1,957 research outputs found

    Stochastic Coalitional Better-response Dynamics and Strong Nash Equilibrium

    Get PDF
    We consider coalition formation among players in an n-player finite strategic game over infinite horizon. At each time a randomly formed coalition makes a joint deviation from a current action profile such that at new action profile all players from the coalition are strictly benefited. Such deviations define a coalitional better-response (CBR) dynamics that is in general stochastic. The CBR dynamics either converges to a strong Nash equilibrium or stucks in a closed cycle. We also assume that at each time a selected coalition makes mistake in deviation with small probability that add mutations (perturbations) into CBR dynamics. We prove that all strong Nash equilibria and closed cycles are stochastically stable, i.e., they are selected by perturbed CBR dynamics as mutations vanish. Similar statement holds for strict strong Nash equilibrium. We apply CBR dynamics to the network formation games and we prove that all strongly stable networks and closed cycles are stochastically stable

    Generic Determinacy of Nash Equilibrium in Network Formation Games

    Get PDF
    This paper shows that the set of probability distributions over networks induced by Nash equilibria of the network formation game proposed by Myerson (1991) is finite for a generic assignment of payoffs to networks. The same result can be extended to several variations of the game found in the literature.Networks; generic finiteness; Nash Equilibrium

    Social Network Formation with Consent

    Get PDF
    We investigate the equilibria of game theoretic models of network formation that are based on individual actions only.Our approach is grounded in three simple and realistic principles: (1) Link formation should be a binary process of consent.(2) Link formation should be costly.(3) The class of network payoff functions should be as general as possible.It is accepted that these consent models have a very large number of equilibria.However, until now no characterization of these equilibria has been established in the literature.We aim to fill this void and provide characterizations of stable networks or the cases of two-sided and one-sided link formation costs.Furthermore, we provide a comparison of Nash equilibria with potential maximizers for a certain specification.game theory;general equilibrium

    Costly Network Formation and Regular Equilibria

    Get PDF
    We prove that for generic network-formation games where players incur some strictly positive cost to propose links the number of Nash equilibria is finite. Furthermore all Nash equilibria are regular and, therefore, stable sets.Network-formation games; Regular equilibrium; Stable sets

    The Role of Trust in Costly Network Formation

    Get PDF
    We investigate game theoretic models of entwork formation that are based on individual actions only. Our approach is grounded in three simple and realistic principles. (1) Link formation should be a binary process of consent. (2) Link formation should be costly. (3) The class of network payoff functions should be as general as possible. We provide charecterizations of stable networks under the hypothesis of mutual consent for the case of two-sided and one-sided link formation costs. Furthermore, we introduce a new eqilibrium concept based on a limited, realistic form of farsightedness or (myopic) ''trust'' in network formation. We provide comparisons of the resulting networks with networks satisfying well known stability concepts developed in the literatureSocial networks, individual stability, pairwsie stability, trust

    A Belief-based Approach to Network Formation

    Get PDF
    In this paper we consider four different game-theoretic approaches to describe the formation of social networks under mutual consent and costly communication. First, we consider Jackson-Wolinsky’s concept of pairwise stability. Next, we introduce a stronger version of this concept based on linking decisions by nodes, denoted as strict pairwise stability. Third, we consider Myerson’s consent game and its Nash equilibria. Fourth, within the context of Myerson’s consent game, we consider self-confirming equilibria based on simple myopic belief systems. We provide an exhaustive comparison of the classes of equilibrium networks that result from each of these four approaches. We determine the conditions under which there is equivalence of pairwise stability and strict pairwise stability. Second, we show that the Nash equilibria of Myerson’s consent game form a super set of the class of pairwise stable networks, while strict pairwise stability and monadic stability are fully equivalent.

    The Role of Trust in Costly Network Formation

    Get PDF
    We consider game theoretic models of social network formation.In this paper we limit our investigation to game theoretic models of network formation that are based on individual actions only.Our approach is based on three simple and realistic principles: (1) Link formation is a binary process of consent.(2) Link formation is costly.(3) The class of network payo functions should be as general as possible.We provide characterizations of stable networks under the hypothesis of mutual consent in the cases of two-sided and one-sided link formation costs. Furthermore, we introduce a new equilibrium concept based on a limited, realistic form of farsightedness or "trust" in network formation.game theory;models;general equilibrium;stability

    HedN Game, a Relational Framework for Network Based Cooperation

    Get PDF
    This paper proposes a new framework for cooperative games based on mathematical relations. Here cooperation is defined as a supportive partnerships represented by a directed network between players (aka hedonic relation). We examine in a specific context, modeled by abstract games how a change of supports induces a modification of strategic interactions between players. Two levels of description are considered: the first one describes the support network formation whereas the second one models the strategic interactions between players. Both are described in a unified formalism, namely CP~game. Stability conditions are stated, emphasizing the connection between these two levels. We also stress the interaction between updates of supports and their impact on the evolution of the context.Cooperative Game, Network, Stability, Hedonic Relation

    Pairwise-Stability and Nash Equilibria in Network Formation

    Get PDF
    Suppose that individual payoffs depend on the network connecting them. Consider the following simultaneous move game of network formation: players announce independently the links they wish to form, and links are formed only under mutual consent. We provide necessary and sufficient conditions on the network link marginal payoffs such that the set of pairwise stable, pairwise-Nash and proper equilibrium networks coincide, where pairwise stable networks are robust to one-link deviations, while pairwise-Nash networks are robust to one-link creation but multi-link severance. Under these conditions, proper equilibria in pure strategies are fully characterized by one-link deviation checks.Network formation, Pairwise-stability, Proper equilibrium
    • …
    corecore