Cooperation by Asymmetric Agents in a Joint Project

The object of study is cooperation in joint projects, where agents may have different desired sophistication levels for the project, and where some of the agents may have low budgets.In this context questions concerning the optimal realizable sophistication level and the distribution of the related costs among the participants are tackled.A related cooperative game, the enterprise game, and a non-cooperative game, the contribution game, are both helpful.It turns out that there is an interesting relation between the core of the convex enterprise game and the set of strong Nash equilibria of the contribution game.Special attention is paid to a rule inspired by the airport landing fee literature.For this rule the project is split up in a sequence of subprojects where the involved participants pay amounts which are, roughly speaking, equal, but not more than their budgets allow.The resulting payoff distribution turns out to be a core element of the related contribution game.game theory;projects

An Algorithm for the Nucleolus of Airport Profit Problems

Airport profit games are a generalization of airport cost games as well as of bankruptcy games.In this paper we present a simple algorithm to compute the nucleolus of airport profit games.In addition we prove that there exists an unique consistent allocation rule in airport profit problems, and it coincides with the nucleolus of the associated TU game.algorithm;airports;profit;allocation;games

A new solution concept for the roommate problem

Abstract The aim of this paper is to propose a new solution concept for the roommate problem with strict preferences. We introduce maximum irreversible matchings and consider almost stable matchings (Abraham et al., 2006) and maximum stable matchings (Tan 1990, 1991b). These solution concepts are all core consistent. We find that almost stable matchings are incompatible with the other two concepts. Hence, to solve the roommate problem we propose matchings that lie at the intersection of the maximum irreversible matchings and maximum stable matchings, which we call Q -stable matchings. We construct an efficient algorithm for computing one element of this set for any roommate problem. We also show that the outcome of our algorithm always belongs to an absorbing set (Inarra et al., 2013)

A new solution for the roommate problem

The aim of this paper is to propose a new solution for the roommate problem with strict references. We introduce the solution of maximum ir reversibility and consider almost stable matchings (Abraham et al. [2]) and maximum stable m atchings (Tan [30] [32]). We find that almost stable matchings are incompatible with the o ther two solutions. Hence, to solve the roommate problem we propose matchings that lie at t he intersection of the maximum irreversible matchings and maximum stable matchings , which are called Q-stable matchings. These matchings are core consistent and we offer an efficient algorithm for computing one of them. The outcome of the algorithm belongs to an ab sorbing set

Cooperation by Asymmetric Agents in a Joint Project

The object of study is cooperation in joint projects, where agents may have different desired sophistication levels for the project, and where some of the agents may have low budgets.In this context questions concerning the optimal realizable sophistication level and the distribution of the related costs among the participants are tackled.A related cooperative game, the enterprise game, and a non-cooperative game, the contribution game, are both helpful.It turns out that there is an interesting relation between the core of the convex enterprise game and the set of strong Nash equilibria of the contribution game.Special attention is paid to a rule inspired by the airport landing fee literature.For this rule the project is split up in a sequence of subprojects where the involved participants pay amounts which are, roughly speaking, equal, but not more than their budgets allow.The resulting payoff distribution turns out to be a core element of the related contribution game

Matching Dynamics with Constraints

We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to another agent. Each agent has a complete preference list over all other agents it can be matched with. However, depending on the constraints and the current state of the game, not all possible partners are available for matching at all times. For correlated preferences, we propose and study a general class of hedonic coalition formation games that we call coalition formation games with constraints. This class includes and extends many recently studied variants of stable matching, such as locally stable matching, socially stable matching, or friendship matching. Perhaps surprisingly, we show that all these variants are encompassed in a class of "consistent" instances that always allow a polynomial improvement sequence to a stable state. In addition, we show that for consistent instances there always exists a polynomial sequence to every reachable state. Our characterization is tight in the sense that we provide exponential lower bounds when each of the requirements for consistency is violated. We also analyze matching with uncorrelated preferences, where we obtain a larger variety of results. While socially stable matching always allows a polynomial sequence to a stable state, for other classes different additional assumptions are sufficient to guarantee the same results. For the problem of reaching a given stable state, we show NP-hardness in almost all considered classes of matching games.Comment: Conference Version in WINE 201