Weight Monotonic Allocation Rules for Communication Situations with Asymmetry

If you have any comment or question on the working paper series, please contact each author. When making a copy or reproduction of the content, please contact us in advance to request permission. The source should explicitly be credited

Efficient extensions of communication values

We study values for transferable utility games enriched by a communication graph. The most well-known such values are component-efficient and characterized by some link-deletion property. We study efficient extensions of such values: for a given component-efficient value, we look for a value that (i) satisfies efficiency, (ii) satisfies the link-deletion property underlying the original component-efficient value, and (iii) coincides with the original component-efficient value whenever the underlying graph is connected. Béal et al. (2015) prove that the Myerson value (Myerson, 1977) admits a unique efficient extension, which has been introduced by van den Brink et al. (2012). We pursue this line of research by showing that the average tree solution (Herings et al., 2008) and the compensation solution (Béal et al., 2012a) admit similar unique efficient extensions, and that there exists no efficient extension of the position Value (Meessen, 1988; Borm et al., 1992). As byproducts, we obtain new characterizations of the average tree solution and the compensation solution, and of their efficient extensions

A strategic implementation of the sequential equal surplus division rule for digraph cooperative games

We provide a strategic implementation of the sequential equal surplus division rule (Béal et al., 2014). Precisely, we design a non-cooperative mechanism of which the unique subgame perfect equilibrium payoffs correspond to the sequential equal surplus division outcome of a superadditive rooted tree TU-game. This mechanism borrowed from the bidding mechanism designed by Pérez-Castrillo and Wettstein (2001), but takes into account the direction of the edges connecting any two players in the rood tree, which reflects some dominance relation between them

Smooth Multibidding Mechanisms

We propose a smooth multibidding mechanism for environments where a group of agents have to choose one out of several projects. Our proposal is related to the multibidding mechanism (Pérez-Castrillo and Wettstein, 2002) but it is “smoother” in the sense that small variations in an agent’s bids do not lead to dramatic changes in the probability of selecting a project. This mechanism is shown to possess several interesting properties. First, the equilibrium outcome is unique. Second, it ensures an equal sharing of the surplus that it induces. Finally, it enables reaching an outcome as close to efficiency as is desired.mechanism design, NIMBY

Smooth multibidding mechanisms

We propose a smooth multibidding mechanism for environments where a group of agents have to choose one out of several projects (possibly with the help of a social planner). Our proposal is related to the multibidding mechanism (Pérez-Castrillo and Wettstein, 2002) but it is "smoother" in the sense that small variations in an agent's bids do not lead to dramatic changes in the probability of selecting a project. This mechanism is shown to possess several interesting properties. Unlike in the study by Pérez Castrillo and Wettstein (2002), the equilibrium outcome is unique. Second, it ensures an equal sharing of the surplus that it induces. Finally, it enables reaching an outcome as close to effciency as is desired

A Strategic Implementation of the Average Tree Solution for Cycle-Free Graph Games

In this note we provide a strategic implementation of the Average Tree solution for zero-monotonic cycle-free graph games. That is, we propose a non-cooperative mechanism of which the unique subgame perfect equilibrium payoffs correspond to the average hierarchical outcome of the game. This mechanism takes into account that a player is only able to communicate with other players (i.e., to make proposals about a division of the surplus of cooperation) when they are connected in the graph. © 2013 Elsevier Inc

Fairness and fairness for neighbors: the difference between the Myerson value and component-wise egalitarian solutions

We replace the axiom of fairness used in the characterization of the Myerson value (Myerson, 1977) by fairness for neighbors in order to characterize the component-wise egalitarian solution. When a link is broken, fairness states the two players incident to the link should be affected similarly while fairness for neighbors states that a player incident to the link and any of his other neighbors should be affected similarly. Fairness for neighbors is also used to characterize the component-wise egalitarian surplus solution and a two-step egalitarian solution. These results highlight that egalitarian and marginalistic allocation rules can be obtained by applying the same equal gain/loss property to different types of players

Investments in Social Ties, Risk Sharing and Inequality

This paper investigates stable and efficient networks in the context of risk-sharing, when it is costly to establish and maintain relationships that facilitate risk-sharing. We find a novel trade-off between efficiency and equality. The most stable effic

Game Theory

The Special Issue “Game Theory” of the journal Mathematics provides a collection of papers that represent modern trends in mathematical game theory and its applications. The works address the problem of constructing and implementation of solution concepts based on classical optimality principles in different classes of games. In the case of non-cooperative behavior of players, the Nash equilibrium as a basic optimality principle is considered in both static and dynamic game settings. In the case of cooperative behavior of players, the situation is more complicated. As is seen from presented papers, the direct use of cooperative optimality principles in dynamic and differential games may bring time or subgame inconsistency of a solution which makes the cooperative schemes unsustainable. The notion of time or subgame consistency is crucial to the success of cooperation in a dynamic framework. In the works devoted to dynamic or differential games, this problem is analyzed and the special regularization procedures proposed to achieve time or subgame consistency of cooperative solutions. Among others, special attention in the presented book is paid to the construction of characteristic functions which determine the power of coalitions in games. The book contains many multi-disciplinary works applied to economic and environmental applications in a coherent manner