This paper proposes a Nash equilibrium model that applies continuous time replicator dynamics to the analysis of oligopoly markets. The robustness of the proposed simple Nash equilibrium model under the simultaneous constraints of allocation of product and market share using a simulation method to derive an optimal solution for production decisions by rival firms in oligopoly markets is tested ...

Let \(a,n \in \mathbb Z^+\), with \(a<n\) and \(\gcd (a,n)=1\). \(P_{a,n}\) denote the lattice parallelogram spanned by (1, 0) (a, n), that is, $$P_{a,n} = \left\{ t_1(1,0)+ t_2(a,n) \, : 0\le t_1,t_2 \le 1 \right\} , $$ and let $$V(a,n) \# \text { of visible points in interior } P_{a,n}.$$ In this paper we prove some elementary (and straightforward) results for V(a, n). The most ...

We compute the Hodge numbers of the polarised (pure) variation of Hodge structure V = grn−1 R f! Z of the Landau-Ginzburg model f : Y → C mirror-dual to a weighted projective space wPn in terms of a variant of Reid’s age function of the anticanonical cone over wPn. This implies, for instance, that wPn has canonical singularities if and only if hn−1,0 V = 1. We state a conjectural formula for th...

1. The problems. In this note we shall discuss some conjectural integral inequalities which are related to quasiconformal mappings, singular integrals, martingales and the calculus of variations.

We state a conjectural relationship between the fermionic form [HKOTY] and the Betti numbers of a Grassmannian over a preprojective algebra or, equivalently , of a lagrangian quiver variety.

We have discovered conjectural near-addition formulas for Somos sequences. We have preliminary evidence suggesting the existence of modular theta functions.

We propose a conjectural explicit formula of generating series of a new type for Gromov–Witten invariants of P of all degrees in full genera.

A conjectural relationship between the GUE partition function with even couplings and certain special cubic Hodge integrals over the moduli spaces of stable algebraic curves is under consideration.

Numerical evidence relevant to the evaluation of the constant κ3 in the conjectural distribution of three-prime Carmichael numbers of Granville and Pomerance (2001) is summarised.