If a game has a unique Nash equilibrium, then this equilibrium is arguably the solution of the game from the refinement's literature point of view. However, it might be that for almost all initial conditions, all strategies in the support of this equilibrium are eliminated by the replicator...

Do evolutionary processes lead economic or biological agents to behave as if they were rational? To test this idea, many authors examined whether evolutionary game dynamics eliminate strictly dominated strategies. We survey, unify, and fill some gaps in this literature in the case of monotonic...

This paper is devoted to regret lower bounds in the classical model of stochastic multi-armed bandit. A well-known result of Lai and Robbins, which has then been extended by Burnetas and Katehakis, has established the presence of a logarithmic bound for all consistent policies. We relax the...

This paper deals with inertia functions in control theory introduced in Aubin, Bernardo and Saint-Pierre (2004, 2005) and their adaptation to dynamical games. The inertia function associates with any initial state-control pair the smallest of the worst norms over time of the velocities of the...

We study the existence of uniform correlated equilibrium payoffs in stochastic games. The correlation devices that we use are either autonomous (they base their choice of signal on previous signals, but not on previous states or actions) or stationary (their choice is independent of any data and...

The thesis presents a construction of a grid that discretizes the threshold model introduced by Geman and Roncoroni (2006) for electricity spot prices, incorporating both mean reversion and jumps, the direction of the latter depending on the price of the underlying at the time of the jump. The...

The aim of this thesis is to investigate some solutions to the pricing of contingent claims in incomplete markets. We first consider the stochastic targetintroduced by Soner and Touzi (2002) for the general super-replication problem, and extended by Bouchard, Elie and Touzi (2009) in order to...

We consider a multivariate financial market with proportional transaction costs as in Kabanov (1999). We study the problem of contingent claim pricing via utility maximization as in Hodges and Neuberger (1989). Using an exponential utility function, we derive a closed form characterization for...

This note establishes that in every 3-3 symmetric game, the replicator dynamics eliminates all strategies that are never used in correlated equilibrium. This extends to the best-response dynamics and to any convex monotonic dynamics. The proof is based on dual reduction.

In this paper we derive the implications of the absence of arbitrage in securities markets models where traded securities are subject to short-sales constraints and where the borrowing and lending rates differ. We show that a securities price system is arbitrage free if and only if there exists...