C92 |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:ppc:wpaper:0011&r=gth |
| By: | Mustapha Ridaoui (Centre d'Economie de la Sorbonne - Paris School of Economics); Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics); Christophe Labreuche (Thales Research & Technology) |
| Abstract: | We consider MultiCriteria Decision Analysis models which are defined over discrete attributes, taking a finite number of values. We do not assume that the model is monotonically increasing with respect to the attributes values. Our aim is to define an importance index for such general models, encompassing Generalized-Additive Independence models as particular cases. They can be seen as being equivalent to k-ary games (multichoice games). We show that classical solutions like the Shapley value are not suitable for such models, essentially because of the efficiency axiom which does not make sense in this context. We propose an importance index which is a kind of average variation of the model along the attributes. We give an axiomatic characterization of it |
| Keywords: | MultiCriteria Decision Analysis; k-ary game; Shapley value |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:17048&r=gth |
| By: | In?s Macho-Stadler (Universitat Aut?noma de Barcelona and Barcelona GSE); David P?rez-Castrillo (Universitat Aut?noma de Barcelona and Barcelona GSE); David Wettstein (BGU) |
| Keywords: | Shapley value, Externalities |
| JEL: | C71 D62 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:bgu:wpaper:1716&r=gth |
| By: | Duersch, Peter; Lambrecht, Marco; Oechssler, Joerg |
| Abstract: | Online and offline gaming has become a multi-billion dollar industry. However, games of chance are prohibited or tightly regulated in many jurisdictions. Thus, the question whether a game predominantly depends on skill or chance has important legal and regulatory implications. In this paper, we suggest a new empirical criterion for distinguishing games of skill from games of chance: All players are ranked according to a "best-fit" Elo algorithm. The wider the distribution of player ratings are in a game, the more important is the role of skill. Most importantly, we provide a new benchmark ("50%-chess") that allows to decide whether games predominantly (more than 50%) depend on chance, as this criterion is often used by courts. We apply the method to large datasets of various two-player games (e.g. chess, poker, backgammon, tetris). Our findings indicate that most popular online games, including poker, are below the threshold of 50% skill and thus depend pre- dominantly on chance. In fact, poker contains about as much skill as chess when 3 out of 4 chess games are replaced by a coin flip. |
| Date: | 2017–12–22 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0643&r=gth |
| By: | Dizdar, Deniz; Moldovanu, Benny; Szech, Nora |
| Abstract: | Agents in a finite two-sided market make costly investments and are then matched assortatively based on these investments. Besides signaling complementary types, investments also generate benefits for partners. We shed light on quantitative properties of the equilibrium investment behavior. The bilateral external benefits induce an investment multiplier effect. This multiplier effect depends in a complex way on agents' uncertainty about their rank within their own market side and on their uncertainty about the types and investments of potential partners. We study how the multiplier effect depends on market size and how it interacts with other important factors such as the costs of investment and the signaling incentives induced by competition for more desirable partners. We use our results to characterize equilibrium utilities in large markets. For small markets, our results lead to bounds on the hold-up problem. |
| Keywords: | matching,signaling,investment,multiplier effect |
| JEL: | C78 D44 D82 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:kitwps:109&r=gth |
| By: | Bio-Akanni ELEGBEDE (IAE DIJON - Université de Bourgogne (CREGO)) |
| Abstract: | In this paper, we define the concept of symmetric Cournot-Walras equilibrium (SCWE thereafter) in a pure exchange economy with differentiated commodities based on Julien and Tricou (2005). We compute this concept of equilibrium to two economies where the oligopolists offer their differentiated goods on the market in order to obtain the competitive good. We obtain three main results. First, we find that, under certain conditions, SCWE-DP allocations and price converge to Walrasian ones. Second, we also find that whether the SCWE-DP is Pareto-dominated or not by Walrasian equilibrium depends on the type of economic agent (oligopolist or competitive). Third, the two economies are linked. |
| Keywords: | Di erentiated commodity; General equilibrium; Cournot-Walras Equilibrium |
| JEL: | C72 D43 D51 L13 L38 |
| Date: | 2017–12 |
| URL: | http://d.repec.org/n?u=RePEc:dij:wpfarg:1171201&r=gth |
| By: | Bozbay, Irem (university of surrey); Peters, Hans (QE / Mathematical economics and game the) |
