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on Game Theory |
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Issue of 2013‒11‒16
nineteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Dominik Karos |
| Abstract: | We generalize the class of apex game by combining a winning coalition of symmetric minor players with�a collection of apex sets which can form winning coalitions only together with a fixed quota of minor players.� By applying power indices to these games and their subgames we generate players' preferences over coalitions which we use to define a coalition formation game.� We focus on strongly monotonic power indices and investigate under which conditions on the initial general apex game there are core stable coalitions in the resulting coalition formation game.� Besides several general results, we develop condition for the Shapley-Shubik index, the Banzhaf index, and the normalized Banzhaf index in particular.� It turns out that many statements can be easily verified for arbitrary collections of apex sets.� Nevertheless, we give some relations between the collection of apex sets and the set of core stable coalitions. |
| Keywords: | Apex Games, Core Stability, Hedonic Games, Strong monotony |
| JEL: | C71 G34 |
| Date: | 2013–10–28 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:680&r=gth |
| By: | Forges, Françoise; Serrano, Roberto |
| Abstract: | This is a brief survey describing some of the recent progress and open problems in the area of cooperative games with incomplete information. We discuss exchange economies, cooperative Bayesian games with orthogonal coalitions, and issues of cooperation in non-cooperative Bayesian games. |
| Keywords: | Strategic Externalities; Non-Cooperative Bayesian Games; Cooperative Games with Orthogonal Coalitions; Exchange Economies; Informational Externalities; |
| JEL: | D82 D51 C72 C71 |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:dau:papers:123456789/8158&r=gth |
| By: | Forges, Françoise; Vida, Péter |
| Abstract: | We show that essentially every communication equilibrium of any finite Bayesian game with two players can be implemented as a strategic form correlated equilibrium of an extended game, in which before choosing actions as in the Bayesian game, the players engage in a possibly fin nitely long (but in equilibrium almost surely fi nite), direct, cheap talk. |
| Keywords: | Bayesian game; pre-play communication; cheap talk; communication equilibrium; correlated equilibrium; Two Player; |
| JEL: | C72 D70 C73 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:dau:papers:123456789/8159&r=gth |
| By: | He, Wei; Sun, Yeneng |
| Abstract: | The existence of stationary Markov perfect equilibria in stochastic games is shown in several contexts under a general condition called "coarser transition kernels". These results include various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with mixtures of constant transition kernels as special cases. The minimality of the condition is illustrated. The results here also shed some new light on a recent example on the nonexistence of stationary equilibrium. The proofs are remarkably simple via establishing a new connection between stochastic games and conditional expectations of correspondences. |
| Keywords: | Stochastic game, stationary Markov perfect equilibrium, equilibrium existence, coarser transition kernel |
| JEL: | C72 C73 |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:51274&r=gth |
| By: | Jean-François Caulier (Centre d'Economie de la Sorbonne); 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: | Most allocation rules for network games presented in the literature assume that the network structure is fixed. We put explicit emphasis on the construction of networks and examine the dynamic formation of networks whose evolution across time periods is stochastic. Time-series of networks are studied that describe processes of network formation where links may appear or disappear at any period. Moreover, convergence to an efficient network is not necessarily prescribed. Transitions from one network to another are random and yield a Markov chain. We propose the link-based allocation rule for such dynamic random network formation processes and provide its axiomatic characterization. By considering a monotone game and a particular (natural) network formation process we recover the link-based flexible network allocation rule of Jackson. |
| Keywords: | Dynamic networks, network game, link-based allocation rule, Markov chain, characterization. |
| JEL: | C71 D85 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:13063&r=gth |
| By: | Lisa Bruttel; Werner GŸth |
