2-Player Nash and Nonsymmetric Bargaining Games: Algorithms and Structural Properties

The solution to a Nash or a nonsymmetric bargaining game is obtained by maximizing a concave function over a convex set, i.e., it is the solution to a convex program. We show that each 2-player game whose convex program has linear constraints, admits a rational solution and such a solution can be found in polynomial time using only an LP solver. If in addition, the game is succinct, i.e., the coefficients in its convex program are ``small'', then its solution can be found in strongly polynomial time. We also give a non-succinct linear game whose solution can be found in strongly polynomial time

Polynomial Solution of Non-Central Potentials

We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.Comment: 18 page

Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations

Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem'' when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time solution to the sign problem is highly desired since it would provide an unbiased and numerically exact method to simulate correlated quantum systems. Here we show, that such a solution is almost certainly unattainable by proving that the sign problem is NP-hard, implying that a generic solution of the sign problem would also solve all problems in the complexity class NP (nondeterministic polynomial) in polynomial time.Comment: 4 page