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Local Dominance

Emiliano Catonini and Jingyi Xue

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Abstract: We define a local notion of dominance that speaks to the true choice problems among actions in a game tree. When we do not restrict players' ability to do contingent reasoning, a reduced strategy is weakly dominant if and only if it prescribes a locally dominant action at every decision node, therefore any dynamic decomposition of a direct mechanism that preserves strategy-proofness is robust to the lack of global planning. Under a form of wishful thinking, we also show that strategy-proofness is robust to the lack of forward planning. Moreover, we identify simple forms of contingent reasoning and foresight, driven by the local viewpoint. We construct a dynamic game that implements the Top Trading Cycles allocation in locally dominant actions under these simple forms of reasoning.

Date: 2020-12, Revised 2021-09
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