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on Game Theory |
| By: | Fabien Lange (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, Keleti Faculty of Economics - Budapest Tech); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | The Shapley value is a central notion defining a rational way to share the total worth of a cooperative game among players. We address a general framework leading to applications to games with communication graphs, where the feasible coalitions form a poset whose all maximal chains have the same length. Considering a new way to define the symmetry among players, we propose an axiomatization of the Shapley value of these games. Borrowing ideas from electric networks theory, we show that our symmetry axiom and the efficiency axiom correspond to the two Kirchhoff's laws in the circuit associated to the Hasse diagram of feasible coalitions. |
| Keywords: | Regular set system; communication situation; regular game; Shapley value; Kirchhoff's laws. |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00496553_v1&r=gth |
| By: | Jörg Franke |
| Abstract: | This paper analyzes the incentive effects of affirmative action in competitive environments modeled as contest games. Competition is between heterogeneous players where heterogeneity might be due to past discrimination. Two policy options are analyzed that tackle the underlying asymmetry: Either it is ignored and the contestants are treated equally, or affirmative action is implemented which compensates discriminated players. It is shown in a simple two-player contest game that a tradeoff between affirmative action and high effort exertion does not exist. Instead, the implementation of affirmative action fosters effort incentives. Similar results hold in the n-player contest as well as under imperfect information if the heterogeneity between contestants is moderate. |
| Keywords: | Asymmetric contest; affirmative action; discrimination |
| JEL: | C72 D63 I38 J78 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:rwi:repape:0185&r=gth |
| By: | John K.-H. Quah; Bruno Strulovici |
| Abstract: | The single crossing property plays a crucial role in monotone comparative statics (Milgrom and Shannon (1994)), yet in some important applications the property cannot be directly assumed or easily derived. Difficulties often arise because the property cannot be aggregated: the sum of two functions with the single crossing property need not have the same property. We obtain the precise conditions under which functions with the single crossing property add up to functions with this property. We apply our results to certain Bayesian games when establishing the monotonicity of strategies is an important step in proving equilibrium existence. In particular, we find conditions under which first-price auctions have monotone equilibria, generalizing the result of Reny and Zamir (2004). |
| Keywords: | Monotone comparative statics, Single crossing property, Bayesian games, Monotone strategies, First-price auctions, Logsupermodularity |
| JEL: | C61 C69 C72 D44 D43 D42 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:493&r=gth |
| By: | Michele Gori (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze) |
| Abstract: | In this paper we investigate whether the process of household formation in a competitive market may beget inefficient outcomes. To this end, we consider a generalization of the Arrow-Debreu exchange economy model in which endogenous household formation is introduced, we propose suitable definitions of equilibrium and efficiency at the economy level and we show that if there are many households which can potentially be formed, then existence of inefficient equilibria is widespread in the model. |
| Keywords: | General Equilibrium; Bargaining; Endogenous household formation; Efficiency; Pareto Optimality; Asymmetric Nash bargaining solution. |
| JEL: | C71 C78 D13 D50 |
| Date: | 2010–06 |
| URL: | http://d.repec.org/n?u=RePEc:flo:wpaper:2010-09&r=gth |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | In the paper, we study a model of influence in a social network. It is assumed that each player has an inclination to say YES or NO which, due to influence of other players, may be different from the decision of the player. The point of departure here is the concept of the Hoede-Bakker index - the notion which computes the overall decisional `power' of a player in a social network. The main drawback of the Hoede-Bakker index is that it hides the actual role of the influence function, analyzing only the final decision in terms of success and failure. In this paper, we separate the influence part from the group decision part, and focus on the description and analysis of the influence part. We propose among other descriptive tools a definition of a (weighted) influence index of a coalition upon an individual. Moreover, we consider different influence functions representative of commonly encountered situations. Finally, we propose a suitable definition of a modified decisional power. |
| Keywords: | influence function, influence index, decisional power, social network |
| Date: | 2010–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00496560_v1&r=gth |
| By: | Simon Angus (School of Economics, Monash University); Virginie Masson (School of Economics, University of Adelaide) |
| Abstract: | The network literature commonly neglects the importance of a clear distinction between interactions and information exchanges. Although convenient, this oversight is not innocuous and may lead to erroneous conclusions when looking at mechanisms such as contagion processes. We use simulation methods and conduct a systematic analysis of the implications of such omission. We show that the lack of distinction between information and interaction structures is not without consequences. More precisely, when agents use a myopic best response, only information exchanges matter and interactions can be ignored. With imitation however, both information and interactions play important yet different roles in contagion. |
| Keywords: | contagion, networks, coordination games, scale-free, small-worlds, best response, imitation |
| JEL: | C73 D85 |
| Date: | 2010–06 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2010-12&r=gth |
| By: | Hertel, Johanna; Smith, John |
| Abstract: | We model an interaction between an informed sender and an uninformed receiver. Like the classic cheap talk setup, the informed player sends a message to an uninformed receiver who is to take an action which affects the payoffs of both players. However, unlike the classic cheap talk setup, the sender can communicate only through the use of discrete messages. In particular, the sender has a finite set of message elements with which to compose messages. The sender incurs a communication cost which is increasing in the number of elements contained in the message. We characterize the resulting equilibria with a permissive out-of-equilibrium restriction. We introduce a stronger out-of-equilibrium requirement and show that if the sender and receiver have aligned preferences regarding the action of the receiver then only the most informative equilibrium exists. When the preferences between players are not aligned, we show that our stronger condition does not guarantee uniqueness and we provide an example where an increase in communication costs can improve communication. As we show in an example, this improvement can occur to such an extent that an equilibrium can outperform the Goltsman et. al. (2009) upper bound for payoffs in mediated communication. |
| Keywords: | information transmission; cheap talk; costly communication |
| JEL: | D82 D83 C72 |
| Date: | 2010–06–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:23560&r=gth |
| By: | Maldonado, Jorge Hignio; Moreno-Sanchez, Rocio del Pilar |
| Abstract: | Economic Experimental Games (EEGs), focused to analyze dilemmas associated with the use of common pool resources, have shown that individuals make extraction decisions that deviate from the suboptimal Nash equilibrium. However, few studies have analyzed whether these deviations towards the social optimum are affected as the stock of resource changes. Performing EEG with local fishermen, we test the hypothesis that the behavior of participants differs under a situation of abundance versus one of scarcity. Our findings show that under a situation of scarcity, players over-extract a given resource, and thus make decisions above the Nash equilibrium; in doing so, they obtain less profit, mine the others-regarding interest, and exacerbate the tragedy of the commons. This result challenges previous findings from the EEG literature. When individuals face abundance of a given resource, however, they deviate downward from the prediction of individualistic behavior. The phenomenon of private, inefficient overexploitation is corrected when management strategies are introduced into the game, something that underlines the importance of institutions. |
| Keywords: | tragedy of the commons intensified, economic experimental games, resource abundance, resource scarcity, dynamic effects, Community/Rural/Urban Development, Environmental Economics and Policy, Institutional and Behavioral Economics, Land Economics/Use, Public Economics, D01, D02, D03, O13, O54, Q01, Q22, C93, C72, C73, C23, |
| Date: | 2009–10–05 |
| URL: | http://d.repec.org/n?u=RePEc:ags:ulaedd:91170&r=gth |