| Abstract: | We consider an information aggregation problem where a group of voters wants to make a `yes' or `no' decision over a single issue. Voters have state-dependent common preferences, but hold possibly conflicting private information about the state in the form of types (signals). We assume that types are distributed from a state-dependent continuous distribution. In this model, Bayesian equilibrium voting and efficient voting coincide, and informative voting means that a voter votes in favor of the issue if and only if the signal exceeds a cut-point level. Our main result is an answer, in the form of a condition on the parameters of the model, to the question when informative voting is efficient. |
| Keywords: | private information, efficient information aggregation, strategic voting |
| JEL: | C70 D70 D71 D80 D82 |
| Date: | 2017–12–12 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2017032&r=gth |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics); Alexis Poindron (Centre d'Economie de la Sorbonne); Agnieszka Rusinowka (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | We study a stochastic model of anonymous influence with conformist and anti-conformist individuals. Each agent with a ‘yes’ or ‘no’ initial opinion on a certain issue can change his opinion due to social influence. We consider anonymous influence, which depends on the number of agents having a certain opinion, but not on their identity. An individual is conformist/anti-conformist if his probability of saying ‘yes’ increases/decreases with the number of ‘yes’- agents. In order to consider a society in which both conformists and anti-conformists co-exist, we investigate a generalized aggregation mechanism based on ordered weighted averages. Additionally, every agent has a coefficient of conformism which is a real number in [-1, 1], with negative/positive values corresponding to anti-conformists/conformists. The two extreme values -1 and 1 represent a pure anti-conformist and a pure conformist, respectively, and the remaining values - so called ‘mixed’ agents. We consider two kinds of a society: without mixed agents, and with mixed agents who play randomly either as conformists or anti-conformists. For both cases of the model, we deliver a qualitative analysis of convergence, i.e., find all absorbing classes and conditions for their occurence |
| Keywords: | influence; anonymity; anti-conformism; convergence; absorbing class |
| JEL: | C7 D7 D85 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:17047&r=gth |
| By: | Aurélie Bonein; Stéphane Turolla |
| Abstract: | Motivated by recent research on product differentiation, we conduct laboratory experiments to study how (aggregate) demand uncertainty influences location choices and price competition in the original Hotelling (1929)’s model. We provide new predictions on the effect of risk attitudes on both decisions under demand uncertainty and confront them with the data. Our experimental results support the predictions that demand uncertainty acts as a differentiation force for risk-neutral and risk-lover subjects. By contrast, we do not verify that demand uncertainty leads risk-averse subjects to agglomerate. This is explained primarily by learning effects and heterogeneous behaviors within this risk profile. Finally, we observe various price-setting behaviors, ranging from an attempt to collude to a price war, depending on the level of differentiation. |
| Keywords: | product differentiation, demand uncertainty, price competition, experiment |
| JEL: | C72 C91 D43 L13 R30 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:rae:wpaper:201712&r=gth |
| By: | Timo Hiller |
| Abstract: | This paper endogenizes the network for the seminal model presented in Ballester et al. (2006) by way of a simple simultaneous move game. Agents choose with whom to associate and how much effort to exert. Effort levels display local strategic complementarities and global strategic substitutes. I show that all pairwise Nash equilibrium networks are nested split graphs. As in Ballester et al. (2006), agents’ equilibrium effort levels are proportional to Bonacich centrality. However, their ranking now coincides with a simpler measure, which is also easier to identify: degree centrality. I then study key player policies, which aim at minimizing aggregate effort levels via the elimination of an agent. In the spirit of network formation, after an agent was eliminated from a pairwise Nash equilibrium network, the remaining agents may revise their effort decisions and adapt their linking behavior. It is shown that, if the parameter governing global strategic substitutes is sufficiently small, then eliminating a most central agent also decreases aggregate effort levels most. This mirrors results obtained by Ballester et al. (2006). However, when global strategic substitutes are large, then, different from Ballester et al. (2006), eliminating a most central agent may not be optimal. Eliminating a most central agent, who in equilibrium also exerts highest criminal effort, decreases competition/congestion effects and increases incentives of the remaining agents to create new links. The latter effect on the aggregate level of crime may outweigh the former. These results are relevant for a wide range of applications, such as juvenile delinquency and crime, R&D expenditure of firms, bank bailouts and trade. |
