Graphs Inducing Totally Balanced and Submodular Chinese Postman Games

Abstract A Chinese postman (CP) game is induced by a a weighted undirected, connected graph in which the edges are identified as players and a vertex is chosen as post-office location. Granot and Granot (2012) characterized graphs that give rise to CP games that are balanced. This note completes this line of research by characterizing graphs that give rise to CP games that are submodular (totally balanced, respectively).

Updating Claims in Bankruptcy Problems

We reexamine the consistency axiom in bankruptcy problems and propose arguments in favor of an alternative definition of a reduced problem. The classical definition updates the size of the estate while keeping agents' claims unaffected. Instead, we suggest updating agents' claims along with the estate. The resulting consistency axiom characterizes the well-known Random Arrival rule as the unique bilaterally consistent extension of the Contested Garment rule to many agents. We also establish that our definition of a reduced bankruptcy problem corresponds to the definition of a reduced TU game proposed in Hart & Mas-Colell (Econometrica, 1989).

Bargaining with Independence of Higher or Irrelevant Claims

This paper studies independence of higher claims and independence of irrelevant claims on the domain of bargaining problems with claims. Independence of higher claims requires that the payoff of an agent does not depend on the higher claim of another agent. Independence of irrelevant claims states that the payoffs should not change when the claims decrease but remain higher than the payoffs. Interestingly, in conjunction with standard axioms from bargaining theory, these properties characterize a new constrained Nash solution, a constrained Kalai-Smorodinsky solution, and a constrained Kalai solution

The [alpha]-serial cost-sharing rule

In this paper we present a family of cost-sharing rules for cost-sharing problems. Each rule in this family can be seen as a combination of the serial cost-sharing rule (Moulin and Shenker, 1992) and the dual serial cost-sharing rule (Albizuri and Zarzuelo, 2007). The parameter [alpha] determines how this combination is obtained. We also provide an axiomatization of this family by using a weaker axiom than the well-known Independence of higher demands axiom (Moulin and Shenker, 1992).Cost-sharing problems Serial cost-sharing rule Dual serial cost-sharing rule

Values and coalition configurations

In this paper we consider coalition configurations (Albizuri et al. in Games Econ Behav 57:1–17, 2006), that is, families of coalitions not necessarily disjoint whose union is the grand coalition, and give a generalization of the Shapley value (Contributions to the theory of games II, Princeton University Press, Princeton, pp 307–317, 1953) and the Owen value (Essays in mathematical economics and game theory, Springer, Berlin, pp 76–88, 1977) when coalition configurations form. This will be an alternative definition to the one given by Albizuri et al.Ministerio de Ciencia e Innovación | Ref. ECO2011-23460Ministerio de Economía y Competitividad | Ref. ECO2012-33618Universidad del País Vasco | Ref. UFI11/5Universidad del País Vasco | Ref. GIU13/31Xunta de Galicia | Ref. 10PXIB362299P

Graphs inducing totally balanced and submodular Chinese postman games

A Chinese postman (CP) game is induced by a weighted undirected, connected graph in which the edges are identified as players and a vertex is chosen as post-office location. Granot and Granot (2012) characterized graphs that give rise to CP games that are balanced. This note completes this line of research by characterizing graphs that give rise to CP games that are submodular (totally balanced, respectively)

A new axiomatization of the Banzhaf semivalue

A new characterization of the Banzhaf semivalue on the domain of monotonic simple games is given. We use the well-known valuation and dummy axioms plus two additional properties. The first one simply requires that the power-index be bigger for those players belonging to more winning coalitions. The second one is the proportionality axiom introduced by Owen in (1982) which is suitable for those simple games that represent an indirect voting process.Banzhaf, power-index