The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria
The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria
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具有异构销售和多单位需求的多合作伙伴分配博弈：竞争均衡
DOI：
10.1007/s00186-012-0395-4
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发表时间：
2012
影响因子：
1.2
通讯作者：
A. Neme
中科院分区：
文献类型：
--
作者：
D. Jaume;Jordi Massó;A. Neme
一个具有异质销售和多单位需求的多合作伙伴分配博弈由一组拥有给定数量的潜在许多不同商品的不可分割单位的卖方和一组重视这些单位并希望购买最多外生固定数量的单位的买方组成。我们定义了这个广义分配博弈的竞争均衡，并仅用线性规划证明了它的存在性。特别是，我们展示了如何计算平衡价格向量的解决方案的对偶线性规划相关联的原始线性规划定义，以找到最佳的分配。仅使用线性规划工具，我们还表明（i）竞争均衡集（价格向量和分配对）具有笛卡尔乘积结构：每个均衡价格向量是具有所有最优分配的竞争均衡的一部分，反之亦然;（ii）（限制）均衡价格向量有一个自然的晶格结构;（iii）如何将这种结构转化为一组代理商的效用，可达到均衡。
A multiple-partners assignment game with heterogeneous sales and multi-unit demands consists of a set of sellers that own a given number of indivisible units of potentially many different goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents’ utilities that are attainable at equilibrium.