On multipartite posets

A poset $\mathbf{P} = (X,\preceq)$ is {\em $m$-partite} if $X$ has a partition $X = X_1 \cup ... \cup X_m$ such that (1) each $X_i$ forms an antichain in $\mathbf{P}$, and (2) $x\prec y$ implies $x\in X_i$ and $y\in X_j$ where $i<j$. In this article we derive a tight asymptotic upper bound on the order dimension of $m$-partite posets in terms of $m$ and their bipartite sub-posets in a constructive and elementary way.Comment: 6 page

THE NORWEGIAN SPRING-SPAWNING HERRING FISHERY: A STYLIZED GAME MODEL

This paper presents an empirically based, game-theoretic model of the exploitation of the Norwegian spring-spawning herring stock, also known as the Atlanto-Scandian herring stock. The model involves five exploiters; Norway, Iceland, the Faroe Islands, the EU, and Russia and an explicit, stochastic migratory behavior of the stock. Under these conditions Markov Perfect (Nash) equilibrium game strategies are calculated and compared to the jointly optimal exploitation pattern. Not surprisingly, it turns out that the solution to the competitive game is hugely inefficient, leading very quickly to the virtual exhaustion of the resource. The scope for cooperative agreements involving the calculation of Shapley values is investigated. Although the grand coalition of all players maximizes overall benefits, such a coalition can hardly be stable over time unless side payments are possible.Resource /Energy Economics and Policy,