An Ordinal Shapley Value for Economic Environments

• Authors: David Pérez-Castrillo.
• BSE Working Paper: 112214 | September 15
• Keywords: Non-transferable utility games , shapley value , ordinal shapley value , consistency , fairness
• JEL codes: C72, D50, D63
• Non-transferable utility games
• shapley value
• ordinal shapley value
• consistency
• fairness

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (T U ) games. We show a solution exists, and call it an Ordinal Shapley value (OSV ). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous. Finally, similarly to the weighted Shapley value for T U games, we construct a weighted OSV as well.