Let vn(p) denote the value of the n-times repeated zero-sum game with incomplete information on one side and full monitoring and let u(p) be the value of the average game G(p). The error term ϵn(p) = vn(p) − cav(u)(p) is then converging to zero at least as rapidly as 1/√n. In this paper, we analyze the convergence of ψn(p) = √nϵn(p) in the games with square payoff matrices such that the optimal strategy of the informed player in the average game G(p) is unique, is completely mixed and does not depend on p. Our main result is that the existence of a solution ψ* to a partial differential equation with appropriate boundary conditions and regularity properties implies the uniform convergence of ψn to the Fenchel conjugate of ψ*. In particular cases, the P.D.E. problem is linear and its solution ψ* is then related to the multidimensional normal distribution.
International audienceWhen two asymmetrically informed risk-neutral agents repeatedly exchange a risky asset for numéraire, they are essentially playing an n-times repeated zero-sum game of incomplete information. In this setting, the price Lq at period q can be defined as the expected liquidation value of the risky asset given players' past moves. This paper indicates that the asymptotics of this price process at equilibrium, as n goes to ∞, is completely independent of the "natural" trading mechanism used at each round: it converges, as n increases, to a Continuous Martingale of Maximal Variation. This martingale class thus provides natural dynamics that could be used in financial econometrics. It contains in particular Black and Scholes' dynamics. We also prove here a mathematical theorem on the asymptotics of martingales of maximal M-variation, extending Mertens and Zamir's paper on the maximal L1-variation of a bounded martingale
Ablation parameters such as velocity, mass, momentum, pressure, and hydrodynamic efficiency have been investigated with plane targets irradiated in the range 3×1011-1015 W cm−2 with 1 nsec pulses and laser wavelengths of 1.06 μm and 0.35 μm. We show that ablation velocity, ablated mass, and momentum are in good agreement with ablation scaling laws deduced from analytical models taking into account inverse bremsstrahlung absorption below the critical density. Nevertheless, processes such as lateral conduction, hot spot, and preheat effects make inaccurate the comparison between ablation pressures, mass ablation rates, or hydrodynamic efficiencies measured for different laser wavelengths. Laser illumination nonuniformities are transmitted to the target in terms of pressure variations. The harmful consequence of a reduced lateral energy flow in 0.35 μm experiments can eclipse the increasing of ablation pressure and hydrodynamic efficiency.
This paper is concerned with the repeated zero-sum games with one-sided information and standard signaling. We introduce here dual games that allow us to analyze the “Markovian” behavior of the uninformed player, and to explicitly compute his optimal strategies. We then apply our results on the dual games to explain the appearance of the normal density in the n−1/2-term of the asymptotic expansion of vn as a consequence of the Central Limit Theorem.
Proceedings Second International Workshop, WINE 2006, Patras, Greece, December 15-17, 2006.International audienceThere are many situations in which a customer's proclivity to buy the product of any firm depends not only on the classical attributes of the product such as its price and quality, but also on who else is buying the same product. We model these situations as games in which firms compete for customers located in a “social network”. Nash Equilibrium (NE) in pure strategies exist and are unique. Indeed there are closed-form formulae for the NE in terms of the exogenous parameters of the model, which enables us to compute NE in polynomial time. An important structural feature of NE is that, if there are no a priori biases between customers and firms, then there is a cut-off level above which high cost firms are blockaded at an NE, while the rest compete uniformly throughout the network. We finally explore the relation between the connectivity of a customer and the money firms spend on him. This relation becomes particularly transparent when externalities are dominant: NE can be characterized in terms of the invariant measures on the recurrent classes of the Markov chain underlying the social network
ond, the short-time dynamics of all the simple fluids over remarkably large ranges of density and temperature are quantitatively described by Eq. (1) which should serve as an important benchmark for theories of the dynamics of dense fluids. Third, the phenomenon of melting has a negligible effect on the short-time dynamics-in marked contrast to the large discontinuities it causes in static properties. Fourth, the measured scattering efficiencies have confirmed recent theoretical estimates for the solid and provide insight into the mechanisms of nonlinear optical effects in simple condensed media.
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