334 citations · 2.6k across the 129 of their papers we have counts for
137 papers
Tropical low-rank approximation and application to optimal control of N-body systems
Marianne Akian, Stephane Gaubert, Shanqing Liu +1
We study the approximation of the value function of deterministic optimal control problems with fixed initial state, motivated by \(N\)-body systems. In this setting, the action fu…
Dynamics of multidimensional Simple Clock Auctions
Jad Zeroual, Marianne Akian, Aurélien Bechler +2
Simple Clock Auctions (SCA) are a mechanism commonly used in spectrum auctions to sell lots of frequency bandwidths. We study such an auction with one player having access to perfe…
Optimal strategy against straightforward bidding in clock auctions
Jad Zeroual, Marianne Akian, Aurélien Bechler +2
We study a model of auction representative of the 5G auction in France. We determine the optimal strategy of a bidder, assuming that the valuations of competitors are unknown to th…
Continuity and approximability of competitive spectral radii
Marianne Akian, Stéphane Gaubert, Loïc Marchesini +1
The competitive spectral radius extends the notion of joint spectral radius to the two-player case: two players alternatively select matrices in prescribed compact sets, resulting…
Spectral Properties of Positive Definite Matrices over Symmetrized Tropical Algebras and Valued Ordered fields
Marianne Akian, Stephane Gaubert, Dariush Kiani +1
We investigate the properties of positive definite and positive semi-definite symmetric matrices within the framework of symmetrized tropical algebra, an extension of tropical alge…
The Competive Spectral Radius of Families of Nonexpansive Mappings
Marianne Akian, Stéphane Gaubert, Loïc Marchesini
We consider a new class of repeated zero-sum games in which the payoff is the escape rate of a switched dynamical system, where at every stage, the transition is given by a nonexpa…