We consider a multilateral sequential bargaining model in which the players may differ in their probability of being selected as the proposer and the rate at which they discount future payoffs. For games in which agreement requires less than unanimous consent, we characterize the set of stationary subgame perfect equilibrium payoffs. With this characterization, we establish the uniqueness of th...

Call S complete if Σ(S) contains all sufficiently large integers. It has been known for some time (see [B]) that if gcd(a, b) = 1 then the (nondecreasing) sequence formed from the values ab with s0 ≤ s, t0 ≤ t ≤ f(s0, t0) is complete, where s0 and t0 are arbitrary, and f(s0, t0) is sufficiently large. In this note we consider the analogous question for sequences formed from pure powers of integ...

Let L be a bounded distributive lattice. In this paper we focus on those functions f : L → L which can be expressed in the language of bounded lattices using variables and constants, the so-called “weighted” lattice polynomial functions. Clearly, such functions must be nondecreasing in each variable, but the converse does not hold in general. Thus it is natural to ask which nondecreasing functi...

We study existence and uniqueness of solutions ([Formula: see text]) [Formula: text] in text], on where is a bounded smooth domain such that constant, continuous nondecreasing function satisfying some integral growth condition two Radon measures, respectively, text]. show the situation differs considerably according measure concentrated at or not. When power we introduce capacity framework whic...

Wang and Yeh proved that if P (x) is a polynomial with nonnegative and nondecreasing coefficients, then P (x + d) is unimodal for any d > 0. A mode of a unimodal polynomial f(x) = a0 + a1x + · · · + amx m is an index k such that ak is the maximum coefficient. Suppose that M∗(P, d) is the smallest mode of P (x + d), and M(P, d) the greatest mode. Wang and Yeh conjectured that if d2 > d1 > 0, the...

Let m be a positive integer whose smallest prime divisor is denoted by p, and let Zm denote the cyclic group of residues modulo m. For a set B = {x1, x2, . . . , xm} of m integers satisfying x1 < x2 < · · · < xm, and an integer j satisfying 2 ≤ j ≤ m, define gj(B) = xj − x1. Furthermore, define fj(m, 2) (define fj(m, Zm)) to be the least integer N such that for every coloring ∆ : {1, . . . ,N} ...

The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P (x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P (x+ 1), which leads to the log-concavity of P (x+ c) for any c ≥ 1 due to Llamas and Mart́ınez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Che...

We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. Our objective is to minimize ∑ wjf(Cj) for any nondecreasing, nonnegative, differentiable cost function f(Cj). We aim for a universal solution that performs well without adaptation for all cost functions for any possible machine behavior. We design a deterministic ...

The properties of solutions of the equation u′′(t) = p1(t)u(τ1(t)) + p2(t)u′(τ2(t)) are investigated where pi : [a, +∞[→ R (i = 1, 2) are locally summable functions, τ1 : [a, +∞[→ R is a measurable function and τ2 : [a, +∞[→ R is a nondecreasing locally absolutely continuous one. Moreover, τi(t) ≥ t (i = 1, 2), p1(t) ≥ 0, p2(t) ≤ (4− ε)τ ′ 2(t)p1(t), ε = const > 0 and ∫ +∞ a (τ1(t)− t)p1(t)dt <...