On optimal partitions, individual values and cooperative games: Does a wiser agent always produce a higher value?

详细信息    查看全文

• 作者：Gershon Wolansky
• 关键词：Optimal mass transport ; Monge ; Kantorovich ; Cooperative games
• 刊名：Mathematics and Financial Economics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：11
• 期：1
• 页码：85-109
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Quantitative Finance; Finance, general; Macroeconomics/Monetary Economics//Financial Economics; Economic Theory/Quantitative Economics/Mathematical Methods; Applications of Mathematics; Statistics for
• 出版者：Springer Berlin Heidelberg
• ISSN：1862-9660
• 卷排序：11

文摘

We consider an optimal partition of resources (e.g. consumers) between several agents, given utility functions (“wisdoms”) for the agents and their capacities. This problem is a variant of optimal transport (Monge–Kantorovich) between two measure spaces where one of the measures is discrete (capacities) and the costs of transport are the wisdoms of the agents. We concentrate on the individual value for each agent under optimal partition and show that, counter-intuitively, this value may decrease if the agent’s wisdom is increased. Sufficient and necessary conditions for the monotonicity with respect to the wisdom functions of the individual values will be given, independently of the other agents. The sharpness of these conditions is also discussed. Motivated by the above we define a cooperative game based on optimal partition and investigate conditions for stability of the grand coalition.