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Has any work been done on market allocations where market participants have utility functions that depend on other players' allocations?

For example, suppose I have a general equilibrium model with three players 1, 2, and 3, and three goods A, B, and C. Suppose player 1's utility depends on the relative utility of players 2 and 3, say with u1 = f(a1, b1, c1) + u2(a2, b2, c2) - u3(a3, b3, c3), where ai is the number of As that player i is allocated. For particular starting allocation, player 1 may block three-cycles of trades that give him more of every good, if those trades decrease u2(a2, b2, c3) - u3(a3, b3, c3).

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  • $\begingroup$ In your example the utility of a player does not merely depend on other players' allocations but on the other players' utilitites. This can result in equation systems with no solutions. An example: $$ U_1 = U_2 + 1, \hskip 20pt U_2 = U_1 + 1. $$ $\endgroup$ – Giskard Dec 15 '16 at 7:21
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    $\begingroup$ Yes. Look up general equilibrium with externalities -- these economies are a classic example of instances where the First Welfare Theorem fails. The standard approach is to derive the equilibrium allocation as if each consumer doesn't care about everyone else's allocation. The model you describe where agents can block certain allocations is typically not thought of as a 'general equilibrium' model. Agents in a standard general equilibrium model are taken to act non-strategically. $\endgroup$ – Theoretical Economist Dec 15 '16 at 8:00
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    $\begingroup$ I used this reference for personal research, but it deals with other-regarding preferences in general equilibrium models: [restud.oxfordjournals.org/content/early/2011/01/24/… (link) $\endgroup$ – Walrasian Auctioneer Dec 15 '16 at 10:54

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