Payoffs in (bimatrix) games are usually not known precisely, but it is often possible to determine lower and upper bounds on payoffs. Such interval valued bimatrix games are considered in this paper. There are many questions arising in this context. First, we discuss the problem of existence of an equilibrium being common for all instances of interval values. We show that this property is equivalent to solvability of a certain linear mixed integer system of equations and inequalities. Second, we characterize the set of all possible equilibria by mean of a linear mixed integer system.
This study investigated the post-spawning dispersal of seven species occurring in a tributary of the Římov Reservoir during
the years 2000-2004. Fish were captured during spawning migration to the tributary, marked and released. The subsequent distribution
of marked fish was followed in the reservoir and tributary during three successive periods 1) early summer, 2) late summer and 3)
the next spawning season. Species were divided into two groups – obligatory tributary spawners (white bream
Blicca bjoerkna
, chub
Squalius cephalus
, bleak
Alburnus alburnus
and asp
Aspius aspius
) that did so predominantly in the tributary of the reservoir and
generalists (bream
Abramis brama
, perch
Perca fluviatilis
and roach
Rutilus rutilus
) that usually spawned in the tributary as well as at
different sites within the reservoir main body. We hypothesized that obligatory tributary spawners would distribute across the reservoir
after spawning according to their species-specific preferences for certain feeding grounds. We expected a relatively low or erratic post-
spawning dispersal for spawning generalists. The results of the study revealed that the post-spawning dispersal of obligatory tributary
spawners is consistent with our hypothesis and they most likely dispersed according to their feeding ground requirements. The post-
spawning dispersal of generalists revealed that the assumed low dispersal was relevant for bream and perch while erratic dispersal was
observed in roach.
Separation is a famous principle and separation properties are important for optimization theory and various applications. In practice, input data are rarely known exactly and it is advisable to deal with parameters. In this article, we are concerned with the basic characteristics (existence, description, stability etc.) of separating hyperplanes of two convex polyhedral sets depending on parameters. We study the case, when parameters are situated in one column of the constraint matrix from the description of the given convex polyhedral set. We provide also a lot of examples carried out on PC.