Entropic Penalties in Finite Games

Flåm, Sjur Didrik; Cavazzuti, E.

doi:10.1007/s10479-005-2264-5

Cited by 5 publications

(1 citation statement)

References 34 publications

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“…This avoids degeneracy of the strategies and allows faster reactions to changes in the environment, see Figure 1. Entropic regularization of games was also considered in [34]. We show that the adapted model is well-posed and has a consistent mean field limit (Theorem 2.4).…”

Section: Contribution and Outlinementioning

confidence: 93%

Data-driven entropic spatially inhomogeneous evolutionary games

Bonafini¹,

Fornasier²,

Schmitzer³

2021

Preprint

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We introduce novel multi-agent interaction models of entropic spatially inhomogeneous evolutionary undisclosed games and their quasi-static limits. These evolutions vastly generalize first and second order dynamics. Besides the well-posedness of these novel forms of multi-agent interactions, we are concerned with the learnability of individual payoff functions from observation data. We formulate the payoff learning as a variational problem, minimizing the discrepancy between the observations and the predictions by the payoff function. The inferred payoff function can then be used to simulate further evolutions, which are fully data-driven. We prove convergence of minimizing solutions obtained from a finite number of observations to a mean field limit and the minimal value provides a quantitative error bound on the data-driven evolutions. The abstract framework is fully constructive and numerically implementable. We illustrate this on computational examples where a ground truth payoff function is known and on examples where this is not the case, including a model for pedestrian movement.

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Section: Contribution and Outlinementioning

confidence: 93%

Data-driven entropic spatially inhomogeneous evolutionary games

Bonafini¹,

Fornasier²,

Schmitzer³

2021

Preprint

View full text Add to dashboard Cite

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Mean-Field Limits for Entropic Multi-Population Dynamical Systems

Almi

D’Eramo²,

Morandotti

et al. 2023

Milan J. Math.

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The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution of the labels, the case of different time scales between the agents’ locations and labels dynamics is considered. The limit system couples a mean-field-type evolution in the space of positions and an instantaneous optimization of the payoff functional in the space of labels.

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