Many modern networks grow from blocks. We study the probabilistic behavior of parameters of a blocks tree, which models several kinds of networks. It grows from building blocks that are themselves rooted trees. We investigate the number of leaves, depth of nodes, total path length, and height of such trees. We use methods from the theory of Pólya urns and martingales.

5We consider the economic lot-sizing game with general concave ordering cost functions. It is 6 well-known that the core of this game is nonempty when the inventory holding costs are linear. 7The main contribution of this work is a combinatorial, primal-dual algorithm that computes a cost 8 allocation in the core of these games in polynomial time. We also show that this algorithm can be 9 used to compute a cost allocation in the core of economic lot-sizing games with remanufacturing 10 under certain assumptions.

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