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.

A new proportional procedure for the n−person cake−cutting problem

We present a new cake−cutting procedure which guarantees everybody a proportional share according to his own valuation.