Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Game-Theoretic Learning and Allocations in Robust Dynamic Coalitional Games
2019
The problem of allocation in coalitional games with noisy observations and dynamic environments is considered. The evolution of the excess is modeled by a stochastic differential inclusion involvin...
Crowd-Averse Cyber-Physical Systems: The Paradigm of Robust Mean-Field Games
2016
For a networked controlled system, we illustrate the paradigm of robust mean-field games. This is a modeling framework at the interface of differential game theory, mathematical physics, and $H_{\infty}$ - optimal control that tries to capture the mutual influence between a crowd and its individuals. First, we establish a mean-field system for such games including the effects of adversarial disturbances. Second, we identify the optimal response of the individuals for a given population behavior. Third, we provide an analysis of equilibria and their stability.
Explicit solutions of Riccati equations appearing in differential games
1990
Abstract In this paper an explicit closed form solution of Riccati differential matrix equations appearing in games theory is given.
TUG-OF-WAR, MARKET MANIPULATION, AND OPTION PRICING
2014
We develop an option pricing model based on a tug-of-war game involving the the issuer and holder of the option. This two-player zero-sum stochastic differential game is formulated in a multi-dimensional financial market and the agents try, respectively, to manipulate/control the drift and the volatility of the asset processes in order to minimize and maximize the expected discounted pay-off defined at the terminal date $T$. We prove that the game has a value and that the value function is the unique viscosity solution to a terminal value problem for a partial differential equation involving the non-linear and completely degenerate parabolic infinity Laplace operator.
Local regularity for time-dependent tug-of-war games with varying probabilities
2016
We study local regularity properties of value functions of time-dependent tug-of-war games. For games with constant probabilities we get local Lipschitz continuity. For more general games with probabilities depending on space and time we obtain H\"older and Harnack estimates. The games have a connection to the normalized $p(x,t)$-parabolic equation $(n+p(x,t))u_t=\Delta u+(p(x,t)-2) \Delta_{\infty}^N u$.
REPEATED GAMES WITH PROBABILISTIC HORIZON
2005
Repeated games with probabilistic horizon are defined as those games where players have a common probability structure over the length of the game's repetition, T. In particular, for each t, they assign a probability pt to the event that "the game ends in period t". In this framework we analyze Generalized Prisoners' Dilemma games in both finite stage and differentiable stage games. Our construction shows that it is possible to reach cooperative equilibria under some conditions on the distribution of the discrete random variable T even if the expected length of the game is finite. More precisely, we completely characterize the existence of sub-game perfect cooperative equilibria in finite s…
Bifurcations of Elementary Graphics
1998
After the regular limit periodic sets, the simplest limit periodic sets are the elementary graphics.
Rational irreducible characters and rational conjugacy classes in finite groups
2007
We prove that a finite group G G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rational-valued irreducible character of odd degree.
Homology of pseudodifferential operators on manifolds with fibered cusps
2003
The Hochschild homology of the algebra of pseudodifferential operators on a manifold with fibered cusps, introduced by Mazzeo and Melrose, is studied and computed using the approach of Brylinski and Getzler. One of the main technical tools is a new convergence criterion for tri-filtered half-plane spectral sequences. Using trace-like functionals that generate the 0 0 -dimensional Hochschild cohomology groups, the index of a fully elliptic fibered cusp operator is expressed as the sum of a local contribution of Atiyah-Singer type and a global term on the boundary. We announce a result relating this boundary term to the adiabatic limit of the eta invariant in a particular case.
Understanding star-fundamental algebras
2021
Star-fundamental algebras are special finite dimensional algebras with involution ∗ * over an algebraically closed field of characteristic zero defined in terms of multialternating ∗ * -polynomials. We prove that the upper-block matrix algebras with involution introduced in Di Vincenzo and La Scala [J. Algebra 317 (2007), pp. 642–657] are star-fundamental. Moreover, any finite dimensional algebra with involution contains a subalgebra mapping homomorphically onto one of such algebras. We also give a characterization of star-fundamental algebras through the representation theory of the symmetric group.