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on Game Theory |
| By: | Christian Trudeau (Department of Economics, University of Windsor); Juan Vidal-Puga (Research Group of Economic Analysis and Departamento de Estatistica e IO, Universidade de Vigo) |
| Abstract: | We introduce a new family of cooperative games for which there is coincidence between the nucleolus and the Shapley value. These so-called clique games are such that players are divided into cliques, with the value created by a coalition linearly increasing with the number of agents belonging to the same clique. Agents can belong to multiple cliques, but for a pair of cliques, at most a single agent belong to their intersection. Finally, if two players do not belong to the same clique, there is at most one way to link the two players through a chain of players, with any two adjacent players in the chain belonging to a common clique. We provide multiple examples for clique games, chief among them minimum cost spanning tree problems. This allows us to obtain new correspondence results between the nucleolus and the Shapley value, as well as other cost sharing methods for the minimum cost spanning tree problem. |
| Keywords: | nucleolus; Shapley value; clique; minimum cost spanning tree. |
| JEL: | C71 D63 |
| Date: | 2017–07 |
| URL: | http://d.repec.org/n?u=RePEc:wis:wpaper:1705&r=gth |
| By: | Oriol Tejada (ETH-Zurich); Mikel Álvarez-Mozos (Universitat de Barcelona) |
| Abstract: | We analyze surplus allocation problems where cooperation between agents is restricted both by a communication graph and by a sequence of embedded partitions of the agent set. For this type of problem, we define and characterize two new values extending the Shapley value and the Banzhaf value respectively. Our results enable the axiomatic comparison between the two values and provide some basic insights for the analysis of fair resource allocation in nowadays fully integrated societies. |
| Keywords: | Coalitional games, Restricted cooperation, Graph restricted communication, Levels structure, Shapley value, Banzhaf value. |
| JEL: | C7 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:ewp:wpaper:363web&r=gth |
| By: | Rene J.R. van den Brink (Vrije Universiteit Amsterdam; Tinbergen Institute, The Netherlands); Agnieszka Rusinowska (Paris School of Economics -- CNRS, University Paris 1) |
| Abstract: | In this paper, we connect the social network theory on centrality measures to the economic theory of preferences and utility. Using the fact that networks form a special class of cooperative TU-games, we provide a foundation for the degree measure as a von Neumann-Morgenstern expected utility function reflecting preferences over being in different positions in different networks. The famous degree measure assigns to every position in a weighted network the sum of the weights of all links with its neighbours. A crucial property of a preference relation over network positions is neutrality to ordinary risk. If a preference relation over network positions satisfies this property and some regularity properties, then it must be represented by a utility function that is a multiple of the degree centrality measure. We show this in three steps. First, we characterize the degree measure as a centrality measure for weighted networks using four natural axioms. Second, we relate these network centrality axioms to properties of preference relations over positions in networks. Third, we show that the expected utility function is equal to a multiple of the degree measure if and only if it represents a regular preference relation that is neutral to ordinary risk. Similarly, we characterize a class of affine combinations of the outdegree and indegree measure in weighted directed networks and deliver its interpretation as a von Neumann-Morgenstern expected utility function. |
| Keywords: | Weighted network; network centrality; utility function; degree centrality; von Neumann-Morgenstern expected utility function; cooperative TU-game; weighted directed network. |
| JEL: | D81 D85 C02 |
| Date: | 2017–07–25 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20170065&r=gth |
| By: | Antonio Jiménez-Martínez (Division of Economics, CIDE) |
| Abstract: | This paper considers a population of agents that are connected through a network that allows them to aggregate locally their pieces of private information about some uncertain (exogenous) parameter of interest. The agents wish to match their actions to the true value of the parameter and to the actions of the other agents. I ask how the design of (interim) efficient (minimally connected) networks depends on the level of complementarity in the agents’ actions. When the level of complementarity is either low or high, efficient networks are characterized by a high number of different neighborhoods and, as a consequence, by low levels of connectivity. For intermediate levels of complementarity in actions, efficient networks tend to feature low numbers of highly connected neighborhoods. The implications of this paper are relevant in security environments where agents are naturally interpreted as analysts who try to forecast the value of a parameter that describes a potential threat to security. |
| Keywords: | Networks, information aggregation, beauty-contests, strategic complementarity, efficiency |
| JEL: | C72 D83 D84 D85 |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:emc:wpaper:dte601&r=gth |
| By: | Cano Berlanga, Sebastian; Vilella, Cori |
| Abstract: | The current paper studies the attribution model used by Google Analytics. Precisely, we use the Cooperative Game Theory to propose a fair distribution of the revenues among the considered channels, in order to facilitate the cooperation and to guarantee stability. We define a transferable utility convex cooperative game from the observed frequencies and we use the Shapley value to allocate the revenues among the di erent channels. Furthermore, we evaluate the impact of an advertising campaign on both, the whole system and each channel. Keywords: attribution model; Shapley value; on-line sales; Cooperative Game Theory |
| Keywords: | Jocs cooperatius, 33 - Economia, |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:urv:wpaper:2072/290758&r=gth |
