|
on Game Theory |
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Issue of 2013‒05‒19
twenty-two papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Rene van den Brink (VU University Amsterdam); Chris Dietz (VU University Amsterdam) |
| Abstract: | A situation in which a finite set of agents can generate certain payoffs by cooperation can be described by a cooperative game with transferable utility (or simply a TU-game) where each agent is represented by one player in the game. In this paper, we assume that one agent can be represented by more than one player. We introduce two solutions for this multi-player agent game model, both being generalizations of the Shapley value for TU-games. The first is the agent-Shapley value and considers the agents in the most unified way in the sense that when an agent enters a coalition then it enters with all its players. The second is the player-Shapley value which takes all players as units, and the payoff of an agent is the sum of the payoffs over all its players. We provide axiomatic characterizations of these two solutions that differ only in a collusion neutrality axiom. The agent-Shapley value satisfies player collusion neutrality stating that collusion of two players belonging to the same agent does not change the payoff of this agent. On the other hand, the player-Shapley value satisfies agent collusion neutrality stating that after a collusion of two agents, the sum of their payoffs does not change. After axiomatizing the player- and agent-Shapley values we apply them to airport games and voting games. |
| Keywords: | Cooperative TU-game, Shapley value, multi-player agent, collusion neutrality, airport games |
| JEL: | C71 |
| Date: | 2012–01–02 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012001&r=gth |
| By: | Rene van den Brink (VU University Amsterdam); Miklos Pinter (Corvinus University) |
| Abstract: | We consider the problem of axiomatizing the Shapley value on the class of assignment games. We first show that several axiomatizations of the Shapley value on the class of all TU-games do not characterize this solution on the class of assignment games by providing alternative solutions that satisfy these axioms. However, when considering an assignment game as a communication graph game where the game is simply the assignment game and the graph is a corresponding bipartite graph buyers are connected with sellers only, we show that Myerson's component efficiency and fairness axioms do characterize the Shapley value on the class of assignment games. Moreover, these two axioms have a natural interpretation for assignment games. Component efficiency yields submarket efficiency stating that the sum of the payoffs of all players in a submarket equals the worth of that submarket, where a submarket is a set of buyers and sellers such that all buyers in this set hav e zero valuation for the goods offered by the sellers outside the set, and all buyers outside the set have zero valuations for the goods offered by sellers inside the set. Fairness of the graph game solution boils down to valuation fairness stating that only changing the valuation of one particular buyer for the good offered by a particular seller changes the payoffs of this buyer and seller by the same amount. |
| Keywords: | Assignment game, Shapley value, communication graph game, submarket efficiency, valuation fairness |
| JEL: | C71 C78 |
| Date: | 2012–09–13 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012092&r=gth |
| By: | Rene van den Brink (VU University Amsterdam); Chris Dietz (VU University Amsterdam) |
| Abstract: | It is known that peer group games are a special class of games with a permission structure. However, peer group games are also a special class of (weighted) digraph games. To be specific, they are digraph games in which the digraph is the transitive closure of a rooted tree. In this paper we first argue that some known results on solutions for peer group games hold more general for digraph games. Second, we generalize both digraph games as well as games with a permission structure into a model called games with a local permission structure, where every player needs permission from its predecessors only in order to generate worth, but does not need its predecessors in order to give permission to its own successors. We introduce and axiomatize a Shapley value type solution for these games, generalizing the conjunctive permission value for games with a permission structure and the beta-measure for weighted digraphs. |
| Keywords: | Cooperative TU-game, peer group game, digraph game, game with a permission structure, local permission structure |
| JEL: | C71 |
| Date: | 2012–11–27 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012126&r=gth |
| By: | Rene van den Brink (VU University Amsterdam); Youngsub Chun (Seoul National University); Yukihiko Funaki (Waseda University); Boram Park (Rutgers University) |
| Abstract: | A (point-valued) solution for cooperative games with transferable utility, or simply TU-games, assigns a payoff vector to every TU-game. In this paper we discuss two classes of equal surplus sharing solutions, one consisting of all convex combinations of the equal division solution and the CIS-value, and its dual class consisting of all convex combinations of the equal division solution and the ENSC-value. We provide several characterizations using either population solidarity or a reduced game consistency in addition to other standard properties. |
| Keywords: | TU-game, equal division solution, CIS-value, ENSC-value, population solidarity, consistency |
| JEL: | C71 |
