Random Decentralized Market Processes for Stable Job Matchings with Competitive Salaries

We analyze a decentralized process in a basic labor market where finitely many heterogeneous firms and workers meet directly and randomly in pursuit of higher payoffs over time and agents may behave myopically. We introduce a general random decentralized market process that almost surely converges in finite time to a competitive equilibrium of the market. A key proposition en route to this result exhibits a finite sequence of successive bilateral trades from an arbitrary initial market state to a stable matching between firms and workers with a scheme of competitive salary offers

A dynamic theory of fidelity networks with an application to the spread of HIV/AIDS

We study the dynamic stability of fidelity networks, which are networks that form in a mating economy of agents of two types (say men and women), where each agent desires direct links with opposite type agents, while engaging in multiple partnerships is considered an act of infidelity. Infidelity is punished more severely for women than for men. We consider two stochastic processes in which agents form and sever links over time based on the reward from doing so, but may also take non-beneficial actions with small probability. In the first process, an agent who invests more time in a relationship makes it stronger and harder to break by his/her partner; in the second, such an agent is perceived as weak. Under the first process, only egalitarian pairwise stable networks (in which all agents have the same number of partners) are visited in the long run, while under the second, only anti-egalitarian pairwise stable networks (in which all women are matched to a small number of men) are. Next, we apply these results to find that under the first process, HIV/AIDS is equally prevalent among men and women, while under the second, women bear a greater burden. The key message is that anti-female discrimination does not necessarily lead to higher HIV/AIDS prevalence among women in the short run, but it does in the long run.fidelity networks; anti-female discrimination; stochastic stability; HIV/AIDS; union formation models

One-seller assignment markets with multi-unit demands

We consider one-seller assignment markets with multi-unit demands and prove that the associated game is buyers-submodular. Therefore the core is non-empty and it has a lattice structure which contains the allocation where every buyer receives his marginal contribution. We prove that in this kind of market, every pairwise-stable outcome is associated to a competitive equilibrium and viceversa. We study conditions under which the buyers-optimal and the seller-optimal core allocations are competitive equilibrium payoff vectors. Moreover, we characterize the markets for which the core coincidences with the set of competitive equilibria payoff vectors. When agents behave strategically, we introduce a procedure that implements the buyers-optimal core allocation as the unique subgame perfect Nash equilibrium outcome

On the structure of cooperative and competitive solutions for a generalized assignment game

We study cooperative and competitive solutions for a many- to-many generalization of Shapley and Shubik (1972)'s assignment game. We consider the Core, three other notions of group stability and two al- ternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related with the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated to the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of ma- trices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view

A survey on assignment markets

The assignment game is a two-sided market, say buyers and sellers, where demand and supply are unitary and utility is transferable by means of prices. This survey is structured in three parts: a first part, from the introduction of the assignment game by Shapley and Shubik (1972) until the publication of the book of Roth and Sotomayor (1990), focused on the notion of core; the subsequent investigations that broaden the scope to other notions of solution for these markets; and its extensions to assignment markets with multiple sides or multiple partnership. These extended two-sided assignment markets, that allow for multiple partnership, better represent the situation in a labour market or an auction

A labor market with heterogeneous firms and workers

A labor market where firms and workers are heterogeneous and may form more than one partnership is considered. A natural concept of core for such markets, different from the concept used by Thompson (1977), is defined. We show that the core is non-empty and is, in general, strictly greater than Thompson's core. Unlike Thompson, we found several dissimilarities between our model and the well known one-to-one case studied in Shapley and Shubik (1972).stable payoff, core, optimal stable payoffs.