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on Game Theory |
| By: | Hannu Salonen (Department of Economics, University of Turku); Mikko A.A. Salonen (Helsinki Center of Economic Research (HECER), University of Helsinki) |
| Abstract: | We study iterated formation of mutually best matches (IMB) in college admissions problems. When IMB produces a maximal individually rational matching, the matching has many good properties like Pareto optimality and stability. If preferences satisfy a single peakedness condition, or have a single crossing property, then IMB produces a maximal individually rational matching. These properties guarantee also that the student proposing Deferred Acceptance algorithm (DA) and the Top Trading Cycles algorithm (TTC) produce the same matching as IMB. We compare these results with some well-known results about when DA is Pareto optimal, or when DA and TTC produce the same matching. |
| Keywords: | Matching, School choice, College admission |
| JEL: | C70 C71 D82 |
| URL: | http://d.repec.org/n?u=RePEc:tkk:dpaper:dp109&r=gth |
| By: | Alexandre Skoda (Centre d'Economie de la Sorbonne) |
| Abstract: | A correspondence P associates to every subset A ? N a partition P(A) of A and to every game (N,v), the P-restricted game (N,vP) defined by vP(A) = ? (F ? P(A)) v(F) for all A ? N. We give necessary and sufficient conditions on P to have inheritance of convexity from (N,v) to (N,vP). The main condition is a cyclic intersecting sequence free condition. As a consequence, we only need to verify inheritance of convexity for unanimity games and for the small class of extremal convex games (N,vS) (for any Ø ? S ? N) defined for any A ? N by vS(A) = |A ? S | ? 1 if |A ? S | ? 1, and vs(A) = 0 otherwise. In particular when (N,v) corresponds to Myerson's network-restricted game inheritance of convexity can be verified by this way. For the Pmin correspondence (Pmin(A) is built by deleting edges of minimum weight in the subgraph GA of a weighted communication graph G, we show that inheritance of convexity for unanimity games already implies inheritance of convexity. Assuming only inheritance of superadditivity, we also compute the Shapley value of the restricted game (N,vP) for an arbitrary correspondence P |
| Keywords: | communication network; cooperative game; restricted game; partitions |
| JEL: | C7 C71 C6 C61 |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:16040&r=gth |
| By: | Alessandra Casella; Jean Francois Laslier; Antonin Macé |
| Abstract: | In polarized committees, majority voting disenfranchises the minority. Allowing voters to spend freely a fixed budget of votes over multiple issues restores some minority power. However, it also creates a complex strategic scenario: a hide-and-seek game between majority and minority voters that corresponds to a decentralized version of the Colonel Blotto game. We offer theoretical results and bring the game to the laboratory. The minority wins as frequently as theory predicts, despite subjects deviating from equilibrium strategies. Because subjects understand the logic of the game — minority voters must concentrate votes unpredictably — the exact choices are of secondary importance, a result that vouches for the robustness of the voting rule to strategic mistakes. |
| JEL: | C72 C92 D71 |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:22231&r=gth |
| By: | Aniol Llorente-Saguer (Queen Mary University of London); Roman M. Sheremeta (Case Western Reserve University and Chapman University); Nora Szech (Karlsruhe Institute of Technology, WZB, and CESifo Institute) |
| Abstract: | A well-known theoretical result in the contest literature is that greater heterogeneity decreases performance of contestants because of the "discouragement effect." Leveling the playing field by favoring weaker contestants through bid-caps and favorable tie-breaking rules can reduce the discouragement effect and increase the designer's revenue. We test these predictions in an experiment. Our data show that indeed, strengthening weaker contestants through tie-breaks and bid-caps significantly diminishes the discouragement effect. Bid-caps can also improve revenue. Most deviations from Nash equilibrium can be explained by the level-k model of reasoning. |
| Keywords: | All-pay auction, Rent-seeking, Bid-caps, Tie-breaks, Contest design |
| JEL: | C72 C91 D72 |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp796&r=gth |
| By: | Aniol Llorente-Saguer (School of Economics and Finance, Queen Mary University of London); Roman M. Sheremeta (Weatherhead School of Management, Case Western Reserve University and Economic Science Institute, Chapman University); Nora Szech (Institute of Economics, Karlsruhe Institute of Technology and WZB and CESifo Institute) |
