Coarse Correlation in Extensive-Form Games

Farina, Gabriele; Bianchi, Tommaso; Sandholm, Tüomas

doi:10.1609/aaai.v34i02.5563

Cited by 18 publications

(26 citation statements)

References 13 publications

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“…Moreover, as pointed out by Celli et al [16], the study of algorithms for team games could shed further light on how to deal with imperfect-recall games, which are receiving increasing attention in the community due to the application of imperfect-recall abstractions to the computation of strategies for large sequential games. As for the computation of correlated equilibria in sequential games, it would be interesting to further investigate whether it is possible to define regret-minimizing procedures for general EFGs leading to refinements of the CCEs, such as EFCCEs [22]. A recent work studying a related problem is Celli et al [15].…”

Section: Discussion and Future Researchmentioning

confidence: 99%

Preplay Communication in Multi-Player Sequential Games: An Overview of Recent Results

Celli

2021

Special Topics in Information Technology

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The computational study of game-theoretic solution concepts is fundamental to describe the optimal behavior of rational agents interacting in a strategic setting, and to predict the most likely outcome of a game. Equilibrium computation techniques have been applied to numerous real-world problems. Among other applications, they are the key building block of the best poker-playing AI agents [5, 6, 27], and have been applied to physical and cybersecurity problems (see, e.g., [18, 20, 21, 30–32]).

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Section: Discussion and Future Researchmentioning

confidence: 99%

Preplay Communication in Multi-Player Sequential Games: An Overview of Recent Results

Celli

2021

Special Topics in Information Technology

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“…Now, as long as we have a "nice" DGF for scaled extensions and a "nice" DGF for the polytope Y, we can apply fast FOMs to the computation of the corresponding type of correlated equilibrium. Appropriate polytopes for Y exist in the case of EFCE [16], EFCCE [10], and NFCCE [10]. In each case, Y is itself a polytope that can be constructed via scaled extension (though simpler than Ξ).…”

Section: Preliminaries On Correlation and Triangle-freenessmentioning

confidence: 99%

“…Substituting (10) into the last inequality yields a proof of the desired strong convexity modulus 1/𝑀 𝑄 . □…”

Section: A Proofs Missing From the Main Bodymentioning

confidence: 99%

Better Regularization for Sequential Decision Spaces: Fast Convergence Rates for Nash, Correlated, and Team Equilibria

Farina,

Kroer,

Sandholm

2021

Preprint

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We study the application of iterative first-order methods to the problem of computing equilibria of largescale two-player extensive-form games. First-order methods must typically be instantiated with a regularizer that serves as a distance-generating function for the decision sets of the players. For the case of two-player zero-sum games, the state-of-the-art theoretical convergence rate for Nash equilibrium is achieved by using the dilated entropy function. In this paper, we introduce a new entropy-based distance-generating function for two-player zero-sum games, and show that this function achieves significantly better strong convexity properties than the dilated entropy, while maintaining the same easily-implemented closed-form proximal mapping. Extensive numerical simulations show that these superior theoretical properties translate into better numerical performance as well.We then generalize our new entropy distance function, as well as general dilated distance functions, to the scaled extension operator. The scaled extension operator is a way to recursively construct convex sets, which generalizes the decision polytope of extensive-form games, as well as the convex polytopes corresponding to correlated and team equilibria. By instantiating first-order methods with our regularizers, we develop the first accelerated first-order methods for computing correlated equilibra and ex-ante coordinated team equilibria. Our methods have a guaranteed 1/𝑇 rate of convergence, along with linear-time proximal updates.

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“…Next, we introduce an equivalent characterization of EFCEs (Farina, Bianchi, and Sandholm 2020). It is based on the following concept of trigger agent, originally due to Gordon, Greenwald, and Marks (2008).…”

Section: Correlation In Extensive-form Gamesmentioning

confidence: 99%

“…We provide a formal statement of the characterization of EFCEs based on trigger agents (see Definition 4), originally introduced by Gordon, Greenwald, and Marks (2008) and Farina et al (2019a) (see also (Farina, Bianchi, and Sandholm 2020) for a more general treatment). We recall that such characterization is based on the fact that µ ∈ ∆ Π is an EFCE if, for every i ∈ N , player i's expected utility when following recommendations is at least as large as the expected utility that any (I, a, μi )-trigger agent for player i can achieve (assuming the opponents' do not deviate from recommendations).…”

Section: B Characterization Of Efces Using Trigger Agentsmentioning

confidence: 99%

Trembling-Hand Perfection and Correlation in Sequential Games

Marchesi¹,

Gatti²

2020

Preprint

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We initiate the study of trembling-hand perfection in sequential (i.e., extensive-form) games with correlation. We introduce the extensive-form perfect correlated equilibrium (EF-PCE) as a refinement of the classical extensive-form correlated equilibrium (EFCE) that amends its weaknesses off the equilibrium path. This is achieved by accounting for the possibility that players may make mistakes while following recommendations independently at each information set of the game. After providing an axiomatic definition of EFPCE, we show that one always exists since any perfect (Nash) equilibrium constitutes an EFPCE, and that it is a refinement of EFCE, as any EFPCE is also an EFCE. Then, we prove that, surprisingly, computing an EFPCE is not harder than finding an EFCE, since the problem can be solved in polynomial time for general n-player extensive-form games (also with chance). This is achieved by formulating the problem as that of finding a limit solution (as ǫ → 0) to a suitably defined trembling LP parametrized by ǫ, featuring exponentially many variables and polynomially many constraints. To this end, we show how a recently developed polynomial-time algorithm for trembling LPs can be adapted to deal with problems having an exponential number of variables. This calls for the solution of a sequence of (non-trembling) LPs with exponentially many variables and polynomially many constraints, which is possible in polynomial time by applying an ellipsoid against hope approach.

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Coarse Correlation in Extensive-Form Games

Cited by 18 publications

References 13 publications

Preplay Communication in Multi-Player Sequential Games: An Overview of Recent Results

Preplay Communication in Multi-Player Sequential Games: An Overview of Recent Results

Better Regularization for Sequential Decision Spaces: Fast Convergence Rates for Nash, Correlated, and Team Equilibria

Trembling-Hand Perfection and Correlation in Sequential Games

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