Division of a resource in a network

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• 研討會日期 : 2015-12-25
• 時間 : 14:30
• 主講人 : Professor Chiu-Yu Ko
• 主持人 : Professor Chun-Hsien Yeh
• 地點 : Conference Room B110
• 演講者簡介 : Professor Ko received his Ph.D. in Economics from Boston College in 2012. He is currently an Assistant Professor at Department of Economics, the National University of Singapore. His research focuses on applied game theory and industrial organization, with particular focus on market and institutional design. For theory of industrial organization, he specializes on R&D and network economics. For applied theory, he works on topics in political economy, economic history and financial market.
• 演講摘要 : A problem consists of a finite group of agents and a finite rectangular grid network with non-negative value attached to every link in the grid. A solution selects, for every problem, a non-decreasing path that connects the origin with the opposite corner of the grid, and split the sum of the values of the links in the selected paths among the agents. A solution is path-consistent if for any given point in the path selected by the solution, the path chosen in the sub-grid formed by that point and the opposite corner of the grid is the remaining of the path selected by the solution. A solution is consistent if it is path-consistent and the value given to an agent is independent on whether the distribution is made at any point in the middle of the path. There is a large class of path-consistent solutions, including: the maximalist path (the selects the path with the largest sum), the minimalist path (that selects the path with the smallest sum) or the myopic path (which selects the link with the largest value among the next two). The paper characterizes the entire class of path-consistent solutions. A description of a large subset of consistent solutions as the maximization of an additively separable function is provided. We also provide a description of the consistent solutions. They require to pick a path-consistent solution and splits the value of a path using an arbitrary function that depends on the value of every link and the direction in which the path is moving. Finally, the paper considers the problem of implementation. We ask which solutions provide agents the incentives to pick the efficient path as a Subgame Perfect Nash equilibrium of the game where they alternatively pick the direction of the path. Surprisingly, only a very small class of solutions meet this requirement. They must pick the efficient path and split the value using an arbitrary monotonic function that depends on the aggregate value of a path. The proportional sharing solutions, where the value of every selected link is split in the same proportion to the agents, are the only consistent solutions that implement the efficient path. The equal sharing solution, where the value of every selected link is split equally among the agents, is the only symmetric method in the class.