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This is the true story of the actual use of a formal, decentralized division procedure to allocate silver heirlooms among eight grandchildren fairly and efficiently without distasteful direct monetary payments. Each grandchild's stated preferences for objects in contention were roughly represented by a von Neumann-Morgenstern utility function. Allocations were made as they would be in a market for probability shares in the objects, assuming each grandchild had a fixed amount of an artificial currency and made optimal purchases. The market-clearing equilibrium prices were chosen as in a second-price auction to reward honest reporting. Although the procedure was decentralized and most participants did not fully understand it or the preference information desired, it handled all major considerations well and was regarded as equitable.
Pratt et al. (Thu,) studied this question.