St.Petersburg Economic seminar (HSE, EU, PDMI) on June, 11: Anna Bogomolnaia (University of Glasgow, HSE St. Petersburg)
Topic: Guarantees in Fair Division: general or monotone preferences
Date & Time: June, 11; 18:00 - 19:00
Where: online platform Zoom
Time: 18:00 - 19:00
Abstract: To divide a "manna" of private items (commodities, workloads, land, time intervals) between n agents, the "worst case" test of fairness is the welfare guaranteed to each agent, irrespective of others' preferences. We use algebraic topology to.show that, if the manna is non atomic and utilities are continuous (not necessarily monotone or convex), we can guarantee the minMax utility: that of our agentís best share in her worst partition of the manna; and implement it by Kuhn's generalisation of Divide and Choose. The larger Maxmin utility - of her worst share in her best partition - cannot be guaranteed, even for two agents.
If for all agents more manna is better than less (or less is better than more), our Bid & Choose rules implement guarantees between minMax and Maxmin by letting agents bid for the smallest (or largest) size of a share they find acceptable.
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