A Well-known Rationing Game

Karl-Martin Ehrhart ()
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Karl-Martin Ehrhart: Universitaet Karlsruhe, Postal: RZ Zirkel 2 D-76128 Karlsruhe

No 01-36, Sonderforschungsbereich 504 Publications from Sonderforschungsbereich 504, Universität Mannheim, Sonderforschungsbereich 504, University of Mannheim

Abstract: Monopolies are frequently characterized by the following allocation rule: if the total demand is not greater than the supply, each buyer receives her desired amount in full; and if the total demand exceeds the supply, the supply is distributed proportionally according to the individual desired amounts. Examples include the fixed rate tender, employed in refinancing operations; transactions in supply chains; the allocation of issued stocks; and the distribution of financial support to competing projects. In such a 'rationing game' there is an incentive for the buyers to ask for more than they actually want and that the allocation rule may generate a game without an equilibrium (including in mixed strategies), even if the supply satisfies the true demand. We therefore conclude that this widely employed rule is an unsatisfactory method for allocating goods. Placing an upper bound on the bids will create a game with an equilibrium; however, buyers may still be induced to exaggerate their demands. An infinite repeated game can have an equilibrium even if the equilibrium set of the stage game is empty. Nonetheless, it is possible to fashion an alternative allocation rule which induces buyers to reveal their true demand.

Pages: 24 pages
Date: 2000-12-01
Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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