For the problem of adjudicating conflicting claims, we study lower bounds on the awards of each agent. We propose extending a lower bound by performing the following operation: (i) for each problem, assign the lower bound and revise the problem accordingly; (ii) assign the bound of the revised problem. The “recursive-extension” of a bound is the lower bound obtained by recursive application of this operation. We provide necessary and sufficient conditions on a lower bound for there to be a unique rule satisfying its recursive-extension. We show that, under these conditions, the rule satisfying the recursive-extension of a bound is the unique rule satisfying the following property: the awards assigned by a rule should be obtainable in two ways: (i) directly applying the rule to the problem or (ii) first assigning the bound and revising the problem accordingly, and then applying the rule to the revised problem. Then, we study whether this procedure leads to well-behaved lower bounds.
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Paper provided by Centro de Investigacion Economica, ITAM in its series Working Papers with number
0705.
Find related papers by JEL classification: C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances
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