Population Games, Stable Games, and Passivity

Fox, Michael J.; Shamma, Jeff S.

doi:10.3390/g4040561

Cited by 70 publications

(8 citation statements)

References 21 publications

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“…Hofbauer and Sandholm (2009) developed a method for finding conditions on the payoff function in a class of evolutionary dynamics, called stable or contractive games, that guarantees convergence of strategies to the Nash equilibrium. Fox and Shamma (2013) showed that stable games are “passive” in the sense of feedback systems theory and generalized the method of Hofbauer and Sandholm using the tools of passivity theory (Willems, 1972a; 1972b). The results were further developed in (Park et al, 2019b) and extended to the case in which a networked group of agents experience communication and computational delays in learning the payoffs.…”

Section: Recent Models For Explaining and Shaping Collective Intellig...mentioning

confidence: 99%

Collective intelligence as a public good

Leonard

Levin

2022

Collective Intelligence

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We discuss measures of collective intelligence in evolved and designed self-organizing ensembles, defining collective intelligence in terms of the benefits to be gained through the exchange of information and other resources, as well as through coordination or cooperation, in the interests of a public good. These benefits can be numerous, from estimating a hard-to-observe cue to efficiently searching for resource. The measures should also account for costs to individuals, such as in attention or energy, and trade-offs for the ensemble, such as the flexibility to respond to an important change in the environment versus stability that is robust to unimportant variability. When there is a tension between the interests of the individual and those of the group, game-theoretic considerations may affect the level of collective intelligence that can be achieved. Models of individual rules that yield collective dynamics with multi-stable solutions provide a means to examine and shape collective intelligence in evolved and designed systems.

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Section: Recent Models For Explaining and Shaping Collective Intellig...mentioning

confidence: 99%

Collective intelligence as a public good

Leonard

Levin

2022

Collective Intelligence

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“…This model is arguably not very realistic for the routing game, as one does not expect users of a network to have an accurate representation of the cost function on every edge, or of the other users of the network. One alternative model of players is a model of repeated play [25,13,26], sometimes called learning models [11] or adjustment models [15]. In such models, one assumes that each player makes decisions iteratively (instead of playing a one-shot game), and uses the outcome of each iteration to adjust their next decision.…”

Section: Learning Models and Convergence To Nash Equilibriamentioning

confidence: 99%

“…In this sense, players "learn" the equilibrium asymptotically. Much progress has been made in recent years in characterizing classes of learning dynamics which are guaranteed to converge to an equilibrium set [14,18,17,13,26,1]. In particular for the routing game, different models of learning have been studied for example in [12,7,20,22,21], with different convergence guarantees.…”

Section: Learning Models and Convergence To Nash Equilibriamentioning

confidence: 99%

On Learning How Players Learn: Estimation of Learning Dynamics in the Routing Game

Lam

Krichene

Bayen

2016

2016 ACM/IEEE 7th International Conference on Cyber-Physical Systems (ICCPS)

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The routing game models congestion in transportation networks, communication networks, and other cyber physical systems in which agents compete for shared resources. We consider an online learning model of player dynamics: at each iteration, every player chooses a route (or a probability distribution over routes, which corresponds to a flow allocation over the physical network), then the joint decision of all players determines the costs of each path, which are then revealed to the players.We pose the following estimation problem: given a sequence of player decisions and the corresponding costs, we would like to estimate the learning model parameters. We consider in particular entropic mirror descent dynamics and reduce the problem to estimating the learning rates of each player.We demonstrate this method using data collected from a routing game experiment, played by human participants on a web application that we developed. When players log in, they are assigned an origin and destination on the graph. They can choose, at each iteration, a distribution over their available routes, and each player seeks to minimize her own cost. We collect a data set using this interface, then apply the proposed method to estimate the learning model parameters. We observe in particular that after an exploration phase, the joint decision of the players remains within a small distance of the Nash equilibrium. We also use the estimated model parameters to predict the flow distribution over routes, and compare these predictions to the actual distribution. Finally, we discuss some of the qualitative implications of the experiments, and give directions for future research.

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“…Stable games have been studied in the context of transportation science (Dafermos, 1980;Smith, 1979), and more recently in the context of feedback control and passive systems (Fox & Shamma, 2013). Examples of strictly stable games include some types of symmetric normal form games, negative dominant diagonal games, and strictly concave potential games.…”

Section: Population Games and Strictly Stable Gamesmentioning

confidence: 99%