In this article, the q-analogues of the linear relations of non-strict multiple zeta values called “the sum formula” and “the cyclic sum formula” are established.

We consider the class of two-person zero-sum allocation games known as Captain Lotto games (Hart 2014). These are Colonel Blotto type games in which the players have capacity constraints. We consider the game with non-strict constraints, and with strict constraints. We show in most cases that when optimal strategies exist, they are necessarily unique. When they don’t exist, we characterize the ...

Jarik Nešetřil suggested to the first author the investigation of notions of homogeneity for relational structures, where “isomorphism” is replaced by “homomorphism” in the definition. Here we look in detail at what happens for posets. For the strict order, all five generalisations of homogeneity coincide, and we give a characterisation of the countable structures that arise. For the non-strict...

Both Lowe and Tsai have presented their own versions of the theory that both indicative subjunctive conditionals are strict conditionals. We critically discuss we find each version wanting.

Conditions α and β are two well-known rationality conditions in the theory of rational choice. This paper examines the implications of weaker versions of these two rationality conditions in the context of solutions to nonconvex bargaining problems. It is shown that, together with the standard axioms of efficiency and strict individual rationality, they imply rationalizability of solutions to no...

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Earlier work showed all of these implications to be strict. Here we re-prove one of the strictness results, using very different arguments. The technique used is a mixture of realizability, forcing in the gu...

Every local minimizer of a smooth constrained optimization problem satisfies the sequential Approximate Karush-Kuhn-Tucker (AKKT) condition. This optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms. It is natural to ask for conditions on the constraints under which AKKT implies KKT. These conditions will be called Strict Constraint Qua...

We study potential theoretic properties of strictly α-stable processes whose Lévy measure is comparable to that of a symmetric αstable process. We show the existence, continuity and strict positivity of transition densities and Green function of the process killed upon exiting a bounded domain. We further show that the exit distributions of the process from a domain satisfying the uniform volum...

I consider competitions in which, conditional on winning or losing, the effort exerted by a competitor does not necessarily decrease his payoff. This happens, for example, in competitions for promotions in which workers are intrinsically motivated, and in research and development races in which better performance implies a higher payoff from winning. I characterize players’ equilibrium payoffs ...