A note on the axiomatization of the Nash equilibrium correspondence

A new axiomatization of the Nash equilibrium correspondence for n-person games based on independence of irrelevant strategies is given. Using a flexible general model, it is proved that the Nash equilibrium correspondence is the only solution to satisfy the axioms of non-emptiness, weak one-person rationality, independence of irrelevant strategies and converse independence of irrelevant strategies on the class of subgames of a fixed finite n-person game which admit at least one Nash equilibrium. It is also shown that these axioms are logically independent.

Family Business Succession in Austria – Satisfaction and the Incumbent-successor Relationship

The transfer of businesses contributes to the dynamics and the development of the economy in Austria. Successful transfers generate numerous positive impacts. Securing both employment and investment, creating new jobs and stimulating growth are some of these effects. Failed transfers can contribute to negative effects, including the loss of jobs and an economic slowdown. Over recent years the number of business handovers in Austria has been rising. The forecasts show that this number will remain high over the next few years. Between 2015 and 2024 more than 42,000 economically sound SMEs will face the challenge of finding an appropriate successor. This means that 26 % of all Austrian SMEs (excluding one-person businesses) and 29 % of all employees in these companies will be affected. The aim of this paper is to provide a multi-faceted discussion of the relevance of affective components in family business transfers. A “good” relationship between the successor and the departing owner fosters the success of a transfer. This relationship involves, among others, the willingness to share relevant information, openness and respect. The satisfaction (with the completed business transfer) is closely interrelated with the relationship between the successor and the departing owner. Consequently, we can assume that affective and emotional components can indeed shape the success of business transfers. Based on that, new future research opportunities are outlined.

Generalized correlated equilibrium for two-person games in extensive form with perfect information

A correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is applied for two-person finite games in extensive form with perfect information. Randomization by an umpire takes place over the leaves of the game tree. At every decision point players have the choice either to follow the recommendation of the umpire blindly or freely choose any other action except the one suggested. This scheme can lead to Pareto-improved outcomes of other correlated equilibria. Computational issues of maximizing a linear function over the set of soft correlated equilibria are considered and a linear-time algorithm in terms of the number of edges in the game tree is given for a special procedure called “subgame perfect optimization”.

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.