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Serial cost sharing. (English) Zbl 0766.90013
Summary: A fixed group of $$n$$ agents share a one input, one output technology with decreasing returns. We propose the following cost sharing formula. Agent 1 with the lowest demand of output $$q_ 1$$ pays $$(1/n)$$th of the cost of $$nq_ 1$$. Agent 2, with the next lowest demand $$q_ 2$$ pays agent 1’s cost share plus $$1/(n-1)$$th of the incremental cost from $$nq_ 1$$ to $$(n-1)q_ 2+q_ 1$$. Agent 3, with the next lowest demand $$q_ 3$$ pays agent 2’s cost share, plus $$1/(n-2)$$th of the incremental cost from $$(n- 1)q_ 2+q_ 1$$ to $$(n-2)q_ 3+q_ 2+q_ 1$$. And so on.
Among agents endowed with convex and monotonic preferences, serial cost sharing is dominance solvable and its unique equilibrium is also robust to coalitional derivations. We show that no other smooth cost sharing mechanism yields a unique Nash equilibrium at all preference profiles.

##### MSC:
 91B24 Microeconomic theory (price theory and economic markets) 91A40 Other game-theoretic models 91B32 Resource and cost allocation (including fair division, apportionment, etc.)
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