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on Game Theory |
| By: | Hans Haller; Roger Lagunoff |
| Date: | 2006–10–27 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000560&r=gth |
| By: | Herings P. Jean-Jacques; Peeters Ronald (METEOR) |
| Abstract: | This paper presents a complete survey of the use of homotopy methods in game theory.Homotopies allow for a robust computation of game-theoretic equilibria and their refinements. Homotopies are also suitable to compute equilibria that are selected by variousselection theories. We present all relevant techniques underlying homotopy algorithms.We give detailed expositions of the Lemke-Howson algorithm and the Van den Elzen-Talman algorithm to compute Nash equilibria in 2-person games, and the Herings-Vanden Elzen, Herings-Peeters, and McKelvey-Palfrey algorithms to compute Nash equilibriain general n-person games. |
| Keywords: | operations research and management science; |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2006045&r=gth |
| By: | Sergiu Hart |
| Date: | 2006–10–27 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000532&r=gth |
| By: | Michel Benaim; Josef Hofbauer; Ed Hopkins |
| Date: | 2006–10–27 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000547&r=gth |
| By: | Vincent P. Crawford |
| Date: | 2006–10–26 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000517&r=gth |
| By: | Herings P. Jean-Jacques; Mauleon Ana; Vannetelbosch Vincent (METEOR) |
| Abstract: | We propose a new concept, the pairwise farsightedly stable set, in order to predict which networks may be formed among farsighted players. A set of networks G is pairwise farsightedly stable (i) if all possible pairwise deviations from any network g ∈ G to a network outside G are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsightedly improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying (i) and (ii). We show that a non-empty pairwise farsightedly stable set always exists and we provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsighted stability yields a Pareto dominating network, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest consistent set. |
| Keywords: | Economics ; |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2006046&r=gth |
| By: | Ana, MAULEON (UNIVERSITE CATHOLIQUE DE LOUVAIN, Center for Operations Research and Econometrics (CORE)); Huasheng, SONG (Zhejiang University); Vincent, VANNETELBOSCH |
| Abstract: | The paper examnes the formation of free trade agreements as a network formation game. We consider a three-country model in which international trade occurs between economies with imperfectly competitive product markets. Labor markets can be unionized and non-unionized in each country. We show that if all countries are of the same type (all of them are either unionized or non-unionized), the global free trade network is both the unique pairwise stable network and the unique efficient network. If some countries are unionized while others are non-unionized, other networks apart from the global free trade network are likely to be pariwise stable. however the efficient network is always the global free trade network. Thus, a conflict between stability and efficiency may occur. Moreover, starting from the network in which no country has signed a free trade agreement, all sequences of networks due to continuously profitable deviations to do not lead (in most cases) to the global free trade network, even when global free trade is stable |
| Keywords: | Free-trade agreements, Network formation games, Unionization |
| JEL: | F15 F16 C70 |
| Date: | 2006–06–15 |
| URL: | http://d.repec.org/n?u=RePEc:ctl:louvec:2006029&r=gth |
| By: | Klaus Bettina; Walzl Markus (METEOR) |
| Abstract: | We consider several notions of setwise stability for many-to-many matching markets with contracts and provide an analysis of the relations between the resulting stable sets and pairwise stable sets for general, substitutable, and strongly substitutable preferences. Apart from obtaining “set inclusion results'''' on all three domains, we prove that for substitutable preferences the set of pairwise stable matchings is nonempty and coincides with the set of weakly setwise stable matchings. For strongly substitutable preferences the set of pairwise stable matchings coincides with the set of setwise stable matchings. We also show that Roth’s (1984) stability coincides with pairwise stability for substitutable preferences. |
| Keywords: | microeconomics ; |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2006041&r=gth |
| By: | Dirk Bergemann; Juuso Välimäki |
| Date: | 2006–10–27 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000580&r=gth |
| By: | Kolen Antoon (METEOR) |
| Abstract: | We describe a genetic algorithm for the partial constraint satisfaction problem. The typical elements of a genetic algorithm, selection, mutation and cross-over, are filled in with combinatorial ideas. For instance, cross-over of two solutions is performed by taking the one or two domain elements in the solutions of each of the variables as the complete domain of the variable. Then a branch-and-bound method is used for solving this small instance. When tested on a class of frequency assignment problems this genetic algorithm produced the best known solutions for all test problems. This feeds the idea that combinatorial ideas may well be useful in genetic algorithms. |
| Keywords: | Economics ; |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2006044&r=gth |