On the implementation of the L-Nash bargaining solution in two-person bargaining games

The “Nash program” initiated by Nash (Econometrica 21:128–140, 1953) is a research agenda aiming at representing every axiomatically determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L-Nash solution first defined by Forgó (Interactive Decisions. Lecture Notes in Economics and Mathematical Systems, vol 229. Springer, Berlin, pp 1–15, 1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative infinity in a fixed direction. In Forgó and Szidarovszky (Eur J Oper Res 147:108–116, 2003), the L-Nash solution was related to the solution of multiciteria decision making and two different axiomatizations of the L-Nash solution were also given in this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two-person bargaining problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement point to obtain the L-Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein’s alternative offer game (Econometrica 50:97–109, 1982) is shown to asymptotically implement the L-Nash solution. If penalty is internalized as a decision variable of one of the players, then a modification of Howard’s game (J Econ Theory 56:142–159, 1992) also implements the L-Nash solution.

Trading between perceived risks and benefits related to biosimilar biological treatment in Crohn’s disease; discrete choice experiment among gastroenterologists

Objective: The objective of the study is to explore preferences of gastroenterologists for biosimilar drugs in Crohn’s Disease and reveal trade-offs between the perceived risks and benefits related to biosimilar drugs. Method: Discrete choice experiment was carried out involving 51 Hungarian gastroenterologists in May, 2014. The following attributes were used to describe hypothetical choice sets: 1) type of the treatment (biosimilar/originator) 2) severity of disease 3) availability of continuous medicine supply 4) frequency of the efficacy check-ups. Multinomial logit model was used to differentiate between three attitude types: 1) always opting for the originator 2) willing to consider biosimilar for biological-naïve patients only 3) willing to consider biosimilar treatment for both types of patients. Conditional logit model was used to estimate the probabilities of choosing a given profile. Results: Men, senior consultants, working in IBD center and treating more patients are more likely to willing to consider biosimilar for biological-naïve patients only. Treatment type (originator/biosimilar) was the most important determinant of choice for patients already treated with biologicals, and the availability of continuous medicine supply in the case biological-naïve patients. The probabilities of choosing the biosimilar with all the benefits offered over the originator under current reimbursement conditions are 89% vs 11% for new patients, and 44% vs 56% for patients already treated with biological. Conclusions: Gastroenterologists were willing to trade between perceived risks and benefits of biosimilars. The continuous medical supply would be one of the major benefits of biosimilars. However, benefits offered in the scenarios do not compensate for the change from the originator to the biosimilar treatment of patients already treated with biologicals.