2020/01/17 by Shyam Chandramouli, Chandramouli, Shyam, Jay Sethuraman +1
Economics, Econometrics and Finance · Medicine · Decision Sciences · #Game Theory and Voting Systems #Organ Donation and Transplantation #Auction Theory and Applications
paper · pdf · doi:10.48550/arxiv.2002.02749
The study of matching theory has gained importance recently with applications\nin Kidney Exchange, House Allocation, School Choice etc. The general theme of\nthese problems is to allocate goods in a fair manner amongst participating\nagents. The agents generally have a unit supply/demand of a good that they want\nto exchange with other agents. On the other hand, Bochet et al. study a more\ngeneral version of the problem where they allow for agents to have arbitrary\nnumber of divisible goods to be rationed to other agents in the network. In\nthis current work, our main focus is on non-bipartite networks where agents\nhave arbitrary units of a homogeneous indivisible good that they want to\nexchange with their neighbors. Our aim is to develop mechanisms that would\nidentify a fair and strategyproof allocation for the agents in the network.\nThus, we generalize the kidney exchange problem to that of a network with\narbitrary capacity of available goods. Our main idea is that this problem and a\ncouple of other related versions of non-bipartite fair allocation problem can\nbe suitably transformed to one of fair allocations on bipartite networks for\nwhich we know of well studied fair allocation mechanisms.\n