| Abstract: | A well-known theoretical result in the contest literature is that greater heterogeneity decreases performance of contestants because of the “discouragement effect.” Leveling the playing field by favoring weaker contestants through bid-caps and favorable tie-breaking rules can reduce the discouragement effect and increase the designer’s revenue. We test these predictions in an experiment. Our data show that indeed, strengthening weaker contestants through tie-breaks and bid-caps significantly diminishes the discouragement effect. Bid-caps can also improve revenue. Most deviations from Nash equilibrium can be explained by the level-k model of reasoning. |
| Keywords: | all-pay auction, rent-seeking, bid-caps, tie-breaks, contest design |
| JEL: | C72 C91 D72 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:16-09&r=gth |
| By: | Casella, Alessandra; Laslier, Jean-Francois; Macé, Antonin |
| Abstract: | In polarized committees, majority voting disenfranchises the minority. Allowing voters to spend freely a fixed budget of votes over multiple issues restores some minority power. However, it also creates a complex strategic scenario: a hide-and-seek game between majority and minority voters that corresponds to a decentralized version of the Colonel Blotto game. We offer theoretical results and bring the game to the laboratory. The minority wins as frequently as theory predicts, despite subjects deviating from equilibrium strategies. Because subjects understand the logic of the game --- minority voters must concentrate votes unpredictably --- the exact choices are of secondary importance. |
| Keywords: | Colonel Blotto; Committees; Polarization; Storable Votes; Tyranny of the Majority |
| JEL: | C72 C92 D71 |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11256&r=gth |
| By: | Becchetti, Leonardo (Associazione Italiana per la Cultura della Cooperazione e del Non Profit); Salustri, Francesco (Associazione Italiana per la Cultura della Cooperazione e del Non Profit) |
| Abstract: | Socially responsible consumers and investors are increasingly using their consumption and saving choices as a “vote with the wallet” to award companies which are at vanguard in reconciling the creation of economic value with social and environmental sustainability. In our paper we model the vote with the wallet as a multiplayer prisoner’s dilemma, outline equilibria and possible solutions to the related coordination failure problem, apply our analysis to domains in which the vote with the wallet is empirically more relevant, and provide policy suggestions. |
| Keywords: | Corporate Social Responsibility; Multiplayer Prisoner’s Dilemma; Voting with the Wallet |
| JEL: | C72 C73 D11 H41 M14 |
| Date: | 2015–09–08 |
| URL: | http://d.repec.org/n?u=RePEc:ris:aiccon:2015_141&r=gth |
| By: | Doruk Iris (Sogang University); Jungmin Lee (Sogang University and Institute for the Study of Labor (IZA)); Alessandro Tavoni (London School of Economics, Grantham Research Institute on Climate Change and Environment) |
| Abstract: | The provision of global public goods, such as climate change mitigation and managing fisheries to avoid overharvesting, requires the coordination of national contributions. The contributions are managed by elected governments who, in turn, are subject to public pressure on the matter. In an experimental setting, we randomly assign subjects into four teams, and ask them to elect a delegate by a secret vote. The elected delegates repeatedly play a one shot public goods game in which the aim is to avoid losses that can ensue if the sum of their contributions falls short of a threshold. Earnings are split evenly among the team members, including the delegate. We find that delegation causes a small reduction in the group contributions. Public pressure, in the form of teammates’ messages to their delegate, has a significant negative effect on contributions, even though the messages are designed to be payoff-inconsequential (i.e., cheap talk). The reason for the latter finding is that delegates tend to focus on the least ambitious suggestion. In other words, they focus on the lower of the two public good contributions preferred by their teammates. This finding is consistent with the prediction of our model, a modified version of regret theory. |
| Keywords: | Delegation, Cooperation, Threshold Public Goods Game, Climate Experiment, Regret Theory |
| JEL: | C72 C92 D81 H4 Q54 |
| Date: | 2016–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2016.26&r=gth |
| By: | Achille Basile (Università di Napoli Federico II); Maria Gabriella Graziano (Università di Napoli Federico II and CSEF); Ciro Tarantino (Università di Napoli Federico II) |
