The Efficiency of Best-Response Dynamics

Feldman, Michal; Snappir, Yuval; Tamir, Tami

doi:10.1007/978-3-319-66700-3_15

Cited by 17 publications

(11 citation statements)

References 43 publications

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“…The third direction studies how the quality of the resulting NE is affected by the choice of the deviating player. Specifically, the order in which players are chosen to perform their best response moves is crucial to the quality of the equilibrium reached [5].…”

Section: B Related Workmentioning

confidence: 99%

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Achieving Good Nash Equilibrium by Temporal Addition of Dummy Players

Dadush¹,

Tamir²

2021

Annals of Computer Science and Information Systems

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We consider cost-sharing games in which resources' costs are fairly shared by their users. The total players' cost in a Nash Equilibrium profile may be significantly higher than the social optimum. We compare and analyze several methods to lead the players to a good Nash Equilibrium by temporal addition of dummy players. The dummy players create artificial load on some resources, that encourage other players to change their strategies.We show that it is NP-hard to calculate an optimal strategy for the dummy players. We then focus on symmetric singleton games for which we suggest several heuristics for the problem. We analyze their performance distinguishing between several classes of instances and several performance measures.

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Section: B Related Workmentioning

confidence: 99%

“…We show that calculating the minimal number of dummies required for this task is NP-hard. Our hardness proof is based on the hardness proof in [5] that considers a problem of determining the order according to which players perform BRD (Best response dynamics).…”

Section: Hardness Proof For General Networkmentioning

confidence: 99%

Achieving Good Nash Equilibrium by Temporal Addition of Dummy Players

Dadush¹,

Tamir²

2021

Annals of Computer Science and Information Systems

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“…Next, we numerically demonstrate that an arbitrary solution, r(t), of the equation (28) converges to the Nash equilibrium point. First, we integrate the equation (28) for the N = 2 case. Figure 5 shows the integral curves of (28) for various initial points.…”

Section: Derivative Best Response Dynamicsmentioning

confidence: 99%

Optimal learning dynamics of multiagent system in restless multiarmed bandit game

Nakayama

Nakamura

Hisakado

et al. 2020

Physica A: Statistical Mechanics and its Applications

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Social learning is learning through the observation of or interaction with other individuals; it is critical in the understanding of the collective behaviors of humans in social physics. We study the learning process of agents in a restless multiarmed bandit (rMAB). The binary payoff of each arm changes randomly and agents maximize their payoffs by exploiting an arm with payoff 1, searching the arm at random (individual learning), or copying an arm exploited by other agents (social learning). The system has Pareto and Nash equilibria in the mixed strategy space of social and individual learning. We study several models in which agents maximize their expected payoffs in the strategy space, and demonstrate analytically and numerically that the system converges to the equilibria. We also conducted an experiment and investigated whether human participants adopt the optimal strategy. In this experiment, three participants play the game. If the reward of each group is proportional to the sum of the payoffs, the median of the social learning rate almost coincides with that of the Pareto equilibrium.

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“…The common research questions are whether BRD converges to a NE, the convergence time, and the quality of the solution (e.g. [5], [6]).…”

Section: A the Placement Problem As A Gamementioning

confidence: 99%

Best Response Dynamics for VLSI Physical Design Placement

Rapoport

Tamir

2019

Proceedings of the 2019 Federated Conference on Computer Science and Information Systems

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The physical design placement problem is one of the hardest and most important problems in micro chips production. The placement defines how to place the electrical components on the chip. We consider the problem as a combinatorial optimization problem, whose instance is defined by a set of 2dimensional rectangles, with various sizes and wire connectivity requirements. We focus on minimizing the placement area and the total wire-length. We propose a local-search method for coping with the problem, based on natural dynamics common in game theory. Specifically, we suggest to perform variants of Best-Response Dynamics (BRD). In our method, we assume that every component is controlled by a selfish agent, who aim at minimizing his individual cost, which depends on his own location and the wire-length of his connections. We suggest several BRD methods, based on selfish migrations of a single or a cooperative of components. We performed a comprehensive experimental study on various test-benches, and compared our results with commonly known algorithms, in particular, with simulated annealing. The results show that selfish local-search, especially when applied with cooperatives of components, may be beneficial for the placement problem.

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The Efficiency of Best-Response Dynamics

Cited by 17 publications

References 43 publications

Achieving Good Nash Equilibrium by Temporal Addition of Dummy Players

Achieving Good Nash Equilibrium by Temporal Addition of Dummy Players

Optimal learning dynamics of multiagent system in restless multiarmed bandit game

Best Response Dynamics for VLSI Physical Design Placement

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