| Abstract: | In the two-person sequential best shot game, first player 1 contributes to a public good and then player 2 is informed about this choice before contributing. The payoff from the public good is the same for both players and depends only on the maximal contribution. Efficient voluntary cooperation in the repeated best shot game therefore requires that only one player should contribute in a given round. To provide better chances for such cooperation, we enrich the sequential best shot base game by a third stage allowing the party with the lower contribution to transfer some of its periodic gain to the other party. Participants easily establish cooperation in the finitely repeated game. When cooperation evolves, it mostly takes the form of ''labor division'', with one participant constantly contributing and the other constantly compensating. However, in a treatment in which compensation is not possible, (more or less symmetric) alternating occurs frequently and turns out to be almost as efficient as labor division. |
| Keywords: | best shot game, coordination, transfer, experiment |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:twi:respas:0086&r=gth |
| By: | Vigeral, Guillaume; Sorin, Sylvain |
| Abstract: | We give new proofs of existence of the limit of the discounted values for two person zero-sum games in the following frameworks: incomplete information, absorbing, recursive. The idea of these new proofs is to use some comparison criteria. |
| Keywords: | variational inequalities; comparison principle; asymptotic value; incomplete information; repeated games; stochastic games; |
| JEL: | C73 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:dau:papers:123456789/8023&r=gth |
| By: | Vigeral, Guillaume |
| Abstract: | We give an example of a zero-sum stochastic game with four states, compact action sets for each player, and continuous payoff and transition functions, such that the discounted value does not converge as the discount factor tends to 0, and the value of the n-stage game does not converge as n goes to infinity. |
| Keywords: | Compact action sets; Uniform value; Asymptotic behavior; Zero sum stochastic games; |
| JEL: | C73 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:dau:papers:123456789/10880&r=gth |
| By: | Stéphane Gonzalez (Centre d'Economie de la Sorbonne - Paris School of Economics); Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | The paper proposes a new concept of solution for TU games, called multicoalitional solution, which makes sense in the context of production games, that is, where v(S) is the production or income per unit of time. By contrast to classical solutions where elements of the solution are payoff vectors, multicoalitional solutions give in addition an allocation time to each coalition, which permits to realize the payoff vector. We give two instances of such solutions, called the d-multicoalitional core and the c-multicoalitional core, and both arise as the strong Nash equilibrium of two games, where in the first utility per active unit of time is maximized, while in the second it is the utility per total unit of time. We show that the d-core (or aspiration core) of Benett, and the c-core of Guesnerie and Oddou are strongly related to the d-multicoalitional and c-multicoalitional cores, respectively, and that the latter ones can be seen as an implementation of the former ones in a noncooperative framework. |
| Keywords: | Cooperative game, core, aspiration core, strong Nash equilibrium. |
| JEL: | C71 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:13062&r=gth |
| By: | Joyee Deb; Julio González Díaz; Jérôme Renault |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:ste:nystbu:13-16&r=gth |
| By: | Sylvain Béal (CRESE, Université de Franche-Comté); Eric Rémila (Gate Lyon Saint-Etienne, Université de Saint-etienne); Philippe Solal (Gate Lyon Saint-Etienne, Université de Saint-etienne) |
| Abstract: | In Béal et al. (2013) two new axioms of invariance, called Addition invariance and Transfer invariance respectively, are introduced to design allocation rules for TU-games. Here, we derive direct sum decompositions of the linear space of TU-games by using the TU-games selected to construct the operations of Addition and Transfer. These decompositions allow us to recover previous characterization results obtained by Béal et al. (2013), to provide new characterizations of well-known (class of) of allocation rules and also to design new allocation rules. |
| Keywords: | addition invariance, transfer invariance, direct-sum decomposition, allocation rules |
| JEL: | C71 |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2013-08&r=gth |
| By: | Geoffroy de Clippel (Dept. of Economics, Brown University); Kareen Rozen (Cowles Foundation, Yale University) |