| Keywords: | Strategic network formation, peer effects, local strategic complements, global strategic substitutes, positive externalities, negative externalities. |
| JEL: | D62 D85 |
| Date: | 2017–12–20 |
| URL: | http://d.repec.org/n?u=RePEc:bri:uobdis:17/693&r=gth |
| By: | Lorenz, Johannes |
| Abstract: | There are two ways for taxpayers to avoid paying taxes: legally, through tax optimization and illegally, through tax evasion. The government reacts by altering the law, and by conducting audits, respectively. These phenomena are modeled as a population game, a strategic interaction between all taxpayers: the more taxpayers optimize, the lower the optimization result as a consequence of the government tightening the tax law. The more taxpayers evade, the higher the risk of detection because of the tax agencies increasing the audit probability. If the government reacts to changed optimization behavior with too large a delay, an equilibrium tax law cannot be reached. Tax codes should be updated rapidly in order to avoid a permanent change of the tax law, which is costly both for the legislator and the taxpayers facing legal uncertainty. |
| Keywords: | tax avoidance,tax evasion,population games |
| JEL: | C73 H26 K34 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:upadvr:v7617&r=gth |
| By: | Maija Halonen-Akatwijuka; In-Uck Park |
| Abstract: | We examine a setup where two agents allocate a fixed budget of humanitarian aid between two equally needy areas. The agents may be biased to one area which is their private information. Without communication aid is allocated inefficiently resulting in gaps and overlaps in response. Direct communication between the agents is ineffective and cannot resolve the coordination failure. We show that coordination can be improved by a mediator, such as an information management system, which filters the information communicated by the agents. Our results can throw light on how to improve the current disaster management systems. |
| Keywords: | coordination, humanitarian aid, public goods, cheap talk, mediated communication, information management system. |
| JEL: | D82 D83 H41 H84 L31 |
| Date: | 2017–12–19 |
| URL: | http://d.repec.org/n?u=RePEc:bri:uobdis:17/691&r=gth |
| By: | Hanna Fromell (University of Groningen); Daniele Nosenzo (University of Nottingham); Trudy Owens (University of Nottingham); Fabio Tufano (University of Nottingham) |
| Abstract: | Previous studies have shown that individuals are less likely to help a person in need when there are “bystanders†present who can also offer help. We designed an experiment to re-examine this “bystander effect†using modified dictator games. We find lower giving rates in the presence of bystanders, confirming the existence of a bystander effect. However, we also show that the recipient’s welfare is greater when bystanders are present, challenging the usual interpretation that the bystander effect is due to an erosion of prosocial values. |
| Keywords: | bystander effect, bystander dilemma, diffusion of responsibility, dictator game, social norms |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:not:notcdx:2017-15&r=gth |
| By: | SPRUMONT, Yves |
| Abstract: | Relative Nash welfarism is a solution to the problem of aggregating von Neumann-Morgenstern preferences over a set of lotteries. It ranks such lotteries according to the product of any collection of 0-normalized von Neumann-Morgenstern utilities they generate. We show that this criterion is characterized by the Weak Pareto Principle, Anonymity, and Independence of Harmless Expansions: the social ranking of two lotteries is unaffected by the addition of any alternative that every agent deems at least as good as the one she originally found worst. Relative Nash welfarism is more appealing than relative utilitarianism in contexts where the best relevant alternative for an agent is difficult to identify with confidence. |
| Keywords: | Preference aggregation; lotteries; relative utilitarianism; Nash product |
| JEL: | D63 D71 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montde:2017-03&r=gth |
| By: | Jiyun Cao (The School of Economics, Nankai University and Collaborative Innovation Center for China Economy, Tianjin, China); Uday Bhanu Sinha (Department of Economics, Delhi School of Economics) |
| Abstract: | The existing literature has considered licensing of a patented innovation either in a homogenous good industry or in a differentiated goods industry. We consider the licensing problem between two firms i.e., licensor and licensee producing the homogenous goods when there is a third firm producing a differentiated good in the market. We find that when the costs of non-innovators are not high, the optimal licensing contract depends on the degree of product differentiation and the innovator has more incentive for innovation when it is an insider than when it is an outsider of this market. |
| Keywords: | licensing, two-part tariff, Cournot oligopoly, homogenous and differentiated goods, incentive for innovation. |
| JEL: | D43 D45 L13 |
| Date: | 2017–12 |
| URL: | http://d.repec.org/n?u=RePEc:cde:cdewps:282&r=gth |