| Abstract: | This paper investigates coalitional fairness in pure exchange economies with asymmetric information. We study allocations of resources which are immune from envy when comparisons take place between coalitions. The model allows negligible and non-negligible traders, only partially informed about the true state of nature at the time of consumption, to exchange any number, possibly infinite, of commodities. Our analysis is based on the Aubin approach to coalitions and cooperation, i.e. on a notion of cooperation allowing traders to take part in one or more coalitions simultaneously employing only shares of their endowments (participation rates). We introduce and study in detail the notion of coalition fairness with participation rates (or Aubin c-fairness) and show that flexibility in cooperation permits to recover the failure of fairness properties of equilibrium allocations. Our results provide applications to several market outcomes (ex-post core, fine core, ex-post competitive equilibria, rational expectations equilibria) and emphasize the consequences of the convexification effect due to participation rates for models with large traders and infinitely many commodities. |
| Keywords: | Aubin coalitions; Fairness; Asymmetric information; Core; Rational expectations equilibria; Lyapunov convexity theorem |
| JEL: | C71 D51 D82 |
| Date: | 2016–05–17 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:442&r=gth |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | We consider a model of opinion formation based on aggregation functions. Each player modifies his opinon by arbitrarily aggregating the current opinion of all players. A player is influential for another player if the opinion of the first one matters for the latter. A generalization of influential player to a coalition whose opinion matters for a player is called influential coalition. Influential players (coalitions) can be graphically represented by the graph (hypergraph) of influence, and the convergence analysis is based on properties of the hypergraphs of influence. In the paper, we focus on the practical issues of applicability of the model w.r.t. the standard opinion formation framework driven by the Markov chain theory. For the qualitative analysis of convergence, knowing the aggregation functions of the players is not required, but one only needs to know the influential coalitions for every player. We propose simple algorithms that permit to fully determine the influential coalitions. We distinguish three cases: the symmetric decomposable model, the anonymous model, and the general model |
| Keywords: | social network; opinion formation; aggregation function; influential coalition; algorithm |
| JEL: | C7 D7 D85 |
| Date: | 2016–04 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:16038&r=gth |
| By: | Ensthaler, Ludwig; Huck, Steffen; Leutgeb, Johannes |
| Abstract: | From the regulation of sports to lawmaking in parliament, in many situations one group of people ("agents") makes decisions that affect payoffs of others ("principals") who are inactive. As the principals have a stake in the agents' decisions they face an incentive to offer payments in order to sway their decisions. Prat and Rustichini (2003) characterize pure-strategy equilibria of such Games Played Through Agents, in which principals commit to action-contingent transfers to agents. Specifically, they predict the equilibrium outcome in pure strategies to be efficient under some conditions. With field data hard to come by, we test the theory in a series of experimental treatments with human principals and computerized agents. The theory explains the data remarkably well. Subjects predominantly offer payments that implement efficient outcomes. In some treatments offers fall short of equilibrium predictions though. These minor deviations from equilibrium behavior are explored in a quantal response equilibrium framework. |
| Keywords: | games played through agents,experiment,quantal response equilibrium |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbeoc:spii2016305&r=gth |
| By: | Salvador Barberà; Antonio Nicolò |
| Abstract: | We consider collective decision problems where some agents have private information about alternatives and others don't. Voting takes place under strategy-proof rules. Prior to voting, informed agents may or may not disclose their private information, thus eventually influencing the preferences of those initially uninformed. We provide general conditions on the voting rules guaranteeing that informed agents will always be induced to disclose what they know. In particular, we apply this general result to environments where agent's preferences are restricted to be single-peaked or separable, and characterize the strategy-proof rules that ensure information disclosure in these settings. |
