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on Game Theory |
| By: | MAULEON, Ana (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)); VANNETELBOSCH, Vincent (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)); VERGOTE, Wouter (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)) |
| Abstract: | We adopt the notion of von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the von Neumann-Morgenstern (myopically) stable sets, von Neumann-Morgenstern farsightedly stable sets cannot include matchings that are not corewise stable ones. Moreover, we show that our main result is robust to many-to-one matching problems with responsive preferences. |
| Keywords: | matching problem, von Neumann-Morgenstern stable sets, farsighted stability |
| JEL: | C71 C78 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2008016&r=gth |
| By: | Eichberger, Jürgen (Sonderforschungsbereich 504); Kelsey, David (Department of Economics, The University of Birmingham) |
| Abstract: | Goeree & Holt (2001) observe that, for some parameter values, Nash equilibrium provides good predictions for actual behaviour in experiments. For other payoff parameters, however, actual behaviour deviates consistently from that predicted by Nash equilibria. They attribute the robust deviations from Nash equilibrium to actual players’ considering not only marginal gains and losses but also total pay-offs. In this paper, we show that optimistic and pessimistic attitudes towards strategic ambiguity may induce such behaviour. |
| Date: | 2008–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:xrs:sfbmaa:08-08&r=gth |
| By: | Said, Maher |
| Abstract: | We examine an environment where goods and privately informed buyers arrive stochastically to a market. A seller in this setting faces a sequential allocation problem with a changing population. We characterize the set of incentive compatible allocation rules and provide a generalized revenue equivalence result. In contrast to a static setting where incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object, in this dynamic setting, incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object sooner. We also characterize the set of efficient allocation rules and show that a dynamic Vickrey-Clarke-Groves mechanism is efficient and dominant strategy incentive compatible. We then derive an optimal direct mechanism. We show that the revenue-maximizing direct mechanism is a pivot mechanism with a reserve price. Finally, we consider sequential ascending auctions in this setting, both with and without a reserve price. We construct memoryless equilibrium bidding strategies in this indirect mechanism. Bidders reveal their private information in every period, yielding the same outcomes as the direct mechanisms. Thus, the sequential ascending auction is a natural institution for achieving either efficient or optimal outcomes. Interestingly, this is not the case for sequential second-price auctions, as the bids in a second-price auction do not reveal sufficient information to realize either the efficient or optimal allocation. |
| Keywords: | Dynamic mechanism design; Random arrivals; Revenue equivalence; Indirect mechanisms; Sequential ascending auctions. |
| JEL: | D44 D82 D83 C73 |
| Date: | 2008–11–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:11456&r=gth |
| By: | Joseph Abdou (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | We study the structure of unstable local effectivity functions defined for n players and p alternatives. A stability index based on the notion of cycle is introduced. In the particular case of simple games, the stability index is closely related to the Nakamura Number. In general it may be any integer between 2 and p. We prove that the stability index for maximal effectivity functions and for maximal local effectivity functions is either 2 or 3. |
| Keywords: | Effectivity function, local effectivity function, acyclicity, stability index, Nakamura Number, acyclicity. |
| JEL: | C70 D71 |
| Date: | 2008–07 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:b08056&r=gth |
| By: | Joseph Abdou (Centre d'Economie de la Sorbonne - Paris School of Economics); Hans Keiding (University of Copenhagen) |
| Abstract: | We introduce a description of the power structure which is inherent in a strategic game form using the concept of an interaction sheaf. The latter assigns to each open set of outcomes a set of interaction arrays, specifying the changes that coalitions can make if outcome belongs to this open set. The interaction sheaf generalizes the notion of effectivity functions which has been widely used in implementation theory, taking into consideration that changes in outcome may be sustained not only by single coalitions but possibly by several coalitions, depending on the underlying strategy choices. Also, it allows us to consider game forms with not necessarily finite sets of outcomes, generalizing the results on solvability of game forms obtained in the finite case in Abdou and Keiding (2003). |
