|
on Game Theory |
| By: | Hamers, Herbert (Tilburg University, Center For Economic Research); Husslage, Bart (Tilburg University, Center For Economic Research); Lindelauf, R. (Tilburg University, Center For Economic Research); Campen, Tjeerd |
| Abstract: | The Shapley value (Shapley (1953)) is one of the most prominent one-point solution concepts in cooperative game theory that divides revenues (or cost, power) that can be obtained by cooperation of players in the game. The Shapley value is mathematically characterized by properties that have appealing real-world interpretations and hence its use in practical settings is easily justified. The down part is that its computational complexity increases exponentially with the number of players in the game. Therefore, in practical problems that consist of more that 25 players the calculation of the Shapley value is usually too time expensive. Among others the Shapley value is applied in the analysis of terrorist networks (cf. Lindelauf et al. (2013)) which generally extend beyond the size of 25 players. In this paper we therefore present a new method to approximate the Shapley value by refining the random sampling method introduced by Castro et al. (2009). We show that our method outperforms the random sampling method, reducing the average error in the Shapley value approximation by almost 30%. Moreover, our new method enables us to analyze the extended WTC 9/11 network of Krebs (2002) that consists of 69 members. This in contrast to the restricted WTC 9/11 network considered in Lindelauf et al. (2013), that only considered the operational cells consisting of the 19 hijackers that conducted the attack. |
| Keywords: | approximation method; Shapley value; cooperattive game theory |
| JEL: | C71 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:8a67b416-1091-4efe-a1a6-721ebeda8272&r=gth |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics); Peter Sudhölter (Department of Business and Economics and COHERE - University of Southern) |
| Abstract: | It is known that for supermodular TU-games, the vertices of the core are the marginal vectors, and this result remains true for games where the set of feasible coalitions is a distributive lattice. Such games are induced by a hierarchy (partial ordre) on players. We propose a larger class of vertices for games on distributive lattices, called min-max vertices, obtained by minimizing or maximizing in a given order the coordinates of a core element. We give a simple formula which does not need to solve an optimization problem to compute these vertices, valid for connected hierarchies and for the general case under some restrictions. We find under which conditions two different orders induce the same vertex for every game, and show that there exist balanced games whose core has vertices which are not min-max vertices if and only if n > 4 |
| Keywords: | TU games; restricted cooperation; game with precedence constraints; core; vertex |
| JEL: | C71 |
| Date: | 2016–07 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:16077&r=gth |
| By: | Musegaas, Marieke (Tilburg University, Center For Economic Research); Borm, Peter (Tilburg University, Center For Economic Research); Quant, Marieke (Tilburg University, Center For Economic Research) |
| Abstract: | The main result of this paper is the convexity of Step out - Step in (SoSi) sequencing games, a class of relaxed sequencing games first analyzed by Musegaas, Borm, and Quant (2015). The proof makes use of a polynomial time algorithm determining the value and an optimal processing order for an arbitrary coalition in a SoSi sequencing game. In particular, we use that in determining an optimal processing order of a coalition S [ fig, the algorithm can start from the optimal processing order found for coalition S and thus all information on this optimal processing order of S can be used. |
| Keywords: | relaxed sequencing games; convexity |
| JEL: | C71 C44 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:f8a803f5-1f6a-4ac4-b4f6-70e0ba254979&r=gth |
| By: | Dietzenbacher, Bas (Tilburg University, Center For Economic Research); Borm, Peter (Tilburg University, Center For Economic Research); Hendrickx, Ruud (Tilburg University, Center For Economic Research) |
| Abstract: | In this paper we introduce and analyze the procedural egalitarian solution for transferable utility games. This new concept is based on the result of a coalitional bargaining procedure in which egalitarian considerations play a central role. The procedural egalitarian solution is the first single-valued solution which coincides with the constrained egalitarian solution of Dutta and Ray (1989) on the class of convex games and which exists for any TU-game. |
| Keywords: | egalitarianism; egalitarian procedure; procedural egalitatian solution; egalitarian stability; constrained equal awards rule |
