Zero-Sum Polymatrix Games: A Generalization of Minmax

Cai, Yang; Candogan, Ozan; Daskalakis, Constantinos; Papadimitriou, Christos H.

doi:10.1287/moor.2015.0745

Cited by 48 publications

(63 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An important question that arises here is whether the straightforward equilibrium structure of zero-sum games extends to the case of a network of competitors. Following [6,7,10], an N -player pairwise zero-/constant-sum polymatrix game consists of an (undirected) interaction graph G ≡ G(N , E) whose set of nodes N represents the competing players, with two nodes i, j ∈ N connected by an edge e = (i, j) in E if and only if the corresponding players compete with each other in a two-player zero-/constant-sum game.…”

Section: 2mentioning

confidence: 99%

Cycles in Adversarial Regularized Learning

Mertikopoulos¹,

Papadimitriou²,

Piliouras³

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

Self Cite

142

251

View full text Add to dashboard Cite

Regularized learning is a fundamental technique in online optimization, machine learning, and many other fields of computer science. A natural question that arises in this context is how regularized learning algorithms behave when faced against each other. We study a natural formulation of this problem by coupling regularized learning dynamics in zero-sum games. We show that the system's behavior is Poincaré recurrent, implying that almost every trajectory revisits any (arbitrarily small) neighborhood of its starting point infinitely often. This cycling behavior is robust to the agents' choice of regularization mechanism (each agent could be using a different regularizer), to positive-affine transformations of the agents' utilities, and it also persists in the case of networked competition (zero-sum polymatrix games).

show abstract

Section: 2mentioning

confidence: 99%

Cycles in Adversarial Regularized Learning

Mertikopoulos¹,

Papadimitriou²,

Piliouras³

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

Self Cite

142

251

View full text Add to dashboard Cite

show abstract

“…In that case, player i's multilateral strategy x i 2 X i implements the same compound strategy x i ' s ij in each bilateral game with neighbor j 2 N (i), so that X i corresponds to the diagonal in j2N (i) S ij . Settings along these lines have been considered, in particular, by Sela (1999) and Cai et al (2016), and will also be used in our examples. Clearly, our set-up is no less general than those settings.…”

Section: Network Gamesmentioning

confidence: 99%

“…1 While variants of …ctitious play are known to converge in large classes of two-person games, the case of n-person games has been explored to a somewhat lesser extent. 2 Inspired by recent developments in the literature (Daskalakis and Papadimitriou, 2009;Cai and Daskalakis, 2011;Cai et al, 2016), the present paper studies the dynamics of …ctitious play in general classes of network games. We start by considering what we call zero-sum networks Fokin, 1987, 1998;Daskalakis and Papadimitriou, 2009;Cai and Daskalakis, 2011;Cai et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

“…An interesting recent strand of literature, related to the interdisciplinary …eld of algorithmic game theory, has taken up the study of networks of two-person games. 7 Cai et al (2016) have clari…ed how far results traditionally known only for two-person zero-sum games (such as solvability by a linear program, existence of a value, equiva-lence of max-min and equilibrium strategies, exchangeability of Nash equilibria, and the relationship to coarse correlated equilibrium) can be extended to zero-sum networks. Moreover, in that class of games, discrete-time no-regret learning algorithms converge to the set of Nash equilibria (Daskalakis and Papadimitriou, 2009;Cai and Daskalakis, 2011).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fictitious play in networks

Ewerhart

Valkanova

2020

Games and Economic Behavior

View full text Add to dashboard Cite

This paper studies …ctitious play in networks of noncooperative twoperson games. We show that continuous-time …ctitious play converges to the set of Nash equilibria if the overall n-person game is zero-sum. Moreover, the rate of convergence is 1= , regardless of the size of the network. In contrast, arbitrary nperson zero-sum games with bilinear payo¤ functions do not possess the continuoustime …ctitious-play property. As extensions, we consider networks in which each bilateral game is either strategically zero-sum, a weighted potential game, or a twoby-two game. In those cases, convergence requires a condition on bilateral payo¤s or, alternatively, that the network is acyclic. Our results hold also for the discrete-time variant of …ctitious play, which implies, in particular, a generalization of Robinson's theorem to arbitrary zero-sum networks. Applications include security games, con ‡ict networks, and decentralized wireless channel selection.

show abstract

“…The addition of fake uniform data as a guiding component suggests that there might be benefit of considering "deep-interactive learning" where there is deepness in the number of players that interact in order to give each other guidance in adversarial training. This could potentially be modelled by zero-sum polymatrix games (Cai et al, 2016).…”

Section: Future Workmentioning

confidence: 99%

Beyond Local Nash Equilibria for Adversarial Networks

Oliehoek

Savani

Gállego

et al. 2019

Communications in Computer and Information Science

View full text Add to dashboard Cite

Save for some special cases, current training methods for Generative Adversarial Networks (GANs) are at best guaranteed to converge to a 'local Nash equilibrium' (LNE). Such LNEs, however, can be arbitrarily far from an actual Nash equilibrium (NE), which implies that there are no guarantees on the quality of the found generator or classifier. This paper proposes to model GANs explicitly as finite games in mixed strategies, thereby ensuring that every LNE is an NE. With this formulation, we propose a solution method that is proven to monotonically converge to a resourcebounded Nash equilibrium (RB-NE): by increasing computational resources we can find better solutions. We empirically demonstrate that our method is less prone to typical GAN problems such as mode collapse, and produces solutions that are less exploitable than those produced by GANs and MGANs, and closely resemble theoretical predictions about NEs. * This version supersedes our earlier arXiv paper (Oliehoek et al., 2017).

show abstract

Zero-Sum Polymatrix Games: A Generalization of Minmax

Cited by 48 publications

References 12 publications

Cycles in Adversarial Regularized Learning

Cycles in Adversarial Regularized Learning

Fictitious play in networks

Beyond Local Nash Equilibria for Adversarial Networks

Contact Info

Product

Resources

About