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on Game Theory |
| By: | Bettina-Elisabeth Klaus (Harvard Business School, Negotiation, Organizations & Markets Unit); Flip Klijn (Institute for Economic Analysis (CSIC)); Markus Walzl (Department of Economics, Bamberg University) |
| Abstract: | Using a bi-choice graph technique (Klaus and Klijn, 2009), we show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter (Proposition 1). Using this characterization of indirect dominance, we investigate von Neumann-Morgenstern farsightedly stable sets. We show that a singleton is von Neumann-Morgenstern farsightedly stable if and only if the matching is stable (Theorem 1). We also present roommate markets with no and with a non-singleton von Neumann-Morgenstern farsightedly stable set (Examples 1 and 2). |
| Keywords: | core, farsighted stability, one- and two-sided matching, roommate markets, von Neumann-Morgenstern stability. |
| JEL: | C62 C71 C78 |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:hbs:wpaper:09-135&r=gth |
| By: | Martin J Osborne; Ariel Rubinstein |
| Date: | 2009–05–21 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:814577000000000225&r=gth |
| By: | Protopapas, M.K.; Kosmatopoulos, E.B.; Battaglia, F. |
| Abstract: | We use co-evolutionary genetic algorithms to model the players' learning process in several Cournot models, and evaluate them in terms of their convergence to the Nash Equilibrium. The ``social-learning'' versions of the two co-evolutionary algorithms we introduce, establish Nash Equilibrium in those models, in contrast to the ``individual learning'' versions which, as we see here, do not imply the convergence of the players' strategies to the Nash outcome. When players use ``canonical co-evolutionary genetic algorithms'' as learning algorithms, the process of the game is an ergodic Markov Chain, and therefore we analyze simulation results using both the relevant methodology and more general statistical tests, to find that in the ``social'' case, states leading to NE play are highly frequent at the stationary distribution of the chain, in contrast to the ``individual learning'' case, when NE is not reached at all in our simulations; to find that the expected Hamming distance of the states at the limiting distribution from the ``NE state'' is significantly smaller in the ``social'' than in the ``individual learning case''; to estimate the expected time that the ``social'' algorithms need to get to the ``NE state'' and verify their robustness and finally to show that a large fraction of the games played are indeed at the Nash Equilibrium. |
| Keywords: | Genetic Algorithms; Cournot oligopoly; Evolutionary Game Theory; Nash Equilibrium |
| JEL: | C73 |
| Date: | 2009–05–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:15375&r=gth |
| By: | Attila Ambrus (Department of Economics, Harvard University); Ben Greiner (School of Economics, University of New South Wales); Parag Pathak (Department of Economics, MIT) |
| Abstract: | We revisit the phenomenon that group decisions differ systematically from decisions of individuals. Our experiment solicits individual and group decisions from the same subjects in two settings, gift-exchange games and lottery choices. With no deliberation and voting, the group decision is determined by the median individual decision, without a shift. With deliberation but no imposed decision rule, the individual one po- sition towards the selfish direction also becomes influential. In lottery choices we find no group shift relative to the median. We demonstrate that the standard practice of comparing means of group and individual decisions would incorrectly identify a level shift. |
| Keywords: | Decision making, lottery, risky choices |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:ads:wpaper:0091&r=gth |
| By: | Predtetchinski Arkadi (METEOR) |
| Abstract: | The paper studies the model of multilateral bargaining over the alternatives representedby points in the m–dimensional Euclidean space. Proposers are chosen randomly and the acceptance of a proposal requires the unanimous approval of it by all the players. The focus of the paper is on the asymptotic behavior of subgame perfect equilibria in pure stationary strategies (called bargaining equilibria) as the breakdown probability tends to zero. Bargaining equilibria are said to be asymptotically unique if the limit of a sequence of bargaining equilibria as the breakdown probability tends to zero is independent of the choice of the sequence and is uniquely determined by the primitives of the model. We show that the limit of any sequence of bargaining equilibria is a zero point of the so–called linearization correspondence. The asymptotic uniqueness of bargaining equilibria is then deduced in each of the following cases: (1) m = n−1, where n is the number of players, (2) m = 1, and (3) in the case where the utility functions are quadratic, for each 1 ≤ m ≤ n−1. In each case the linearization correspondence is shown to have a unique zero. Result 1 hasbeen established earlier in Miyakawa and Laruelle and Valenciano. Result 2 is subsumed by the result in Predtetchinski. Result 3 is new. |
| Keywords: | microeconomics ; |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2009023&r=gth |
| By: | Bettina-Elisabeth Klaus (Harvard Business School, Negotiation, Organizations & Markets Unit); Flip Klijn (Institute for Economic Analysis (CSIC)); Markus Walzl (Department of Economics, Bamberg University) |
| Abstract: | In this note we study von Neumann-Morgenstern farsightedly stable sets for Shapley and Scarf (1974) housing markets. Kawasaki (2008) shows that the set of competitive allocations coincides with the unique von Neumann-Morgenstern stable set based on a farsighted version of antisymmetric weak dominance (cf., Wako, 1999). We demonstrate that the set of competitive allocations also coincides with the unique von Neumann-Morgenstern stable set based on a farsighted version of strong dominance (cf., Roth and Postlewaite, 1977) if no individual is indifferent between his endowment and the endowment of someone else. |
| Keywords: | housing markets, indivisible goods, farsightedness, von Neumann-Morgenstern stable sets, top trading cycles, competitive allocations |
| JEL: | D63 D70 |
| Date: | 2009–04 |
| URL: | http://d.repec.org/n?u=RePEc:hbs:wpaper:09-129&r=gth |
| By: | Marion Oury (HEC Paris); Olivier Tercieux (Paris School of Economics and CNRS) |
| Abstract: | It is well-known that mechanism design literature makes many simplifying infor- mational assumptions in particular in terms of common knowledge of the environment among players. In this paper, we introduce a notion of continuous implementation and characterize when a social choice function is continuously implementable. More specif- ically, we say that a social choice function is continuously (partially) implementable if it is (partially) implementable for types in the model under study and it continues to be (partially) implementable for types "close" to this initial model. We ?rst show that if the model is of complete information a social choice function is continuously (partially) implementable only if it satis?es Maskin?s monotonicity. We then extend this result to general incomplete information settings and show that a social choice function is continuously (partially) implementable only if it is fully implementable in iterative dominance. For ?nite mechanisms, this condition is also su¢ cient. We also discuss implications of this characterization for the virtual implementation approach. |
| Keywords: | High order beliefs, robust implementation |
| JEL: | C79 D82 |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:ads:wpaper:0090&r=gth |
| By: | David M. McEvoy |
| Abstract: | Most coalitions that form to increase contributions to a public good do not require full participation by all users of the public good, and therefore create incentives for free riding. If given the opportunity to opt out of a voluntary coalition, in theory, agents should try to be among the first to do so, forcing the remaining undecided agents to bear the cost of participating in the coalition. This study tests the predicted sequence of participation decisions in voluntary coalitions using real-time threshold public goods experiments. We find that subjects’ behavior is more consistent with the theoretical predictions when the difference in payoffs between coalition members and free-riding non-members is relatively large. Key Words: voluntary coalitions, voluntary agreements, public goods experiments, free riding |
| JEL: | H41 C92 C72 Q50 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:apl:wpaper:09-14&r=gth |