10,436 research outputs found
Stability and Equilibrium Selection in a Link Formation Game
In this paper we use a non cooperative equilibrium selection approach as a notion of stability in link formation games. Specifically, we follow the global games approach first introduced by Carlsson and van Damme (1993), to study the robustness of the set of Nash equilibria for a class of link formation games in strategic form with supermodular payoff functions. Interestingly, the equilibrium selected is in conflict with those predicted by the traditional cooperative refinements. Moreover, we get a conflict between stability and efficiency even when no such conflict exists with the cooperative refinements. We discuss some practical issues that these different theoretical approaches raise in reality. The paper also provides an extension of the global game theory that can be applied beyond network literature.Global Games, Equilibrium Selection, Networks.
Global Games with Strategic Substitutes
In this paper we use a non cooperative equilibrium selection approach as a notion of stability in link formation games. Specifically, we follow the global games approach first introduced by Carlsson and van Damme (1993), to study the robustness of the set of Nash equilibria for a class of link formation games in strategic form with supermodular payo. functions. Interestingly, the equilibrium selected is in conflict with those predicted by the traditional cooperative refinements. Moreover, we get a conflict between stability and e.ciency even when no such conflict exists with the cooperative refinements. We discuss some practical issues that these di.erent theoretical approaches raise in reality. The paper also provides an extension of the global game theory that can be applied beyond network literature.Games, Networks, Equilibrium Selection.
Distributed dynamic reinforcement of efficient outcomes in multiagent coordination and network formation
We analyze reinforcement learning under so-called âdynamic reinforcementâ. In reinforcement learning, each agentrepeatedly interacts with an unknown environment (i.e., other agents), receives a reward, and updates the probabilities of its next action based on its own previous actions and received rewards. Unlike standard reinforcement learning, dynamic reinforcement uses a combination of long term rewards and recent rewards to construct myopically forward looking action selection probabilities. We analyze the long term stability of the learning dynamics for general games with pure strategy Nash equilibria and specialize the results for coordination games and distributed network formation. In this class of problems, more than one stable equilibrium (i.e., coordination configuration) may exist. We demonstrate equilibrium selection under dynamic reinforcement. In particular, we show how a single agent is able to destabilize an equilibrium in favor of another by appropriately adjusting its dynamic reinforcement parameters. We contrast the conclusions with prior game theoretic results according to which the risk dominant equilibrium is the only robust equilibrium when agents â decisions are subject to small randomized perturbations. The analysis throughout is based on the ODE method for stochastic approximations, where a special form of perturbation in the learning dynamics allows for analyzing its behavior at the boundary points of the state space
Stochastic Coalitional Better-response Dynamics and Strong Nash Equilibrium
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
Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics
Evolutionary game dynamics is one of the most fruitful frameworks for
studying evolution in different disciplines, from Biology to Economics. Within
this context, the approach of choice for many researchers is the so-called
replicator equation, that describes mathematically the idea that those
individuals performing better have more offspring and thus their frequency in
the population grows. While very many interesting results have been obtained
with this equation in the three decades elapsed since it was first proposed, it
is important to realize the limits of its applicability. One particularly
relevant issue in this respect is that of non-mean-field effects, that may
arise from temporal fluctuations or from spatial correlations, both neglected
in the replicator equation. This review discusses these temporal and spatial
effects focusing on the non-trivial modifications they induce when compared to
the outcome of replicator dynamics. Alongside this question, the hypothesis of
linearity and its relation to the choice of the rule for strategy update is
also analyzed. The discussion is presented in terms of the emergence of
cooperation, as one of the current key problems in Biology and in other
disciplines.Comment: Review, 48 pages, 26 figure
Approximate Equilibrium and Incentivizing Social Coordination
We study techniques to incentivize self-interested agents to form socially
desirable solutions in scenarios where they benefit from mutual coordination.
Towards this end, we consider coordination games where agents have different
intrinsic preferences but they stand to gain if others choose the same strategy
as them. For non-trivial versions of our game, stable solutions like Nash
Equilibrium may not exist, or may be socially inefficient even when they do
exist. This motivates us to focus on designing efficient algorithms to compute
(almost) stable solutions like Approximate Equilibrium that can be realized if
agents are provided some additional incentives. Our results apply in many
settings like adoption of new products, project selection, and group formation,
where a central authority can direct agents towards a strategy but agents may
defect if they have better alternatives. We show that for any given instance,
we can either compute a high quality approximate equilibrium or a near-optimal
solution that can be stabilized by providing small payments to some players. We
then generalize our model to encompass situations where player relationships
may exhibit complementarities and present an algorithm to compute an
Approximate Equilibrium whose stability factor is linear in the degree of
complementarity. Our results imply that a little influence is necessary in
order to ensure that selfish players coordinate and form socially efficient
solutions.Comment: A preliminary version of this work will appear in AAAI-14:
Twenty-Eighth Conference on Artificial Intelligenc
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