| By: | Osório, António (António Miguel) |
| Abstract: | This paper examines different Brownian information structures over varying time intervals. We focus on the non-limit case, and on the trade-offs between information quality and quantity when making a decision whether to cooperate or defect in a prisoners' dilemma game. In the best-case scenario, the information quality gains are strong enough so that agents can substitute information quantity with information quality. In the second best-case scenario, the information quality gains are weak and must be compensated for with additional information quantity. In this case, information quality improves but not quickly enough to dispense with the use of information quantity. For suficiently large time intervals, information degrades and monitoring becomes mostly based on information quantity. The results depend crucially on the particular information structure and on the rate at which information quality improves or decays with respect to the discounting incentives. JEL: C73, D82, D86. KEYWORDS: Repeated Games; Frequent Monitoring; Information Quantity; In- formation Quality. |
| Keywords: | Jocs, Teoria de, Informació, Teoria de la, 33 - Economia, |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:urv:wpaper:2072/290761&r=gth |
| By: | Philippe Bich (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics); Lisa Morhaim (CRED - Centre de Recherche en Economie et Droit - UP2 - Université Panthéon-Assas - M.E.N.E.S.R. - Ministère de l'Éducation nationale, de l’Enseignement supérieur et de la Recherche) |
| Abstract: | We provide the existence of pairwise stable weighted networks under assumptions similar to Nash theorem. In particular, contrarily to the case of unweighted networks, the existence of closed improving cycles does not prevent the existence of Pairwise stable weighted networks. Then, we extend our existence result, allowing payoffs to depend on some game-theoretic strategies. Many applications are given. |
| Keywords: | Pairwise Stable Network,Weighted Network |
| Date: | 2017–07–19 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01564591&r=gth |
| By: | Yutaka Kayaba (Faculty of Economics, The University of Tokyo); Hitoshi Matsushima (Faculty of Economics, The University of Tokyo); Tomohisa Toyama (Division of Liberal Arts, Kogakuin University, The University of Tokyo) |
| Abstract: | We experimentally examine repeated prisoner’s dilemma with random termination, in which monitoring is imperfect and private. Our estimation indicates that a significant proportion of subjects follow generous tit-for-tat strategies, straightforward extensions of tit-for-tat. However, the observed retaliating policies are inconsistent with the generous tit-for-tat equilibria. Contrary to the theory, subjects tend to retaliate more with high accuracy than with low accuracy. Specifically, they tend to retaliate more than the theory predicts with high accuracy, while they tend to retaliate lesser with low accuracy. In order to describe these results as unique equilibrium, we demonstrate an alternative theory that incorporates naïveté and reciprocity. |
| Date: | 2017–07 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2017cf1056&r=gth |
| By: | Myatt, David P (London Business School); Wallace, Chris (University of Leicester) |
| Abstract: | In an asymmetric coordination (or anti-coordination) game, players acquire and use signals about a payoff-relevant fundamental from multiple costly information sources. Some sources have greater clarity than others, and generate signals that are more correlated and so more public. Players wish to take actions close to the fundamental but also close to (or far away from) others’ actions. This paper studies how asymmetries in the game, represented as the weights that link players to neighbours on a network, affect how they use and acquire information. Relatively centrally located players (in the sense of Bonacich, when applied to the dependence of players’ payoffs upon the actions of others) acquire fewer signals from relatively clear information sources; they acquire less information in total; and they place more emphasis on relatively public signals |
| Keywords: | Networks ; Bonacich Centrality ; Information Acquisition and Use ; Public and Private Information JEL classification numbers: C72 ; D83 ; D85 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:wcreta:32&r=gth |
| By: | Egbert, Henrik |
| Abstract: | This paper addresses the similarity between behavioural economics and social anthropology with respect to approaches on repeated reciprocity. The case at hand is the application of the Centipede game to Marcel Mauss’s concept of the Gift. In a Centipede game players interact in an alternating sequence of decisions to take or to pass an endowment. Mauss describes sequences of reciprocal giving in potlatch cultures, in which strict obligations determine choice options. The paper shows that models developed in behavioural economics, such as the Centipede game, can also be applied to prominent contexts in economic anthropology. |
| Keywords: | Gift, Centipede game, Potlatch game, Marcel Mauss, reciprocity |
| JEL: | Z13 |
| Date: | 2017–07–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:80324&r=gth |
| By: | Giménez Gómez, José M. (José Manuel); Subiza, Begoña |
| Abstract: | A minimum cost spanning tree problem analyzes the way to efficiently connect individuals to a source when they are located at different places. Several rules have been defined to solve this problem. Our objective here is to propose a new approach that differentiates some costs that may deserve compensations (involuntary costs) from some other connection costs that may be considered voluntary. We therefore define a solidarity egalitarian solution, through which, the total cost is allocated by considering pay-backs to equalize the involuntary costs, thus fulfilling the weak stability condition of individual rationality. Keywords: Minimum cost spanning tree, Solidarity, Cost sharing, Egalitarian JEL classification: C71, D63, D71. |
| Keywords: | Jocs cooperatius, 33 - Economia, |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:urv:wpaper:2072/290742&r=gth |