Patrick Legros
Professor of Economics
Strongly Durable Allocations
I define a new concept of stability for allocations which i call strong durability. A pair consisting of a mechanism and a bayesian equilibrium is strongly durable if for any alternative mechanism and for any sequential equilibrium of the voting game between the two mechanisms the interim utility payoffs of the players in the sequential equilibrium are less than or equal to those obtained in the bayesian equilibrium of the initial mechanism. An allocation is strongly durable if there exists a strongly durable pair that implements this allocation. Strong durability is defined with respect to a class of mechanisms; strong durable allocations are necessarily focally implemented, i.e., there exists a mechanism and an equilibrium of this mechanism that implement that allocation and the given equilibrium interim dominates all the other equilibria of the mechanism. In fact, under a regularity condition, it can be shown that at most one type can be mde worse off in any other equilibrium of the mechanism in the special case of independent values and independent types. If any type of mechanism can be used then strong durability is equivalent to interim efficiency.
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