Adaptive constraint satisfaction for Markov decision process congestion games: Application to transportation networks

Li, Sarah H. Q.; Yu, Yue; Miguel, Nicolas I.; Calderone, Dan; Ratliff, Lillian J.; Açıkmeşe, Behçet

doi:10.1016/j.automatica.2023.110879

Cited by 1 publication

(3 citation statements)

References 15 publications

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“…Proof. We prove this proposition by showing that Assumption 1 and the coupled KKT conditions of ( 16) together imply the correlated equilibrium condition in (6). From [30,Thm.3.3], the coupled KKT conditions of ( 16) are necessary and sufficient for (α 1 , .…”

Section: Equivalence Between Generalized Nash Equilibrium and Correla...mentioning

confidence: 84%

“…Intuitively, condition (6) implies that player i cannot independently swap action a i for âi while the other players play a −i and achieve a lower expected cost. On the set of correlated strategies induced by joint strategies, the correlated equilibrium condition ( 6) is equivalent to the Nash equilibrium condition (3).…”

Section: Equilibria Concepts In Normal Form Gamesmentioning

confidence: 99%

“…By utilizing a correlation device that enables players to coordinate their actions, a correlated equilibrium is more effective than the Nash equilibrium at optimizing the social welfare, especially in competitive games with three or more players [4]. In particular, such games arise naturally in urban mobility [5], [6], robotics [7], and power markets [8]. Since correlated S.H.Q.…”

Section: Introductionmentioning

confidence: 99%

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A differentiable path-following method to compute Nash equilibria in robust normal-form games

Liu,

Chen,

Dang

2023

Optimization

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In competitive multi-player interactions, simultaneous optimality is a key requirement for establishing strategic equilibria. This property is explicit when the game-theoretic equilibrium is the simultaneously optimal solution of coupled optimization problems. However, no such optimization problems exist for the correlated equilibrium, a strategic equilibrium where the players can correlate their actions. We address the lack of a coupled optimization framework for the correlated equilibrium by introducing an unnormalized game-an extension of normal-form games in which the player strategies are lifted to unnormalized measures over the joint actions. We show that the set of fully mixed generalized Nash equilibria of this unnormalized game is a subset of the correlated equilibrium of the normal-form game. Furthermore, we introduce an entropy regularization to the unnormalized game and prove that the entropy-regularized generalized Nash equilibrium is a sub-optimal correlated equilibrium of the normal form game where the degree of sub-optimality depends on the magnitude of regularization. We prove that the entropyregularized unnormalized game has a closed-form solution, and empirically verify its computational efficacy at approximating the correlated equilibrium of normal-form games.

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Section: Equivalence Between Generalized Nash Equilibrium and Correla...mentioning

confidence: 84%

Section: Equilibria Concepts In Normal Form Gamesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A differentiable path-following method to compute Nash equilibria in robust normal-form games

Liu,

Chen,

Dang

2023

Optimization

View full text Add to dashboard Cite

show abstract

Adaptive constraint satisfaction for Markov decision process congestion games: Application to transportation networks

Cited by 1 publication

References 15 publications

A differentiable path-following method to compute Nash equilibria in robust normal-form games

A differentiable path-following method to compute Nash equilibria in robust normal-form games

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