| Abstract: | This paper experimentally investigates cooperative game theory from a normative perspective. Subjects designated as Decision Makers express their view on what is fair for others, by recommending a payoff allocation for three subjects (Recipients) whose substitutabilities and complementarities are captured by a characteristic function. We show that axioms and solution concepts from cooperative game theory provide valuable insights into the data. Axiomatic and regression analysis suggest that Decision Makers' choices can be (noisily) described as a convex combination of the Shapley value and equal split solution. A mixture model analysis, examining the distribution of Just Deserts indices describing how far one goes in the direction of the Shapley value, reveals heterogeneity across characteristic functions. Aggregating opinions by averaging, however, shows that the societal view of what is fair remains remarkably consistent across problems. |
| Keywords: | Cooperative game theory, Fairness, Experiment |
| JEL: | D63 D03 C71 C91 |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1925&r=gth |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Benjamin Brooks (Dept. of Economics, Princeton University); Stephen Morris (Dept. of Economics, Princeton University) |
| Abstract: | We study how the outcomes of a private-value first price auction can vary with bidders' information, for a fixed distribution of private values. In a two bidder, two value, setting, we characterize all combinations of bidder surplus and revenue that can arise, and identify the information structure that minimizes revenue. The extremal information structure that minimizes revenue entails each bidder observing a noisy and correlated signal about the other bidder's value. In the general environment with many bidders and many values, we characterize the minimum bidder surplus of each bidder and maximum revenue across all information structures. The extremal information structure that simultaneously attains these bounds entails an efficient allocation, bidders knowing whether they will win or lose, losers bidding their true value and winners being induced to bid high by partial information about the highest losing bid. Our analysis uses a linear algebraic characterization of equilibria across all information structures, and we report simulations of properties of the set of all equilibria. |
| Keywords: | First price auction, Mechanism design, Robust predictions, Private information, Bayes correlated equilibrium |
| JEL: | C72 D44 D82 D83 |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1926&r=gth |
| By: | Michalis Drouvelis (University of Birmingham); Alejandro Saporiti (University of Manchester); Nicolaas J. Vriend (Queen Mary, University of London) |
| Abstract: | classical one-dimensional election game with two candidates. These candidates are interested in power and ideology, but their weights on these two motives are not necessarily identical. Apart from obtaining the well known median voter result and the two-sided policy differentiation outcome, the paper uncovers the existence of two new equilibrium configurations, called 'one-sided' and 'probabilistic' policy differentiation, respectively. Our analysis shows how these equilibrium configurations depend on the relative interests in power (resp., ideology) and the uncertainty about voters' preferences. The theoretical predictions are supported by the data collected from a laboratory experiment, as we observe convergence to the Nash equilibrium values at the aggregate as well as at the individual levels in all treatments, and the comparative statics effects across treatments are as predicted by the theory. |
| Keywords: | Electoral competition, Power, Ideology, Uncertainty, Nash equilibrium, Experimental evidence. |
| JEL: | C72 C90 D72 |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp710&r=gth |
| By: | Dal Bó, Pedro; Fréchette, Guillaume R. |
| Abstract: | We use a novel experimental design to identify the subjects' strategies in an infinitely repeated prisoners' dilemma experiment. We ask subjects to design strategies that will play in their place. We find that eliciting strategies has negligible effects on their behavior, supporting the validity of this method. We find the chosen strategies include some common ones such as Tit-For-Tat and Grim trigger. However, other strategies that are considered to have desirable properties, such as Win-Stay-Lose-Shift, are not prevalent. We also find that the strategies used to support cooperation change with the parameters of the game. Finally, our results confirm that long-run miscoordination can arise. -- In einem neuen experimentellen Design versuchen wir die Strategien von Teilnehmern an einem unendlich wiederholten 'Gefangenendilemma' zu identifizieren. Die Teilnehmer werden gebeten, Strategien zu entwerfen, die an ihrer Stelle spielen sollen. Dabei stellt sich heraus, dass die Erhebung von Strategien nur marginale Auswirkungen auf das Verhalten der Teilnehmer hat, was für die Validität dieser Methode spricht. Unter den gewählten Strategien sind allgemein verbreitete, wie Tit-for-Tat und Grim-Trigger. Andere Strategien dagegen mit erwünschten Eigenschaften wie das 'Win-Stay, Lose-Shift' sind hingegen nicht so gebräuchlich. Zudem stellt sich heraus, dass die Strategien, die Kooperation unterstützen sollen, sich mit den Parametern des Spiels verändern. Schließlich belegen unsere Resultate, dass es zu einer langfristigen Fehlkoordination kommen kann. |
