Local Dominance

We define a local notion of dominance that speaks to the true choice problems among actions in a game tree and does not rely on global planning. 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, from our local perspective, we can identify rough forms of contingent reasoning that are particularly natural. We construct a dynamic game that implements the Top Trading Cycles allocation under a minimal form of contingent reasoning, related to independence of irrelevant alternatives.