A simplified implementation of the least squares solution for pairwise comparisons matrices

This is a follow up to "Solution of the least squares method problem of pairwise comparisons matrix" by Bozóki published by this journal in 2008. Familiarity with this paper is essential and assumed. For lower inconsistency and decreased accuracy, our proposed solutions run in seconds instead of days. As such, they may be useful for researchers willing to use the least squares method (LSM) instead of the geometric means (GM) method.

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.

Maximizing the Efficiency of Greenhouse Gas Related Consumer Policy

Consumer policy approaches regarding green products and solutions can be differentiated by their main focus. “Green positioning” is basically targeted at environmentally aware consumers, while “efficiency-focused positioning” concentrates on the efficiency gain of the product or solution, targeting the whole society, regardless of consumers' environmental awareness. The paper argues that the scope and total environmental benefit can be increased if green products or solutions are promoted in different ways, not only as “green” but also based on other arguments (like cost-efficiency, return on investment, etc.). The paper suggests a model for improving the efficiency of greenhouse gas (GHG)-related consumer policy. Based on the marginal social cost curve and the marginal private cost curve, different (green, yellow, and red) zones of action are identified. GHG mitigation options chosen from those zones are then evaluated with the help of profiling method, addressing the barriers to implementation. Profiling may help design an implementation strategy for the selected options and make consumer policy more effective and acceptable for mass market. Case study results show three different ways of positioning of GHG-related consumer policy in Hungary from 2000 and give practical examples of profiling, based on the latest marginal social cost curve and the contemporary energy saving policy of the state regarding the residential sector.

Maximizing the Efficiency of Greenhouse Gas Related Consumer Policy

Consumer policy approaches regarding green products and solutions can be differentiated by their main focus. “Green positioning” is basically targeted at environmentally aware consumers, while “efficiency-focused positioning” concentrates on the efficiency gain of the product or solution, targeting the whole society, regardless of consumers' environmental awareness. The paper argues that the scope and total environmental benefit can be increased if green products or solutions are promoted in different ways, not only as “green” but also based on other arguments (like cost-efficiency, return on investment, etc.). The paper suggests a model for improving the efficiency of greenhouse gas (GHG)-related consumer policy. Based on the marginal social cost curve and the marginal private cost curve, different (green, yellow, and red) zones of action are identified. GHG mitigation options chosen from those zones are then evaluated with the help of profiling method, addressing the barriers to implementation. Profiling may help design an implementation strategy for the selected options and make consumer policy more effective and acceptable for mass market. Case study results show three different ways of positioning of GHG-related consumer policy in Hungary from 2000 and give practical examples of profiling, based on the latest marginal social cost curve and the contemporary energy saving policy of the state regarding the residential sector.

The Shapley value for airport and irrigation games

In this paper cost sharing problems are considered. We focus on problems given by rooted trees, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, called irrigation games. A formal notion of irrigation games is introduced, and the characterization of the class of these games is provided. The well-known class of airport games Littlechild and Thompson (1977) is a subclass of irrigation games. The Shapley value Shapley (1953) is probably the most popular solution concept for transferable utility cooperative games. Dubey (1982) and Moulin and Shenker (1992) show respectively, that Shapley's Shapley (1953) and Young (1985)'s axiomatizations of the Shapley value are valid on the class of airport games. In this paper we show that Dubey (1982)'s and Moulin and Shenker (1992)'s results can be proved by applying Shapley (1953)'s and Young (1985)'s proofs, that is those results are direct consequences of Shapley (1953)'s and Young (1985)'s results. Furthermore, we extend Dubey (1982)'s and Moulin and Shenker (1992)'s results to the class of irrigation games, that is we provide two characterizations of the Shapley value for cost sharing problems given by rooted trees. We also note that for irrigation games the Shapley value is always stable, that is it is always in the core Gillies (1959).

On axiomatizations of the Shapley value for assignment games

We consider the problem of axiomatizing the Shapley value on the class of assignment games. We first show that several axiomatizations of the Shapley value on the class of all TU-games do not characterize this solution on the class of assignment games by providing alternative solutions that satisfy these axioms. However, when considering an assignment game as a communication graph game where the game is simply the assignment game and the graph is a corresponding bipartite graph buyers are connected with sellers only, we show that Myerson's component efficiency and fairness axioms do characterize the Shapley value on the class of assignment games. Moreover, these two axioms have a natural interpretation for assignment games. Component efficiency yields submarket efficiency stating that the sum of the payoffs of all players in a submarket equals the worth of that submarket, where a submarket is a set of buyers and sellers such that all buyers in this set have zero valuation for the goods offered by the sellers outside the set, and all buyers outside the set have zero valuations for the goods offered by sellers inside the set. Fairness of the graph game solution boils down to valuation fairness stating that only changing the valuation of one particular buyer for the good offered by a particular seller changes the payoffs of this buyer and seller by the same amount.