A noncooperative foundation of the asymmetric Nash bargaining solution

We consider a noncooperative multilateral bargaining model with heterogeneous time preferences in which the first rejector of a proposal in the current round becomes the proposer in the next round. We show the existence of a stationary subgame perfect equilibrium (SSPE), characterize SSPEs and show the efficiency of SSPEs. We show that any sequence of SSPE payoff profiles converges to the asymmetric Nash bargaining solution weighted by the inverses of discount rates as the bargaining friction vanishes.     

Office-based and home-care for older adults in primary care: A comparative analysis using the Nash bargaining solution

Three care delivery settings are compared in this study: office-based care, home-care, and mixed-care, i.e., office-based care combined with home-care, in solo, small, medium, and large primary care practices. The objective of this paper is to identify which of these settings better achieves the secondary goals of the so-called quadruple aim, i.e., reducing costs, improving the patient experience, and improving the physician experience. A multi-objective integer programming formulation is developed to capture the elements of strategic health care planning. The formulation considers the minimization of four objective functions: the total cost of care workers, the total number of care workers, the total rejected demand and unsatisfied preferred care location, and the total panel size of the providers. Instead of computing the entire Pareto frontier, we used the Nash bargaining solution to determine a single Pareto optimal solution for the problem. The approach was tested using real world instances, which can be adjusted to any specific primary care practice. The numerical results show that none of the settings provides the smallest values in all objective functions. The choice of a setting for a primary care practice depends on the secondary goals that the practice desires to emphasize, and, in most cases, it is independent of the type of practice size. For the analyzed instances, a calculated overall score for each setting determined that, on average, the settings based on home-care strengthen the achievement of the secondary goals of the quadruple aim more so than in comparison to the office-based physician settings.     

Taxes on labour and unemployment in a shirking model with union bargaining

This paper studies the impact of a cut in labour taxes in a model that combines two explanations for equilibrium unemployment: employee shirking and union bargaining. It is shown that if the ratio of unemployment compensation to the net-of-tax wages is kept fixed, a tax cut leads to higher unemployment. When the unemployment benefits are fixed in real terms, the effect of a tax cut on unemployment is ambiguous. Adverse employment effects are ruled out if unions are powerless or the labour share is constant.     

On the convergence to the Cournot equilibrium in a productive asset oligopoly

We derive a feedback equilibrium of a dynamic Cournot game where production requires exploitation of a renewable asset. As in the classical Cournot model, quantity-setting firms compete in the same market for a given homogeneous good. We show that, when the asset stock grows sufficiently fast, the unique globally asymptotically stable steady state of the dynamic Cournot game corresponds to the static Cournot solution. Initial differences between firms’ production rates due to asymmetric allocations of asset stocks tend to disappear over time. When instead the asset stock grows slowly, the system does not converge to any stationary point. We also show that, within the class of linear feedback equilibrium strategies, besides the couple of strategies that stabilizes the states for every possible initial conditions, there exists another couple which is more efficient, in that it leads to higher stationary equilibrium profits for both firms, closer to the collusive outcome. Finally, we show that, as the discount rate approaches zero, there exist multiple linear feedback equilibrium strategies that induce a price trajectory that converges asymptotically to a price which is above the static Cournot equilibrium price.