On the uniqueness of Groves mechanisms and the payoff equivalence principle

The uniqueness of dynamic Groves mechanisms on restricted domains

“…Holmström (1979) has subsequently established a result for any smoothly connected domain of valuation functions, which thus implies the previous results. Carbajal (2010) has provided a necessary and sufficient condition for the uniqueness, which naturally implies most of the previous results. 1 Therefore, when searching for mechanisms that additionally satisfy other desirable properties, such as individual rationality and budget balance, we can restrict our attention to Groves mechanisms.…”

“…Having defined these total functions, we henceforth follow Carbajal (2010) as closely as possible to demonstrate that many of the results for the dynamic setting can be obtained by porting the corresponding results of the static mechanism design. We need additional assumptions.…”

“…Our approach is to appropriately define the total valuation function, which is the expected discounted sum of each period's valuation function from the allocation and thus a dynamic counterpart of the static valuation function, and then to port the results for static Groves mechanisms to the dynamic setting. In particular, we port the recent results of Carbajal (2010) which provide a necessary and sufficient condition for the uniqueness of Groves mechanisms as well as a sufficient condition on restricted domains. The final section contains a brief summary.…”

“…Please refer to the original papers for details. Please refer also to Carbajal (2010) for a discussion on the significance of his results in comparison to other payoff equivalence results in static mechanism design.…”

“…They are outcome efficient and dominant strategy incentive compatible, that is, they maximize the sum of players' valuations from the allocation and induce truth-telling as a dominant strategy equilibrium. Moreover, Green and Laffont (1977), Walker (1978), Holmström (1979) and Carbajal (2010) have shown that every outcome efficient and dominant strategy incentive compatible mechanism is a Groves mechanism. In particular, Green and Laffont (1977) have proven the uniqueness result both for unrestricted domains and for a restricted domain containing continuous valuation functions, whereas Walker (1978) has proven the uniqueness result for the class of concave valuation functions on a convex subset of a Euclidean space.…”