| Keywords: | strategy-proofness, information disclosure, voting rules, Single-peaked preferences, Committees |
| JEL: | D70 D71 D82 |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:904&r=gth |
| By: | Philipp Möhlmeier (BiGSEM - University Bielefeld); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne - Paris School of Economics); Emily Tanimura (Centre d'Economie de la Sorbonne) |
| Abstract: | In a network formation framework, where payoffs reflect an agent's ability to access information from direct and indirect contacts, we integrate negative externalities due to connectivity associated with two types of effects: competition for the access to information, and rivalrous use of information. We consider two separate models to capture the first and the second situations, respectively. In the first model, we assume that information is a non-rivalrous good but that there is competition for the access to information, for example because an agent with many contacts must share his time between them and thus has fewer opportunities to pass on information to each particular contact. The main idea is that the probability that each neighbor receives the information decreases with the number of contacts the sender has. In the second model, we assume that there is not competition for the access to information but that the use of information is rivalrous. In this case, it is assumed that when people receive the information before me, the harmful effect is greater than when others receive the information at the same time as myself. Our results concern pairwise stability and efficiency in both models and allow us to compare and contrast the effects of two kinds of competition for information |
| Keywords: | network formation; connections model; information; negative externalities; pairwise stability; efficiency |
| JEL: | D85 C70 |
| Date: | 2016–04 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:16033&r=gth |
| By: | Michele Polo |
| Abstract: | This Chapter reviews the theoretical liteature on entry games and free entry equilibria. We show that a wide range of symmetric oligopoly models share common comparative statics properties. Individual profits and quantities decrease in the number of firms, and tend to competitive or monopolistic competitive equilibria when the number of firms increases indefinitely. The maximum number of firms sustainable in a symmetric long run equilibrium depends on technology (economies of scale), preferences (market size) and strategies (toughness of price competition). On the normative side, in homogeneous product markets the business stealing effect drives the result of excessive entry, whereas adding product differentiation and the utillity from variety may revert the result. We then consider asymmetric free entry equilibria that exploit the aggregative nature of many oligopoly models. Finally, we discuss endogenous sunk costs and persistent concentration and frictionless entry and contestable markets. |
| Keywords: | Entry, Free entry equilibria, endogenous and exogsnous sunk costs, contestable markets |
| JEL: | L1 L13 D43 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:bcu:iefewp:iefewp87&r=gth |
| By: | Paul J. Healy (Department of Economics, Ohio State University); Yaron Azrieli (Department of Economics, Ohio State University); Christopher P. Chambers (Department of Economics, University of California, San Diego) |
| Abstract: | Experimental economists currently lack a convention for how to pay subjects in experiments with multiple tasks. We provide a theoretical framework for analyzing this question. Assuming monotonicity (dominated gambles are never chosen) and nothing else, we prove that paying for one randomly-chosen problem — the random problem selection (RPS) mechanism — is essentially the only incentive compatible mechanism. Paying for every period is similarly justified when we assume only a ‘no complementarities at the top’ (NCaT) condition. To help experimenters decide which is appropriate for their particular experiment, we also discuss empirical tests of these two assumptions. |
| Keywords: | Experimental design, decision theory, mechanism design |
| JEL: | C90 D01 D81 |
| Date: | 2016–01 |
| URL: | http://d.repec.org/n?u=RePEc:osu:osuewp:16-03&r=gth |
| By: | Braz Camargo; Dino Gerardi; Lucas Maestri |
| Abstract: | We study efficiency in decentralized markets with aggregate uncertainty and one-sided private information. There is a continuum of mass one of uninformed buyers and a continuum of mass one of informed sellers. Buyers and sellers are randomly and anonymously matched in pairs over time, and buyers make the offers. We show that all equilibria become efficient as trading frictions vanish. |
