مقاله انگلیسی رایگان در مورد ثبات و مزایده در بازار کار با امنیت شغلی – الزویر ۲۰۱۷

The purpose of this note is to study a connection between a model of labor markets with regulation recently defined and analyzed in Fu et al. (2017) and a model of simultaneous single-item auctions which was originally suggested by Bikhchandani (1999) and which has received significant attention in the last few years in the computer science literature on algorithmic game theory. This connection yields new results in both models. In particular, the results of Fu et al. (2017) on labor markets with regulation imply (via the connection we establish here) new bounds on the price of anarchy and the price of stability of simultaneous second price auctions as well as new guarantees on the existence of pure Nash equilibria in this auction game. In the classical labor market model due to Kelso and Crawford (1982) there is a set of firms N, a set of workers M, and a production function v n : 2 M → ℜ+ for every firm n ∈ N, where v n (S) is the production value of firm n if it hires a subset workers S ∈ ۲ M . Three main results of this theory are that gross-substitutability of all production functions is a sufficient condition for the existence of a stable matching of workers and firms, that all stable matchings are efficient, and that in fact gross-substitutability is also a necessary condition for the above two properties to hold (this last property is due to Gul and Stacchetti (1999)). Bikhchandani (1999) studies a complete-information auction game where firms compete simultaneously for employees by proposing salaries, and employees pursue the highest offer. This is known in the literature on combinatorial auctions as a First Price Item Bidding (FPIB) auction. Bikhchandani (1999) shows a connection between this auction game and the classic labor market model described above, by showing a correspondence between the set of Nash equilibrium (NE) outcomes of the FPIB game and the set of stable outcomes of a labor market.3 In a recent paper (Fu et al., 2017) we modify the classic labor market model and study labor markets with regulation designed to provide employees with job security. To capture job security we have introduced a weaker solution concept termed JS-stability (where JS stands for job security). That previous paper has three main results: it provides sufficient conditions on the structure of the production functions that ensure the existence of JS-stability, it shows that the welfare in any JS-stable outcome is at least half of the optimal welfare, and it describes necessary and sufficient conditions for the existence of efficient JS-stable outcomes. These results therefore provide a mirror image of the three main results of classic labor markets (without job security) described above. Continuing this thread of thought, our result in this current note parallels the connection between the classic labor market and the FPIB game of Bikhchandani (1999). Specifically, we show a connection between labor markets with job security and the Second Price Item Bidding (SPIB) auction game, introduced in Christodoulou et al. (2008). The difference between FPIB and SPIB is that in the latter an employee’s salary is determined by the second highest offer and not the first. While Bikhchandani (1999) shows a correspondence between the set of pure NE outcomes of the FPIB auction game and the set of stable matchings of the classic labor market (without regulation), we show here a correspondence between the set of pure NE outcomes of the SPIB auction game and the set of JS-stable outcomes in our model of labor markets with regulation. The two theories of labor markets with and without job security are therefore parallel with respect to this property as well. As mentioned above, as an immediate corollary of this connection we obtain several results regarding existence of pure Nash equilibria in the SPIB auction game, and the price of anarchy and price of stability in this game. Section 2 gives more details on the model of a labor market with regulation. Section 3 analyzes the connection between the labor market model and the auction model, and describes some corollaries that this connection yields.