| Date: | 2012–12–07 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012136&r=gth |
| By: | Mikel Alvarez-Mozos (University of Santiago de Compostela); Rene van den Brink (VU University Amsterdam); Gerard van der Laan (VU University Amsterdam); Oriol Tejada (ETH Zuerich) |
| Abstract: | In a standard TU-game it is assumed that every subset of the player set can form a coalition and earn its worth. One of the first models where restrictions in cooperation are considered is the one of games with coalition structure. In such games the player set is partitioned into unions and players can only cooperate within their own union. Owen introduced a value for games with coalition structure under the assumption that also the unions can cooperate among them. Winter extended this value to games with levels structure of cooperation, which consists of a game and a finite sequence of partitions defined on the player set, each of them being coarser than the previous one. A share function for TU-games is a type of solution that assigns to every game a vector whose components add up to one, and thus they can be interpreted as players' shares in the worth to be allocated. Extending the approach to games with coalition structure developed by van den Brink and van der Laan (2005), we introduce a class of share functions for games with levels structure of cooperation by defining, for each player and each level, a standard TU-game. The share given to each player is then defined as the product of her shares in the games at every level. We show several desirable properties and provide axiomatic characterizations of this class of LS-share functions. |
| Keywords: | cooperative game, Shapley value, coalition structure, share functions, levels structure of cooperation |
| JEL: | C71 |
| Date: | 2012–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012052&r=gth |
| By: | Genjiu Xu (Northwestern Polytechnical University, Xi'an, P.R. China); René van den Brink (VU University Amsterdam); Gerard van der Laan (VU University Amsterdam); Hao Sun (Northwestern Polytechnical University, Xi'an, P.R. China) |
| Abstract: | Hamiache (2001) assigns to every TU game a so-called associated game and then shows that the Shapley value is characterized as the unique solution for TU games satisfying the inessential game property, continuity and associated consistency. The latter notion means that for every game the Shapley value of the associated game is equal to the Shapley value of the game itself. In this paper we show that also the EANS-value as well as the CIS-value are characterized by these three properties for appropriately modified notions of the associated game. This shows that these three values only differ with respect to the associated game. The characterization is obtained by applying the matrix approach as the pivotal technique for characterizing linear values of TU games in terms of associated consistency. |
| Keywords: | TU games, Shapley value, EANS-value, CIS-value, associated consistency, matrix approach |
| JEL: | C71 |
| Date: | 2012–10–08 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012105&r=gth |
| By: | Rene van den Brink (VU University Amsterdam); Jean-Jacques Herings (Maastricht University); Gerard van der Laan (VU University Amsterdam); Dolf Talman (Tilburg University) |
| Abstract: | In the literature various models of games with restricted cooperation can be found. In those models, instead of allowing for all subsets of the set of players to form, it is assumed that the set of feasible coalitions is a proper subset of the power set of the set of players. In this paper we consider such sets of feasible coalitions that follow from a permission structure on the set of players, in which players need permission to cooperate with other players. We assume the permission structure to be an oriented tree. This means that there is one player at the top of the permission structure and for every other player there is a unique directed path from the top player to this player. We introduce a new solution for these games based on the idea of the Average Tree value for cycle-free communication graph games. We provide two axiomatizations for this new value and compare it with the conjunctive permission value. |
| Keywords: | TU game, restricted cooperation, permission structure, Shapley value, Average Tree value, axiomatization |
| JEL: | C71 |
| Date: | 2012–01–24 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012023&r=gth |
| By: | Matthijs van Veelen (University of Amsterdam); Julian Garcia (Max-Planck-Institute for Evolutionary Biology) |
| Abstract: | We explore evolutionary dynamics for repeated games with small, but positive complexity costs. To understand the dynamics, we extend a folk theorem result by Cooper (1996) to continuation probabilities, or discount rates, smaller than 1. While this result delineates which payoffs can be supported by neutrally stable strategies, the only strategy that is evolutionarily stable, and has a uniform invasion barrier, is All D. However, with sufficiently small complexity costs, indirect invasions - but now through 'almost neutral' mutants - become an important ingredient of the dynamics. These indirect invasions include stepping stone paths out of full defection. |
| Keywords: | repeated games, evolutionary game theory, complexity costs, indirect invasions, robustness against indirect invasions, neutrally stable strategy, evolutionarily stable strategy, iterated prisoners dilemma |
| JEL: | C73 |
| Date: | 2012–09–06 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012089&r=gth |
| By: | Arantza Estevez-Fernandez (VU University Amsterdam); Hans Reijnierse (CentER, Tilburg University) |
