11,436 research outputs found
Designing Networks with Good Equilibria under Uncertainty
We consider the problem of designing network cost-sharing protocols with good
equilibria under uncertainty. The underlying game is a multicast game in a
rooted undirected graph with nonnegative edge costs. A set of k terminal
vertices or players need to establish connectivity with the root. The social
optimum is the Minimum Steiner Tree. We are interested in situations where the
designer has incomplete information about the input. We propose two different
models, the adversarial and the stochastic. In both models, the designer has
prior knowledge of the underlying metric but the requested subset of the
players is not known and is activated either in an adversarial manner
(adversarial model) or is drawn from a known probability distribution
(stochastic model).
In the adversarial model, the designer's goal is to choose a single,
universal protocol that has low Price of Anarchy (PoA) for all possible
requested subsets of players. The main question we address is: to what extent
can prior knowledge of the underlying metric help in the design? We first
demonstrate that there exist graphs (outerplanar) where knowledge of the
underlying metric can dramatically improve the performance of good network
design. Then, in our main technical result, we show that there exist graph
metrics, for which knowing the underlying metric does not help and any
universal protocol has PoA of , which is tight. We attack this
problem by developing new techniques that employ powerful tools from extremal
combinatorics, and more specifically Ramsey Theory in high dimensional
hypercubes.
Then we switch to the stochastic model, where each player is independently
activated. We show that there exists a randomized ordered protocol that
achieves constant PoA. By using standard derandomization techniques, we produce
a deterministic ordered protocol with constant PoA.Comment: This version has additional results about stochastic inpu
Designing Networks with Good Equilibria under Uncertainty
We consider the problem of designing network cost-sharing protocols with good equilibria under uncertainty. The underlying game is a multicast game in a rooted undirected graph with nonnegative edge costs. A set of terminal vertices or players needs to establish connectivity with the root. The social optimum is the minimum Steiner tree. We study situations where the designer has incomplete information about the input. We propose two different models, the adversarial and the stochastic. In both models, the designer has prior knowledge of the underlying graph metric, but the requested subset of the players is not known and is activated either in an adversarial manner (adversarial model) or is drawn from a known probability distribution (stochastic model). In the adversarial model, the goal of the designer is to choose a single, universal cost-sharing protocol that has low Price of Anarchy (PoA) for all possible requested subsets of players. The main question we address is, to what extent can prior knowledge of the underlying graph metric help in the design? We first demonstrate that there exist classes of graphs where knowledge of the underlying graph metric can dramatically improve the performance of good network cost-sharing design. For outerplanar graph metrics, we provide a universal cost-sharing protocol with constant PoA, in contrast to protocols that, by ignoring the graph metric, cannot achieve PoA better than . Then, in our main technical result, we show that there exist graph metrics for which knowing the underlying graph metric does not help and any universal protocol has PoA of , which is tight. We attack this problem by developing new techniques that employ powerful tools from extremal combinatorics, and more specifically Ramsey theory in high-dimensional hypercubes. Then we switch to the stochastic model, where the players are activated according to some probability distribution that is known to the designer. We show that there exists a randomized ordered protocol that achieves constant PoA. If, further, each player is activated independently with some probability, by using standard derandomization techniques, we produce a deterministic ordered protocol that achieves constant PoA. We remark that the first result holds also for the black-box model, where the probabilities are not known to the designer, but she is allowed to draw independent (polynomially many) samples. Read More: https://epubs.siam.org/doi/10.1137/16M109669
Designing cost-sharing methods for Bayesian games
We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players
Computer Science and Game Theory: A Brief Survey
There has been a remarkable increase in work at the interface of computer
science and game theory in the past decade. In this article I survey some of
the main themes of work in the area, with a focus on the work in computer
science. Given the length constraints, I make no attempt at being
comprehensive, especially since other surveys are also available, and a
comprehensive survey book will appear shortly.Comment: To appear; Palgrave Dictionary of Economic
Distributed Game Theoretic Optimization and Management of Multichannel ALOHA Networks
The problem of distributed rate maximization in multi-channel ALOHA networks
is considered. First, we study the problem of constrained distributed rate
maximization, where user rates are subject to total transmission probability
constraints. We propose a best-response algorithm, where each user updates its
strategy to increase its rate according to the channel state information and
the current channel utilization. We prove the convergence of the algorithm to a
Nash equilibrium in both homogeneous and heterogeneous networks using the
theory of potential games. The performance of the best-response dynamic is
analyzed and compared to a simple transmission scheme, where users transmit
over the channel with the highest collision-free utility. Then, we consider the
case where users are not restricted by transmission probability constraints.
Distributed rate maximization under uncertainty is considered to achieve both
efficiency and fairness among users. We propose a distributed scheme where
users adjust their transmission probability to maximize their rates according
to the current network state, while maintaining the desired load on the
channels. We show that our approach plays an important role in achieving the
Nash bargaining solution among users. Sequential and parallel algorithms are
proposed to achieve the target solution in a distributed manner. The
efficiencies of the algorithms are demonstrated through both theoretical and
simulation results.Comment: 34 pages, 6 figures, accepted for publication in the IEEE/ACM
Transactions on Networking, part of this work was presented at IEEE CAMSAP
201
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