On Convexity for NTU-Games

For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept.Convexity can be defined in a number of ways, each having its own specific attractions.Basically, these definitions fall into two categories, namely those based on a supermodular interpretation and those based on a marginalistic interpretation.For games with non-transferable utility, however, the literature only offers two kinds of convexity, ordinal and cardinal convexity, which both extend the supermodular interpretation.In this paper, we introduce and analyse three new types of convexity for NTU-games that generalise the marginalistic interpretation of convexity.game theory

Game theory

game theory

Egalitarianism in Nontransferable Utility Games

This paper studies egalitarianism in the context of nontransferable utility games by introducing and analyzing the egalitarian value. This new solution concept is based on an egalitarian negotiation procedure in which egalitarian opportunities of coalitions are explicitly taken into account. We formulate conditions under which it leads to a core element and discuss the egalitarian value for the well-known Roth-Shafer examples. Moreover, we characterize the new value on the class of bankruptcy games and bargaining games

An Ordinal Shapley Value for Economic Environments

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and refer to it as an Ordinal Shapley value (OSV). The OSV associates with each problem an allocation as well as a matrix of concessions ``measuring'' the gains each agent foregoes in favor of the other agents. We analyze the structure of the concessions, and show they are unique and symmetric. Next we characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone in an agent's initial endowments and satisfies anonymity. Finally, similarly to the weighted Shapley value for TU games, we construct a weighted OSV as well.Non-Transferable utility games, Shapley value, consistency, fairness

Core equivalence theorems for infinite convex games

We show that the core of a continuous convex game on a measurable space of players is a von Neumann-Morgenstern stable set. We also extend the definition of the Mas-Colell bargaining set to games with a measurable space of players, and show that for continuous convex games the core may be strictly included in the bargaining set but it coincides with the set of all countably additive payoff measures in the bargaining set. We provide examples which show that the continuity assumption is essential to our results

An Ordinal Shapley Value for Economic Environments (Revised Version)

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it the Ordinal Shapley value (OSV). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous. Finally, similarly to the weighted Shapely value for TU games, we construct a weighted OSV as well.Non-Transferable utility games, Shapley value, Ordinal Shapley value, consistency, fairness.

On Convexity for NTU-Games

For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept.Convexity can be defined in a number of ways, each having its own specific attractions.Basically, these definitions fall into two categories, namely those based on a supermodular interpretation and those based on a marginalistic interpretation.For games with non-transferable utility, however, the literature only offers two kinds of convexity, ordinal and cardinal convexity, which both extend the supermodular interpretation.In this paper, we introduce and analyse three new types of convexity for NTU-games that generalise the marginalistic interpretation of convexity.

Applications of Negotiation Theory to Water Issues

The purpose of the paper is to review the applications of non-cooperative bargaining theory to water related issues – which fall in the category of formal models of negotiation. The ultimate aim is that to, on the one hand, identify the conditions under which agreements are likely to emerge, and their characteristics; and, on the other hand, to support policy makers in devising the “rules of the game” that could help obtain a desired result. Despite the fact that allocation of natural resources, especially of trans-boundary nature, has all the characteristics of a negotiation problem, there are not many applications of formal negotiation theory to the issue. Therefore, this paper first discusses the non-cooperative bargaining models applied to water allocation problems found in the literature. Particular attention will be given to those directly modelling the process of negotiation, although some attempts at finding strategies to maintain the efficient allocation solution will also be illustrated. In addition, this paper will focus on Negotiation Support Systems (NSS), developed to support the process of negotiation. This field of research is still relatively new, however, and NSS have not yet found much use in real life negotiation. The paper will conclude by highlighting the key remaining gaps in the literature.Negotiation theory, Water, Agreeements, Stochasticity, Stakeholders