| Abstract: | In this paper, we analyze cost sharing problems arising from a general service by explicitly taking into account the generated revenues. To this cost-revenue sharing problem, we associate a cooperative game with transferable utility, called cost-revenue game. By considering cooperation among the agents using the general service, the value of a coalition is defined as the maximum net profit that the coalition may obtain by means of cooperation. As a result, a coalition may profit from not allowing all its members to get the service that generates the revenues. We focus on the study of the core of cost-revenue games. Under the assumption that cooperation among the members of the grand coalition grants the use of the service under consideration to all its members, it is shown that a cost-revenue game has a non-empty core for any vector of revenues if, and only if, the dual game of the cost game has a large core. Using this result, we investigate minimum cost spanning tree games with revenues. We show that if every connection cost can take only two values (low or high cost), then, the corresponding minimum cost spanning tree game with revenues has a non-empty core. Furthermore, we provide an example of a minimum cost spanning tree game with revenues with an empty core where every connection cost can take only one of three values (low, medium, or high cost). |
| Keywords: | Cost-revenue allocation problem, cooperative game, core, minimum cost spanning tree problem |
| JEL: | C71 |
| Date: | 2012–09–27 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012101&r=gth |
| By: | Arantza Estévez-Fernández (VU University Amsterdam); María Gloria Fiestras-Janeiro (Vigo University); Manuel Alfredo Mosquera (Vigo University); Estela Sánchez- Rodríguez (Vigo University) |
| Abstract: | In this paper we establish a relationship between the core cover of a compromise admissible game and the core of a particular bankruptcy game: the core cover of a compromise admissible game is, indeed, a translation of the set of coalitional stable allocations captured by an associated bankruptcy game. Moreover, we analyze the combinatorial complexity of the core cover and, consequently, of the core of a compromise stable game. |
| Keywords: | Cooperative game theory, compromise admissible games, bankruptcy, core cover, complexity |
| JEL: | C71 |
| Date: | 2012–02–10 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012012&r=gth |
| By: | Conrado Manuel (Universidad Complutense de Madrid); Enrique Gonzalez-Aranguena (Universidad Complutense de Madrid); Rene van den Brink| (VU University Amsterdam) |
| Abstract: | In this paper we provide new axiomatizations of the Shapley value for TU-games using axioms that are based on relational aspects in the interactions among players. Some of these relational aspects, in particular the economic or social interest of each player in cooperating with each other, can be found embedded in the characteristic function. We define a particular relation among the players that it is based on mutual indifference. The first new axiom expresses that the payoffs of two players who are not indifferent to each other are affected in the same way if they become enemies and do not cooperate with each other anymore. The second new axiom expresses that the payoff of a player is not affected if players to whom it is indifferent leave the game. We show that the Shapley value is characterized by these two axioms together with the well-known efficiency axiom. Further, we show that another axiomatization of the Shapley value is obtained if we replace t he second axiom and efficiency by the axiom which applies the efficiency condition to every class of indifferent players. Finally, we extend the previous results to the case of weighted Shapley values. |
| Keywords: | TU-game, Shapley value, axiomatization, indifferent players, weighted Shapley values |
| JEL: | C71 |
| Date: | 2012–04–11 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012036&r=gth |
| By: | Giuseppe De Marco (Università di Napoli Parthenope and CSEF); Maria Romaniello (Seconda Università di Napoli) |
| Abstract: | In this paper, we look at the (Kajii and Ui) mixed equilibrium notion, which has been recognized by previous literature as a natural solution concept for incomplete information games in which players have multiple priors on the space of payoff relevant states. We investigate the problem of stability of mixed equilibria with respect to perturbations on the sets of multiple priors. We find out that the (Painlevé-Kuratowski) convergence of posteriors ensures that stability holds; whereas, convergence of priors is not enough to obtain stability since it does not always implies convergence of posteriors when we consider updating rules (for multiple priors) based on the classical Bayesian approach. |
| Keywords: | Incomplete information games, multiple priors, equilibrium stability |
| Date: | 2013–05–13 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:332&r=gth |
| By: | Pascal Billand (Universite de Lyon, Universite Jean Monnet, Saint-Etienne, CNRS, GATE); Christophe Bravard (Universite de Lyon, Universite Jean Monnet, Saint-Etienne, CNRS, GATE); Jurjen Kamphorst (Erasmus University Rotterdam); Sudipta Sarangi (DIW Berlin and Louisiana State University) |
