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on Game Theory |
| By: | Page Jr, Frank H (Department of Finance, University of Alabama); Wooders, Myrna H (Department of Economics, Vanderbilt University and Department of Economics, University of Warwick) |
| Abstract: | We make four main contributions to the theory of network formation. (1) The problem of network formation with farsighted agents can be formulated as an abstract network formation game. (2) In any farsighted network formation game the feasible set of networks contains a unique, finite, disjoint collection of nonempty subsets having the property that each subset forms a strategic basin of attraction. These basins of attraction contain all the networks that are likely to emerge and persist if individuals behave farsightedly in playing the network formation game. (3) A von Neumann Morgenstern stable set of the farsighted network formation game is constructed by selecting one network from each basin of attraction. We refer to any such von Neumann-Morgenstern stable set as a farsighted basis. (4) The core of the farsighted network formation game is constructed by selecting one network from each basin of attraction containing a single network. We call this notion of the core, the farsighted core. We conclude that the farsighted core is nonempty if and only if there exists at least one farsighted basin of attraction containing a single network. To relate our three equilibrium and stability notions (basins of attraction, farsighted basis, and farsighted core) to recent work by Jackson and Wolinsky (1996), we define a notion of pairwise stability similar to the Jackson-Wolinsky notion and we show that the farsighted core is contained in the set of pairwise stable networks. Finally, we introduce, via an example, competitive contracting networks and highlight how the analysis of these networks requires the new features of our network formation model. |
| Keywords: | Basins of attraction ; Network formation ; Supernetworks ; Farsighted core ; Nash networks |
| JEL: | A14 D20 J00 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:724&r=gth |
| By: | Viossat, Yannick (Dept. of Economics, Stockholm School of Economics) |
| Abstract: | In (Viossat, 2006, "The replicator dynamics does not lead to correlated equilibria", forthcoming in Games and Economic Behavior), it was shown that the single-population replicator dynamics may eliminate all pure strategies in the support of at least one correlated equilibrium, and this from an open set of initial conditions. Here, we generalize this result by showing that it holds on an open set of games, and for many other dynamics, including the best-response dynamics, the Brown-von Neumann-Nash dynamics and any monotonic or weakly-sign preserving dynamics satisfying some standard regularity conditions. It is also shown that, for the replicator dynamics and the best-response dynamics, elimination of all strategies used in correlated equilibria is robust to the addition of mixed strategies as new pure strategies. |
| Keywords: | Correlated equilibrium; evolutionary dynamics |
| JEL: | C72 C73 |
| Date: | 2006–05–15 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hastef:0629&r=gth |
| By: | Bloch, Francis (GREQAM, Universite d Aix-Marseille,); Dutta, Bhaskar (Department of Economics, University of Warwick) |
| Abstract: | This paper analyzes the formation of communication networks when players choose endogenously their investment on communication links. We consider two alternative de?nitions of network reliability ; product reliability, where the decay of information depends on the product of the strength of communication links, and min reliability where the speed of connection is a¤ected by the weakest communication link. When investments are separable, the architecture of the efficient network depends crucially on the shape of the transformation function linking investments to the quality of communication links. With increasing marginal returns to investment, the efficient network is a star ; with decreasing marginal returns, the con?ict between maximization of direct and indirect bene?ts prevents a complete characterization of efficient networks. However, with min reliability, the efficient network must be a tree. Furthermore, in the particular case of linear transformation functions, in an e¢ cient network, all links must have equal strength. When investments are perfect complements, the results change drastically : under product reliability, the efficient network must contain a cycle, and is in fact a circle for small societies. With min reliability, the e¢ cient network is either a circle or a line. As in classical models of network formation, e fficient networks may not be supported by private invesment decisions. We provide examples to show that the star may not be stable when the transformation functions is strictly convex. We also note that with perfect substitutes and perfect complements (when the e¢ cient network displays a very symmetric structure), the e¢ cient network can indeed be supported by private investments when the society is large. |
| Keywords: | communication networks ; network reliability |
| JEL: | D85 C70 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:723&r=gth |
| By: | Olivier Compte; Philippe Jehiel |
| Date: | 2006–06–05 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000085&r=gth |
| By: | Thomas Rupp (Institut für Volkswirtschaftslehre (Department of Economics), Technische Universität Darmstadt (Darmstadt University of Technology)) |
| Abstract: | Guided by game theory, we develop a model to explain behavioral equilibria under uncertainty and interaction with the spot market on balancing markets. We offer some insights for the general model and derive explicit solutions for a specific model in which the error distributions and pricing function are given. The most interesting conclusions are the unique existence of an equilibrium and that no participant acts contrary to the aggregate market (either all buy or sell power) and all strategies are, normalized, equal (which is rather counter-intuitive). Furthermore, the aggregate behavior is a stochastic process varying around its own variance. |
| Keywords: | game theory, nash equilibrium, regulated energy market, balancing power market |
| JEL: | C73 D58 Q41 D40 |
| Date: | 2006–05 |
| URL: | http://d.repec.org/n?u=RePEc:tud:ddpiec:171&r=gth |
| By: | Dutta, Bhaskar (Department of Economics, University of Warwick); Peter, Hans (Department of Quantitative Economics, University of Maastricht); Sen, Arunava (Indian Statistical Institute, New Delhi) |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:722&r=gth |
| By: | Andrea Attar (IDEI, Toulouse); Eloisa Campioni (LUISS, University of Rome); Gwenaël Piaser (Department of Economics, University Of Venice Cà Foscari); Uday Rajan (Ross School of Business, University of Michigan) |
| Abstract: | In multiple principal, multiple agent models of moral hazard, we provide conditions under which the outcomes of equilibria in direct mechanisms are preserved when principals can offer indirect communication schemes. We discuss the role of random allocations and recommendations and relate the result to the existing literature. |
| Keywords: | Moral Hazard, Multiple Agents, Direct Mechanism. |
| JEL: | D82 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:32_06&r=gth |
| By: | Maurice Salles (CREM-CNRS) |
| Abstract: | Michael Dummett worked on the theoretical aspects of aggregation of individual preferences and on the strategic aspects of voting theory. He also extended Black’s analysis of single-peaked preferences for majority rule to the case of voting games (majority games), offering a greater flexibility for the expression of voters’ preferences. He is also with Donald Saari one of the major advocates of the use of Borda’s rule in actual voting. In two books and a paper, he proposed many examples showing the advantages and defects of many voting rules used in the world |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:tut:cremwp:200616&r=gth |