| Keywords: | Nash equilibrium, strong equilibrium, solvability, effectivity, acyclicity. |
| JEL: | C70 D71 |
| Date: | 2008–04 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:b08040&r=gth |
| By: | Caterina Calsamiglia; Guillaume Haeringer; Flip Klijn |
| Abstract: | The literature on school choice assumes that families can submit a preference list over all the schools they want to be assigned to. However, in many real-life instances families are only allowed to submit a list containing a limited number of schools. Subjects' incentives are drastically affected, as more individuals manipulate their preferences. Including a safety school in the constrained list explains most manipulations. Competitiveness across schools play an important role. Constraining choices increases segregation and affects the stability and efficiency of the final allocation. Remarkably, the constraint reduces significantly the proportion of subjects playing a dominated strategy. |
| Keywords: | school choice, matching, experiment |
| JEL: | C72 C78 D78 I20 |
| Date: | 2008–11–17 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:757.08&r=gth |
| By: | KOUTSOUGERAS, Leonidas; ZIROS, Nicholas |
| Abstract: | We show that in large finite economies, core allocations can be approximately decentralized as Nash (rather than Walras) equilibrium. We argue that this excrcise is an essential complement to asymptotic core equivalence results, because it implies that in some approximate sense individual attempts to manipulate the decentralizing prices cannot be beneficial, which fits precisely the interpretation of asymptotic core convergence, namely the emergence of price taking. |
| Keywords: | core, Nash equilibrium, asymptotic proximity, decentralization. |
| JEL: | D43 D50 C72 |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2008026&r=gth |
| By: | DEHEZ, Pierre (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)); TELLONE, Daniela (CEREC, Facultés Universitaires Saint-Louis) |
| Abstract: | A group of agents considers collaborating on a project which requires putting together elements owned by some of them. These elements are pure public goods with exclusion i.e. nonrival but excludable goods like for instance knowledge, data or information, patents or copyrights. The present paper addresses the question of how should agents be compensated for the goods they own. It is shown that this problem can be framed as a cost sharing game – called "data game" – to which standard cost sharing rules like the Shapley value or the nucleolus can then be applied and compared. |
| Keywords: | cost sharing, compensation, Shapley value. |
| JEL: | C71 D46 M41 |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2008010&r=gth |
| By: | Julio Davila (Centre d'Economie de la Sorbonne - Paris School of Economics); Jan Eeckhout (University of Pennsylvania); César Martinelli (Instituto Technologico Autonomo de Mexico) |
| Abstract: | In a simple public good economy, we propose a natural bargaining procedure whose equilibria converge to Lindahl allocations as the cost of bargaining vanishes. The procedure splits the decision over the allocation in a decision about personalized prices and a decision about output levels for the public good. Since this procedure does not assume price-taking behavior, it provides a strategic foundation for the personalized taxes inherent to the Lindahl solution to the public goods problem. |
| Keywords: | Public goods, bargaining, alternating offers. |
| JEL: | C78 H41 |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:b08041&r=gth |
| By: | Johannes Horner (Cowles Foundation, Yale University); Larry Samuelson (Cowles Foundation, Yale University) |
| Abstract: | We consider the problem of a monopolist with an object to sell before some deadline, facing n buyers with independent private values. The monopolist posts prices but has no commitment power. We show that the monopolist can always secure at least the larger of the static monopoly profit and the revenue from a Dutch auction with a zero reserve price. When there are only a few buyers, her profits are higher than this bound, and she essentially posts unacceptable prices up to the very end, at which point prices collapse to a "reservation price" that exceeds marginal cost. When there are many buyers, the seller abandons this reservation price in order to more effectively screen buyers. Her optimal policy then replicates a Dutch auction, with prices decreasing continuously over time. With more units to sell, prices jump up after each sale. |
| Keywords: | Revenue management, Intertemporal price discrimination, Coase conjecture, Perishable goods, Reserve price, Dutch auction |
| JEL: | C72 D42 D82 |
| Date: | 2008–11 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1684&r=gth |