| JEL: | C71 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:1863cb23-d1b2-4f2e-aa18-fd6982b2f7de&r=gth |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | The chapter studies the vector space of set functions on a finite set X, which can be alternatively seen as pseudo-Boolean functions, and including as a special cases games. We present several bases (unanimity games, Walsh and parity functions) and make an emphasis on the Fourier transform. Then we establish the basic duality between bases and invertible linear transform (e.g., the Möbius transform, the Fourier transform and interaction transforms). We apply it to solve the well-known inverse problem in cooperative game theory (find all games with same Shapley value), and to find various equivalent expressions of the Choquet integral |
| Keywords: | basis; set functions; TU games; Fourier transform; Möbius transform; interaction Shapley value; Choquet integral |
| JEL: | C71 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:16078&r=gth |
| By: | Julia Müller (Institute for Organisational Economics, University of Münster); Christiane Schwieren (Alfred-Weber-Institute for Economics, University of Heidelberg); Florian Spitzer (Department of Strategy and Innovation, Vienna University of Economics and Business) |
| Abstract: | Many recent experimental studies have shown that some subjects destroy other subjects’ incomes without receiving any material benefit, and that they even incur costs to do so. In this paper, we study the boundary conditions of this phenomenon, which is referred to as anti-social behavior. We introduce a four-player destruction game, in which we vary the framing and the presence of another activity, running in parallel to the destruction game. We observe a substantial amount of destruction in the baseline condition without the parallel activity, and with a framing in the spirit of previous destruction experiments. Our results indicate that a parallel activity as well as a framing emphasizing joint ownership of the item that can be destroyed reduces destruction almost to zero. We therefore argue that the emergence of anti-social behavior is highly contingent on the contextual environment. |
| Keywords: | anti-social behavior, joy of destruction, experiment, framing, boredom |
| JEL: | A13 C72 C91 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:wiw:wiwwuw:wuwp238&r=gth |
| By: | Morone, Andrea; Temerario, Tiziana |
| Abstract: | We analysed dyads strategies in one-shot public goods game. By means of a laboratory experiment, using a variant of the strategy-method, we found that more than one third of the dyads are conditional cooperators, whereas 18% can be categorised as free riders. |
| Keywords: | Voluntary contributions,Conditional cooperation,Free riding,Strategy-method |
| JEL: | H41 C91 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:esprep:148356&r=gth |
| By: | Itaya, Jun-ichi; Cornes, Richard |
| Abstract: | A rapidly growing literature analyzes models in which firms maximize objectives other than profit and enjoy market power. Examples include the labor-managed firm, mixed oligopoly, and delegation models. These models typically retain the aggregative structure of the conventional Cournot model of imperfect competition. We exploit this fact and apply the framework recently developed by Cornes and Hartley (2005, 2011) to analyze the properties of the equilibrium in such games. We show that existing treatments often make more restrictive assumptions than necessary to generate their results. Specifically, we identify conditions sufficient to ensure the existence of a unique equilibrium, and we explore the comparative static properties of these conditions. |
| Keywords: | Aggregative Game, Oligopoly, Hahn’s Condition, Non-profit Maximization, Share Function, |
| Date: | 2016–11–06 |
| URL: | http://d.repec.org/n?u=RePEc:hok:dpaper:307&r=gth |
| By: | Joy A. Buchanan (Interdisciplinary Center for Economic Science and Department of Economics, George Mason University); Matthew K. McMahon (Interdisciplinary Center for Economic Science and Department of Economics, George Mason University); Matthew Simpson (Department of Statistics, University of Missouri - Columbia); Bart J. Wilson (Economic Science Institute, Chapman University) |
| Abstract: | We investigate the degree to which people in a shopping mall express other-regarding behavior in the dictator game. Whereas many studies have attempted to increase the social distance between the dictator and experimenter and between the dictator and dictatee, we attempt to minimize that social distance between random strangers by video recording the decisions with the permission of the dictators to display their image on the Internet. Offers made by dictators are high relative to other experiments and a nontrivial number give the entire experimental windfall away, however a nontrivial number of people keep everything as well. |
| Keywords: | experimental economics, social distance, dictator game |
