Federica Garin

Distributed best response dynamics with high playing rates in potential games

In this paper we design and analyze distributed best response dynamics to compute Nash equilibria in potential games. This algorithm uses local Poisson clocks for each player, and does not rely on the usual but unrealistic assumption that players take no time to compute their best response. If this time (denoted δ) is taken into account, distributed best response dynamics may suffer from overlaps: one player starts to play while another player has not changed its strategy yet. Overlaps may lead to drops of the potential but we can show that they do not jeopardize eventual convergence to a Nash equilibrium. Our main result is to use a Markovian approach to show that the average execution time of the algorithm can be bounded from above by e γ δn log n log log n (1 + o(1)) and from below by δn log n log log n (1 + o(1)), where γ is the Euler constant, n is the number of players and δ is the time taken by one player to compute its best response. These bounds are obtained by using an asymptotically optimal playing rate λ. Our analytic bounds show that this λ is high: ˆ λ = log log n−log log log n δ. This induces a large probability of overlap (ˆ p = 1 − log log n/ log n). In practice, numerical simulations also show that using high playing rates is efficient, with an optimal probability of overlap p opt ≈ 0.78 up to n = 250. This implies that best response dynamics are unexpectedly efficient to compute Nash equilibria, even in a distributed setting.

Structural and Strongly Structural Input and State Observability of Linear Network Systems

This paper studies linear network systems affected by multiple unknown inputs with the objective of reconstructing both the initial state and the unknown input with one time-step delay. We state conditions under which both the whole network state and the unknown input can be reconstructed from output measurements, over every window of length <inline-formula><tex-math notation=LaTeX>

Energy-Aware Radio Chip Management for Wireless Control

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Reduced model for control in a hydroelectric unit at off-design operation

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Distributed Best Response Algorithms for Potential Games

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Unbiased Filtering for State and Unknown Input with Delay

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Distributed Optimal Traffic Lights Design for Large-Scale Urban Networks

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Structural delay-1 input-and-state observability

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Best Response Algorithms for Random Network Games

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Strong Structural Input and State Observability of LTV Network Systems with Multiple Unknown Inputs

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