| Abstract: | Social networks, be it on the internet or in real life, facilitate information flows. We model this by giving agents incentives to link with others and receive information through those links. In many networks agents will value confirmation of the information they receive from others. Our paper analyzes the impact such a need for confirmation has on the social networks which are formed. We first study the existence of Nash equilibria and then characterize the set of strict Nash networks. Next, we characterize the set of strictly efficient networks and discuss the relationship between strictly efficient networks and strict Nash networks. |
| Keywords: | connections model, confirmation, two-way flow models |
| JEL: | C72 D85 |
| Date: | 2012–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012019&r=gth |
| By: | Jona Linde (University of Amsterdam); Joep Sonnemans (University of Amsterdam); Jan Tuinstra (University of Amsterdam) |
| Abstract: | Minority games are a stylized description of strategic situations with both coordination and competition. These games are widely studied using either simulations or laboratory experiments. Simulations can show the dynamics of aggregate behavior, but the results of such simulations depend on the type of strategies used. So far experiments provided little guidance on the type of strategies people use because the set of possible strategies is very large. We therefore use a multi-round strategy method experiment to directly elicit people's strategies. Between rounds participants can adjust their strategy and test the performance of (possible) new strategies against strategies from the previous round. Strategies gathered in the experiment are subjected to an evolutionary competition. The strategies people use are very heterogeneous although aggregate outcomes resemble the symmetric Nash equilibrium. The strategies that survive evolutionary competition achieve much higher levels of coordination. |
| Keywords: | minority game, strategy experiment, evolution, simulation |
| JEL: | C63 C72 C91 D03 |
| Date: | 2013–03–07 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2013043&r=gth |
| By: | Harold Houba (VU University Amsterdam); Gerard van der Laan (VU University Amsterdam); Yuyu Zeng (VU University Amsterdam) |
| Abstract: | We study multiple agents along a general river structure that is expressed by a geography matrix and who have access to limited local resources, quasi-linear preferences over water and money and cost functions dependent upon river inflow and own extraction. Unanimity bargaining determines the water allocation and monetary transfers. We translate International Water Law into either disagreement outcomes or individual aspiration levels. In the former case, we apply the asymmetric Nash bargaining solution, in the latter case the agents have to compromise in order to agree and we apply the asymmetric Nash rationing solution. In both cases the optimization problem is separable into two subproblems: the efficient water allocation that maximizes utilitarian welfare given the geography matrix; and the determination of the monetary transfers associated with the weights. We show that the Nash rationing solution may result in nonparticipation, therefore we generalize to the case with participation constraints. |
| Keywords: | River Basin Management, International Water Law, Negotiations, Externalities, Political Economy of Property Rights |
| JEL: | C70 D60 Q53 |
| Date: | 2013–04–02 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2013051&r=gth |
| By: | Gerard van der Laan (VU University Amsterdam); Nigel Moes (VU University Amsterdam) |
| Abstract: | In this paper we study international river pollution problems. We introduce a model in which the agents (countries) located along a river derive benefit while causing pollution, but also incur environmental costs of experiencing pollution from all upstream agents. We find that total pollution in the model decreases when the agents decide to cooperate. The resulting gain in social welfare can be distributed among the agents based on the property rights over the river. Using principles from international water law we suggest 'fair' ways of distributing the property rights and therefore the cooperative gain. |
| Keywords: | international river, pollution, externality, property rights, value |
| JEL: | C70 D60 Q53 |
| Date: | 2012–01–19 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012006&r=gth |
| By: | Yukihiko Funaki (Waseda University); Harold Houba (VU University Amsterdam); Evgenia Motchenkova (VU University Amsterdam) |
| Abstract: | We consider price-fee competition in bilateral oligopolies with perfectly-divisible goods, non-expandable infrastructures, concentrated agents on both sides, and constant marginal costs. We define and characterize stable market outcomes. Buyers exclusively trade with the supplier with whom they achieve maximal bilateral joint welfare. Prices equal marginal costs. Threats to switch suppliers set maximal fees. These also arise from a negotiation model that extends price competition. Competition in both prices and fees necessarily emerges. It improves welfare compared to price competition, but consumer surpluses do not increase. The minimal infrastructure achieving maximal aggregate welfare differs from the one that protects buyers most. |
| Keywords: | Assignment Games, Infrastructure, Negotiations, Non-linear pricing, Market Power, Countervailing power |
| JEL: | C78 L10 L14 D43 R10 |
| Date: | 2012–12–14 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012139&r=gth |
| By: | Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group); Anastasios Koukoumelis (Max Planck Institute of Economics, Strategic Interaction Group); M. Vittoria Levati (Max Planck Institute of Economics, Strategic Interaction Group, and Department of Economics, University of Verona); Matteo Ploner (DECO-CEEL, University of Trento) |
