## DESIGNING STABLE MECHANISMS FOR ECONOMIC ENVIRONMENTS

Citations: | 1 - 0 self |

### BibTeX

@MISC{Healy_designingstable,

author = {Paul J. Healy and Laurent Mathevet},

title = {DESIGNING STABLE MECHANISMS FOR ECONOMIC ENVIRONMENTS },

year = {}

}

### OpenURL

### Abstract

We study the design of mechanisms that implement Lindahl or Walrasian allocations and whose Nash equilibria are dynamically stable for a wide class of adaptive dynamics. We argue that supermodularity is not a desirable stability criterion in this mechanism design context, focusing instead on contractive mechanisms. We provide necessary and sufficient conditions for a mechanism to Nash implement Lindahl or Walrasian allocations, show that these conditions are inconsistent with the contraction property when message spaces are onedimensional, and then show how to use additional dimensions to achieve dynamic stability while gaining budget balance out of equilibrium.

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Citation Context ... For example, dominant strategy equilibria are certainly dynamically stable for nearly any reasonable learning process. Unfortunately, standard impossibility results severely limit its applicability (=-=Green and Laffont, 1977-=-; Roberts, 1979). Furthermore, if the dominant strategy is not strict, then myopically-adapting agents may converge to undesirable Nash equilibria, as was observed in tests of the Vickrey-Clarke-Grove... |

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Citation Context ... not restrict the feasible consumption set to the positive orthant. Since no mechanism can Nash implement Walrasian or Lindahl equilibria when boundary equilibria are permitted (see Hurwicz, 1979a or =-=Jackson, 2001-=-), it is necessary to rule out such equilibria either by allowing unbounded consumption bundles, or by restricting preferences so that boundary equilibria never obtain. The latter approach is more com... |

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Citation Context ... models, ours does not restrict the feasible consumption set to the positive orthant. Since no mechanism can Nash implement Walrasian or Lindahl equilibria when boundary equilibria are permitted (see =-=Hurwicz, 1979-=-a or Jackson, 2001), it is necessary to rule out such equilibria either by allowing unbounded consumption bundles, or by restricting preferences so that boundary equilibria never obtain. The latter ap... |

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Citation Context ...ustin, TX 78712, U.S.A.; lmath@mail.utexas.edu. 12 HEALY AND MATHEVET these mechanisms can best be described using myopic learning dynamics, such as bestresponse play to a recent history of actions (=-=Chen and Plott, 1996-=-; Chen and Tang, 1998; Chen and Gazzale, 2004; Healy, 2006). Thus, mechanisms that induce dynamically stable games will drive play to equilibrium, while mechanisms that induce unstable games will not.... |

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Citation Context ... strict, then myopically-adapting agents may converge to undesirable Nash equilibria, as was observed in tests of the Vickrey-Clarke-Groves mechanism by Cason et al. (2003) and Healy (2006) (see also =-=Saijo et al., 2007-=-).8 HEALY AND MATHEVET Abreu and Matsushima (1992) provide a mechanism that has a dominance-solvable equilibrium whose outcome is a lottery placing an arbitrarily large weight on the desired allocati... |

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Citation Context ...VET these mechanisms can best be described using myopic learning dynamics, such as bestresponse play to a recent history of actions (Chen and Plott, 1996; Chen and Tang, 1998; Chen and Gazzale, 2004; =-=Healy, 2006-=-). Thus, mechanisms that induce dynamically stable games will drive play to equilibrium, while mechanisms that induce unstable games will not. These ‘wind tunnel’ tests suggest that theorists should a... |

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Citation Context ...ms of Hurwicz and Walker are known to have poor stability properties, and experimental results (Chen and Tang, 1998; Healy, 2006) confirm that this severely hinders performance. Kim (1987) (following =-=Jordan, 1986-=-) shows that for a certain class of preferences, all Nash-Lindahl mechanisms must be unstable for at least one preference profile in the class. As mentioned above, Vega-Redondo (1989); de Trenqualye (... |

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Citation Context ...ents select equilibrium strategies when playing a mechanism. The general impossibility results when applying the weak requirement of dominant strategy equilibrium (Gibbard, 1973; Satterthwaite, 1975; =-=Hurwicz and Walker, 1990-=-; Zhou, 1991) led to the search for mechanisms that implement optimal public goods allocations when players are assumed to select Nash equilibrium strategies. Groves and Ledyard (1977), Hurwicz (1979b... |

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Citation Context ... To demonstrate the gap between weak implementation and full implementation, consider the equal-tax voluntary contribution mechanism, where Mi =R 1 for each i, y(m) = ∑ i mi and xi(m) = −κy(m)/n (see =-=Groves and Ledyard, 1980-=- or Healy, 2006). The hypotheses of the first part of Theorem 5 are satisfied, so this mechanism weakly Nash implements the Lindahl correspondence. But Assumption 5 fails at any θ that has a Lindahl e... |

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Citation Context ...at the Walrasian allocations. Second, adaptive learning models in the competitive mechanism focus on tâtonnement-like adjustment processes where stability is, in general, not guaranteed (Scarf, 1960; =-=Hirota, 1985-=-) and where feasibility (off-equilibrium) of the consumption plans is also a problem. We focus instead on designing game-theoretic mechanisms that are fully-balanced—hence trades are feasible off-equi... |

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Citation Context ...ment parameter grows large; in either case, attainability of equilibrium becomes a concern. If preferences are not quasilinear, then the Groves-Ledyard mechanism may have many undesirable equilibria (=-=Bergstrom et al., 1983-=-); however, these equilibria may not be a concern since they are unstable and disappear when the punishment parameter is sufficiently large (Page and Tassier, 2004). Chen and Tang (1998) show that the... |

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6 |
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Citation Context ...rategy equilibria are certainly dynamically stable for nearly any reasonable learning process. Unfortunately, standard impossibility results severely limit its applicability (Green and Laffont, 1977; =-=Roberts, 1979-=-). Furthermore, if the dominant strategy is not strict, then myopically-adapting agents may converge to undesirable Nash equilibria, as was observed in tests of the Vickrey-Clarke-Groves mechanism by ... |

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(Show Context)
Citation Context ... at least −1. Beyond a second threshold of γ ′′ > γ ′ the slope becomes positive, inducing a supermodular game. Thus, choosing a high enough γ to guarantee supermodularity (as in Chen and Tang, 1998; =-=Chen, 2002-=-; and Van Essen, 2009b) is more than sufficient to also guarantee that the mechanism is contractive. Figure III shows the slope of the linear best response function in the Groves-Ledyard mechanism for... |

4 |
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(Show Context)
Citation Context ...ecise (placing more weight on the desired allocation) the dimensionality of the message space diverges to infinity. Furthermore, laboratory tests of the mechanism (Sefton and Yavas, 1996, inspired by =-=Glazer and Rosenthal, 1992-=-) find that subjects do not move toward the equilibrium over 14 periods of play. This suggests that the speed at which iterated dominance is respected by learning is slow, or nonexistent. These result... |

4 |
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(Show Context)
Citation Context ...ypically a special case of the more-general ‘social choice’ environments studied by Arrow (1951) or Maskin (1999), for example. 2 Our necessary condition was first suggested by Brock (1980) (see also =-=Groves and Ledyard, 1987-=-), though not proved generally. Reichelstein and Reiter (1988) use differential geometry techniques to explore the minimal message space size needed for Walrasian implementation in Nash equilibrium. T... |

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3 | Incentive compatible mechanisms for pure public goods: A survey of experimental research - Chen - 2004 |