| JEL: | A13 C70 C93 D63 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:gms:wpaper:1061&r=gth |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | Set functions are widely used in many domains of Operations Research (cooperative game theory, decision under risk and uncertainty, combinatorial optimization) under different names (TU-game, capacity, nonadditive measure, pseudo-Boolean function, etc…). Remarkable families of set functions form polyhedra, e.g., the polytope of capacities, the polytope of p-additive capacities, the cone of supermodular games, etc…. Also, the core of a set function, defined as the set of additive set functions dominating that set function, is a polyhedron which is of fundamental importance in game theory, decision making and combinatorial optimization. This survey paper gives an overview of these notions and studies all these polyhedra |
| Keywords: | TU-game; capacity; nonadditive measure; pseudo-Boolean function; Möbius transform; supermodular game; p-additive game; multichoice game; core |
| JEL: | C71 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:16081&r=gth |
| By: | Biung-Ghi Ju (Department of Economics, Seoul National University, Korea); Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide, Spain, and CORE, Université catholique de Louvain, Belgium) |
| Abstract: | Robert Nozick allegedly introduced his liberal theory of private ownership as an objection to theories of end-state justice. Nevertheless, we show that, in a stylized framework for the allocation of goods in joint ventures, both approaches can be seen as complementary. More precisely, in such a context, self-ownership (the basis for Nozick’s entitlement theory of justice) followed by voluntary transfer (Nozick’s principle of just transfer) can lead to end-state fairness (as well as Pareto efficiency). Furthermore, under a certain solidarity condition, the only way to achieve end-state fairness, following Nozick’s procedure, is to endorse an egalitarian rule for the initial assignment of rights. |
| Keywords: | fairness, claims, no-envy, individual rationality, egalitarianism, efficiency, Walrasian exchange |
| JEL: | D63 D71 |
| Date: | 2016–11–18 |
| URL: | http://d.repec.org/n?u=RePEc:ums:papers:2016-14&r=gth |
| By: | Ayelet Gneezy; Uri Gneezy; Joan Llull; Pedro Rey-Biel |
| Abstract: | Understanding what affects satisfaction from consumption is fundamental to studying economic behavior. However, measuring subjective hedonic experiences is not trivial, in particular when studying experience goods in which quality is difficult to observe prior to consumption. We report the results of a field experiment with a theater show in which the audience pays at the end of the show under pay-what-you-want pricing. Using questionnaires, we measure expected enjoyment before the show, as well as the realized enjoyment after. Correlating the amounts paid with the expected and realized enjoyment, we find that individuals with a larger gap between reported expectations and enjoyment pay significantly more. Once we account for the satisfaction gap, the level of expected enjoyment or realized enjoyment has no significant effect in predicting payments. |
| Keywords: | experience goods; pay-what-you-want; expectations |
| JEL: | C72 C91 D81 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:944&r=gth |
| By: | Partha Dasgupta; Tapan Mitra; Gerhard Sorger |
| Abstract: | We study a socio-ecological model in which a continuum of consumers harvest a common property renewable natural resource. Markov perfect Nash equilibria of the cor- responding non-cooperative game are derived and are compared with collectively optimal harvesting policies. The underlying mechanisms that drive open-access commons in our model are shaped by population size, harvesting costs, and the ecosystem's productivity. If other things equal population is small relative to harvesting costs, unmanaged commons do not face destruction. More strikingly, they are harvested at the collectively optimal rate. Property rights do not matter in that parametric regime because the resource has no social scarcity value. However, if other things equal population is large relative to harvesting costs, open-access renewable natural resources suffer from the tragedy of the commons. Property rights matter there because the resource has a social scarcity price. The pop- ulation size relative to harvesting costs at which the socio-ecological system bifurcates is an increasing function of the ecosystem's productivity. A sudden crash in productivity, population overshoot, or decline in harvesting costs can tip an unmanaged common into ruin. The model provides a way to interpret historical and archaeological ndings on the collapse of those societies that have been studied by scholars. |
| JEL: | D01 C73 Q20 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:vie:viennp:1608&r=gth |