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This paper defines the notion of a local equilibrium of quality , , in a discrete exchange economy: a partial allocation and item prices that guarantee certain stability properties parametrized by the numbers and . The quality measures the fit between the allocation and the prices: the larger and the closer the fit. For this notion provides a graceful degradation for the conditional equilibria of Fu, Kleinberg and Lavi (2012) which are exactly the local equilibria of quality . For the local equilibria of quality are more stable than conditional equilibria. Any local equilibrium of quality provides, without any assumption on the type of the agents’ valuations, an allocation whose value is at least the optimal fractional allocation. In any economy in which all agents’ valuations are -submodular, i.e., exhibit complementarity bounded by , there is a local equilibrium of quality . In such an economy any greedy allocation provides a local equilibrium of quality . Walrasian equilibria are not amenable to such graceful degradation. 相似文献
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We study the house allocation problem with existing tenants: houses (stand for “indivisible objects”) are to be allocated to agents; each agent needs exactly one house and has strict preferences; houses are initially unowned; agents initially do not own houses; the remaining agents (the so-called “existing tenants”) initially own the remaining houses (each owns one). In this setting, we consider various randomized allocation rules under which voluntary participation of existing tenants is assured and the randomization procedure either treats agents equally or discriminates against some (or all) of the existing tenants. We obtain two equivalence results, which generalize the equivalence results in Abdulkadiroğlu and Sönmez (1999) and Sönmez and Ünver (2005). 相似文献
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We consider a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter and the distribution of the time series of innovations. In particular, we consider the full range of cases in which satisfies and as , where is the sample size. Results of this type are needed to establish the uniform asymptotic properties of the LS and quasi-GLS statistics. 相似文献