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تعداد صفحات این فایل: ۱۳ صفحه

بخشی از مقاله انگلیسیعنوان انگلیسی:Stability and auctions in labor markets with job security~~en~~

Abstract

Fu et al. (2016) introduced a stability concept for labor markets with job security. We show that their proposed outcomes form Nash equilibria of an auction where firms compete for workers. This parallels literature on stable outcomes and similar auctions, and yields new price of anarchy bounds.

Assigning workers through an auction

The notion of a stable outcome tells us what we can expect from an outcome in a labor market. Put differently, a non-stable outcome is something we cannot expect, as either one of the players (firms or workers) has negative utility, and in this case it can simply walk away from the market, or alternatively a coalition of a firm and workers can jointly walk away from the market and be better off. However, how markets reach stability is left open. To cope with this question we look at the market as a non-cooperative complete-information game (i.e., production functions of firms are common knowledge) where firms bid simultaneously for workers. Each worker is then assigned to work for the highest bidder at a salary equal the second highest bid. We refer to this game as a second-price item-bidding (SPIB) auction.

Nash equilibrium outcomes of this game were first analyzed by Christodoulou et al. (2008). Note that a trivial Nash equilibrium always exists in any SPIB auction, where one bidder bids ‘‘infinity’’ on every item and every other bidder bids zero. Such equilibria are neither interesting nor realistic. To exclude such equilibria, a bidder is said to be no-overbidding if the sum of her bids on any subset of items is no larger than her valuation for the subset. An equilibrium is no-overbidding if all bidders’ equilibrium strategies are no-overbidding. Christodoulou et al. (2008) showed that pure no-overbidding Nash equilibria are guaranteed to exist for SPIB auctions when all production functions are fractionally subadditive. Several additional papers continued to study this model, analyzing its ‘‘price of anarchy’’, which measures the efficiency level guaranteed by any no-overbidding Nash equilibrium, when it exists, relative to the optimal efficiency level. For example, Bhawalkar and Roughgarden (2011) showed that when buyers’ valuations are subadditive, a no-overbidding equilibrium, when it exists, always guarantees an efficiency level that is at least half of the maximum possible. The literature also studies the ‘‘price of stability’’ of various models, which is the efficiency that the best Nash equilibrium outcome guarantees relative to the optimal efficiency.

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