| Keywords: | infinitely repeated games,prisoner's dilemma,cooperation,strategies,experimental economics |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbeoc:spii2013311&r=gth |
| By: | Lisa Bruttel (Department of Economics, University of Konstanz, Germany); Tim Friehe (Center for Advanced Studies in Law and Economics, University of Bonn, Germany) |
| Abstract: | This paper presents results from an experiment studying a two-person 4x4 pure coordination game. We seek to identify a labeling of actions that induces subjects to select all options with the same probability. Such a display of actions must be free from salient properties that might be used by participants to coordinate. Testing 23 different sets of labels, we identify two sets that produce a distribution of subjects’ choices which approximate the uniform distribution quite well. Our design can be used in studies intending to compare the behavior of subjects who play against a random mechanism with that of participants who play against human counterparts. |
| Keywords: | coordination game, experiment, mixed strategy, level k |
| JEL: | C71 C92 D83 |
| Date: | 2013–07–19 |
| URL: | http://d.repec.org/n?u=RePEc:knz:dpteco:1320&r=gth |
| By: | Manuel Förster (CORE - Université Catholique de Louvain et Centre d'Economie de la Sorbonne); Ana Mauleon (CORE - Université Catholique de Louvain et CEREC - Université Saint-Louis - Bruxelles); Vincent Vannetelbosch (Università di Trento and LEM Scuola Superiore Sant'Anna) |
| Abstract: | We investigate the role of manipulation in a model of opinion formation where agents have opinions about some common question of interest. Agents repeatedly communicate with their neighbors in the social network, can exert some effort to manipulate the trust of others, and update their opinions taking weighted averages of neighbors' opinions. The incentives to manipulate are given by the agents' preferences. We show that manipulation can modify the trust structure and lead to a connected society, and thus, make the society reaching a consensus. Manipulation fosters opinion leadership, but the manipulated agent may even gain influence on the long-run opinions. In sufficiently homophilic societies, manipulation accelerates (slows down) convergence if it decreases (increases) homophily. Finally, we investigate the tension between information aggregation and spread of misinformation. We find that if the ability of the manipulating agent is weak and the agents underselling (overselling) their information gain (lose) overall influence, then manipulation reduces misinformation and agents converge jointly to more accurate opinions about some underlying true state. |
| Keywords: | Social networks, trust, manipulation, opinion leadership, consensus, Wisdom of crowds. |
| JEL: | D83 D85 Z13 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:13065&r=gth |
| By: | Huijink, S.; Borm, P.E.M.; Reijnierse, J.H.; Kleppe, J. (Tilburg University, Center for Economic Research) |
| Abstract: | Abstract: This article characterizes the per capita nucleolus for bankruptcy games as a bankruptcy rule. This rule, called the cligths rule, is based on the wellknown constrained equal awards principle. The essential feature of the rule however is that, for each bankruptcy problem, it takes into account a vector of clights. These clights only depend on the vector of claims while the height of the estate determines whether the clights should be interpreted as modified claims or as rights. Finally, it is seen that both the clights rule and the Aumann-Maschler rule can be captured within the family of so-called claim and right rules. |
| Keywords: | Bankruptcy;(per capita) nucleolus |
| JEL: | C71 G33 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2013059&r=gth |
| By: | Toomas Hinnosaar |
| Abstract: | I study an auction format called penny auctions. In these auctions, every bid increases the price by a small amount, but it is costly to place a bid. The auction ends if more than some predetermined amount of time has passed since the last bid. Outcomes of real penny auctions are surprising: even selling cash can give the seller an order of magnitude higher or lower revenue than the nominal value. Sometimes the winner of the auction pays very little compared to many of the losers at the same auction. The unexpected outcomes have led to the accusations that the penny auction sites are either scams or gambling or both. I propose a tractable model of penny auctions and show that the high variance of outcomes is a property of the auction format. Even absent of any randomization, the equilibria in penny auctions are close to lotteries from the buyers’ perspective. |
| Keywords: | penny auction, Internet auctions, bid fees, gambling |
| JEL: | D11 D44 C73 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:cca:wpaper:305&r=gth |