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.

Horizontal diversity of higher education institutions. The case of Hungary – in European context

In the European Higher Education Area the diversification of higher education is considered to be an emphasized value, a guarantee of creativity. The various institutional rankings are the displays of vertical diversity, but in parallel with these, there is an increasing attention directed at horizontal diversity, the entirety of the institutions' activities. The European Mapping Project (U-map) undertook this challenge. The paper presents the research program, which is an attempt to adapt the U-map model to Hungary. According to the results, the U-map method which was intended for application on an international level, is very useful in the identification of the main groups of institutions in a specific national higher education system as well, and may provide a basis for the creation of institutional strategies and the development of the institutions’ network.