| Abstract: | This paper experimentally examines a procedurally fair provision mech- anism allowing members of a small community to determine, via their bids, which of four alternative public projects to implement. Previous experi- ments with positive cost projects have demonstrated that the mechanism is efficiency enhancing. Our experiment tests whether the mechanism re- mains conducive to efficiency when negative cost, but less efficient, projects are made available. We find that this is not the case. On the other hand, we detect no significant difference in bid levels depending on whether mixed feelings are present or absent, and on whether the others' valuations are known or unknown. |
| Keywords: | Public projects, Bidding behavior, Procedural fairness, Experiment |
| JEL: | C72 C92 D63 H44 |
| Date: | 2013–05–13 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2013-021&r=gth |
| By: | Byeongju Jeong |
| Abstract: | I present a model in which randomly matched pairs of people bargain over the division of output in each period. Output can be consumed or stored for later consumption. People are identical except possibly in wealth (i.e., the stored output). The one-period utility is linear except for the starvation disutility (i.e., the additional drop in utility under no consumption). The starvation disutility weakens the bargaining position of a poor person and strengthens that of a rich person in an otherwise symmetric bargaining, providing the incentive to accumulate wealth. Policies that deincentivize wealth accumulation (e.g., wealth tax, progressive income tax) can make both the rich and the poor become better off. matters. |
| Keywords: | bargain; wealth accumulation; starvation disutility; wealth tax; income tax; |
| JEL: | C78 D31 E21 H21 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:cer:papers:wp479&r=gth |
| By: | René van den Brink (VU University Amsterdam); Frank Steffen (The University of Liverpool Management School) |
| Abstract: | The main purpose of the present paper is to disentangle the mix-up of the notions of success and satisfaction which is prevailing in the voting power literature. We demonstrate that both notions are conceptually distinct, and discuss their relationship and measurement. We show that satisfaction contains success as one component, and that both coincide under the canonical set-up of a simultaneous decision-making mechanism as it is predominant in the voting power literature. However, we provide two examples of sequential decision-making mechanisms in order to illustrate the difference between success and satisfaction. In the context of the discussion of both notions we also address their relationship to different types of luck. |
| Keywords: | success, satisfaction, luck, power |
| JEL: | C79 D02 D71 |
| Date: | 2012–03–27 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012030&r=gth |
| By: | Enke, Benjamin (University of Bonn); Zimmermann, Florian (University of Bonn) |
| Abstract: | Many information structures generate correlated rather than mutually independent signals, the news media being a prime example. This paper shows experimentally that in such contexts many people neglect these correlations in the updating process and treat correlated information as independent. In consequence, people's beliefs are excessively sensitive to well-connected information sources, implying a pattern of "overshooting" beliefs. Additionally, in an experimental asset market, correlation neglect not only drives overoptimism and overpessimism at the individual level, but also affects aggregate outcomes in a systematic manner. In particular, the excessive confidence swings caused by correlated signals give rise to predictable price bubbles and crashes. These findings are reminiscent of popular narratives according to which aggregate booms and busts might be driven by the spread of "stories". Our results also lend direct support to recent models of boundedly rational social learning. |
| Keywords: | beliefs, correlation neglect, experiments, markets, overshooting |
| JEL: | C91 D03 D83 D84 D40 |
| Date: | 2013–04 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp7372&r=gth |
| By: | Ramon Flores (Universidad Carlos III de Madrid); Maurice Koster (University of Amsterdam); Ines Lindner (VU University Amsterdam); Elisenda Molina (Universidad Carlos III de Madrid) |
| Abstract: | This paper proposes a new measure for a group's ability to lead society to adopt their standard of behavior, which in particular takes account of the time the group takes to convince the whole society to adopt their position. This notion of a group's power to initiate action is computed as the reciprocal of the resistance against it, which is in turn given by the expected absorption time of a related finite state partial Markov chain that captures the social dynamics. The measure is applicable and meaningful in a variety of models where interaction between agents is formalized through (weighted) binary relations. Using Percolation Theory, it is shown that the group power is monotonic as a function of groups of agents. We also explain the differences between our measure and those discussed in the literature on Graph Theory, and illustrate all these concerns by a thorough analysis of two particular cases: the Wolfe Primate Data and the 11S hijackers' network. |
| Keywords: | Collective action, Social networks, Influence and diffusion models, Network intervention, Group centrality measures |
| JEL: | C79 D01 D71 |
| Date: | 2012–03–29 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2012032&r=gth |