| JEL: | C70 C78 D82 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:cca:wpaper:453&r=gth |
| By: | Michael R. Powers (Tsinghua University); Martin Shubik (Cowles Foundation, Yale University); Wen Wang (Nankai University) |
| Abstract: | We offer a detailed examination of a broad class of 2 × 2 matrix games as a first step toward considering measures of resource distribution and efficiency of outcomes. In the present essay, only noncooperative equilibria and entropic outcomes are considered, and a crude measure of efficiency employed. Other solution concepts and the formal construction of an efficiency index will be addressed in a companion paper. |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2039&r=gth |
| By: | Hugo Cruz-Sanchez |
| Abstract: | We provide foundations for decisions in face of unlikely events by extending the standard framework of Savage to include preferences indexed by a family of events. We derive a subjective lexicographic expected utility representation which allows for infinitely many lexicographically ordered levels of events and for event-dependent attitudes toward risk. Our model thus provides foundations for models in finance that rely on different attitudes toward risk (e.g. Skiadas [9]) and for off-equilibrium reasonings in infinite dynamic games, thus extending and generalizing the analysis in Blume, Brandenburger and Dekel [3]. |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1605.07680&r=gth |
| By: | Philipp Möhlmeier (BiGSEM - Bielefeld University - Center for Mathematical Economics); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics); Emily Tanimura (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | In a network formation framework, where payoffs reflect an agent's ability to access information from direct and indirect contacts, we integrate negative externalities due to connectivity associated with two types of effects: competition for the access to information, and rivalrous use of information. We consider two separate models to capture the first and the second situations, respectively. In the first model, we assume that information is a non-rivalrous good but that there is competition for the access to information, for example because an agent with many contacts must share his time between them and thus has fewer opportunities to pass on information to each particular contact. The main idea is that the probability that each neighbor receives the information decreases with the number of contacts the sender has. In the second model, we assume that there is not competition for the access to information but that the use of information is rivalrous. In this case, it is assumed that when people receive the information before me, the harmful effect is greater than when others receive the information at the same time as myself. Our results concern pairwise stability and efficiency in both models and allow us to compare and contrast the effects of two kinds of competition for information. |
| Abstract: | Dans un cadre de formation de réseau, où les gains reflètent la capacité d'un agent pour accéder aux informations de contacts directs et indirects, nous intégrons des externalités négatives dues à la connectivité associé à deux types d'effets : la concurrence pour l'accès à l'information, et l'utilisation de la rivalité de l'information. Nous considérons deux modèles distincts pour capturer la première et la seconde situation, respectivement. Dans le premier modèle, nous supposons que l'information est un bien non-rivalité, mais qu'il existe une concurrence pour l'accès à l'information, par exemple en raison d'un agent avec de nombreux contacts qui doit partager son temps entre eux et a donc moins d'occasions de transmettre des informations à chaque contact. L'idée principale est que la probabilité que chaque voisin reçoit l'information diminue avec le nombre de contacts qu'a l'expéditeur. Dans le second modèle, nous supposons qu'il n'y a pas de concurrence pour l'accès à l'information, mais que l'utilisation de l'information est compétitive. En outre, il est supposé que les personnes qui reçoivent l'information avant moi ont un effet plus néfaste sur mon utilité que les personnes qui reçoivent l'information en même temps que moi. Nos résultats concernent la stabilité par paire et l'efficacité dans les deux modèles et nous permettent de comparer et contraster les effets de deux types de concurrence pour obtenir des informations. |
| Keywords: | network formation,connections model,negative externalities,pairwise stability,efficiency,formation de réseaux,modèle des connexions,information,externalités négatives,stabilité,efficacité |
| Date: | 2016–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01316936&r=gth |