Symmetric Convex Games and Stable Structures

We study the model of link formation that was introduced by Aumann and Myerson (1988) and focus on symmetric convex games with transferable utilities. We answer an open question in the literature by showing that in a specific symmetric convex game with six players a structure that results in the same payoffs as the full cooperation structure can be formed according to a subgame perfect Nash equilibrium.symmetric convex game;undirected graph;link formation;stable structures

Directed Communication Networks

In this paper we model the formation of directed communication networks.A directed communication network is represented by a directed graph.Firstly, we study an allocation rule satisfying two appealing properties, component efficiency and directed fairness.We show that such an allocation rule exists if and only if we restrict ourselves to a class of directed graphs that naturally comes to the fore in the setting of hierarchical structures.Subsequently, we discuss several possibilities to model the formation of directed communication networks and provide some preliminary results

Incomplete stable structures in symmetric convex games

We study the model of link formation that was introduced by Aumann and Myerson [in: A. Roth (Ed.), The Shapley Value. Cambridge Univ. Press, 1988, pp. 175–191] and focus on symmetric convex games with transferable utilities. We show that with at most five players the full cooperation structure results according to a subgame perfect Nash equilibrium. Moreover, if the game is strictly convex then every subgame perfect Nash equilibrium results in a structure that is payoff equivalent to the full cooperation structure. Subsequently, we analyze a game with six players that is symmetric and strictly convex. We show that there exists a subgame perfect Nash equilibrium that results in an incomplete structure in which two players are worse off than in the full cooperation structure, whereas four players are better off. Independent of the initial order any pair of players can end up being exploited

Incomplete Stable Structures In Symmetric Convex Games

We study the model of link formation that was introduced by Aumann and Myerson (1988) and focus on symmetric convex games with transferable utilities. We show that with at most five players the full cooperation structure results according to a subgame perfect Nash equilibrium.Moreover, if the game is strictly convex then every subgame perfect Nash equilibrium results in a structure that is payoff equivalent to the full cooperation structure. Subsequently, we analyze a game with six players that is symmetric and strictly convex.We show that there exists a subgame Nash equilibrium that results in an incomplete structure in which two players are worse off than in the full cooperation structure, whereas four players are better off.Independent of the initial order any pair of players can end up being exploited.