Airport problems and consistent allocation rules

Axiomatic and strategic justifications for the constrained equal benefits rule in the airport problem

“…It says that the agent with the smaller cost contributes half of her cost, and the other contributes the remainder. Second is the CEB rule (Potters and Sudhölter, 1999). 2 The principles of bilateral consistency and converse consistency have been studied extensively in a great variety of models such as taxation, bargaining, social choice, etc.…”

“…For a survey of the literature on the consistency principle and its converse, see Thomson (2010). 3 Potters and Sudhölter (1999) refer to the rule as the "modified nucleolus". The terminology we adopt is due to Thomson (2004).…”

“…2 We apply the two principles to the airport problem, calling the resulting properties "Left-endpoint Subtraction (LS) bilateral consistency" and "LS converse consistency", and study their implications. We show that the "Constrained Equal Benefits (CEB) rule" (Potters and Sudhölter, 1999), 3 which equalizes agents' benefits (at a contributions vector, the benefit of an agent is the difference between her cost (an agent's cost is the cost of satisfying her need) and her contribution) subject to no one receiving a subsidy, is LS bilaterally consistent and LS conversely consistent. Moreover, it is the only LS bilaterally consistent (or LS conversely consistent) rule satisfying either "order preservation for benefits" and "cost monotonicity", or "equal treatment of equals" and "last-agent cost additivity".…”

A polynomial rule for the problem of sharing delay costs in PERT networks

“…Potters and Sudhölter [6] show that the s,w rule is the Weighted Shapley Value and belongs to the Core of the cost game c(S) = C(max i∈S q i ) where (q) = max i∈N q i . The next proposition generalizes this property for any .…”

On the core and nucleolus of directed acyclic graph games

“…There are many variants of this problem depending on the underlying graph structure (single path (Potters and Sudhölter, 1999), tree (Megiddo, 1978;Bjørndal et al, 2004;Maschler et al, 2010), complete graph (Bird, 1976;Huberman, 1981, 1984), etc. ), on whether the nodes carry cost (or a reward) or not (Granot and Maschler, 1998;van den Nouweland et al, 1993), and on whether there are one or more sources (Rosenthal, 1987;Granot and Granot, 1992;Kuipers, 1997).…”