We propose a measure of strategic complexity for a class of strategy-proof mechanisms, which includes all strategy-proof mechanisms used in practice. Our rankings are consistent with the coarser ones implied by the solution concepts of (strong) obvious strategy-proofness (Li, 2017b, Pycia and Troyan, 2023b). The added flexibility of our approach allows a designer to balance a mechanism’s simplicity with other objectives. Our measure characterizes the Ausubel (2004) auction as the simplest way to implement the VCG outcome in multi-unit allocation problems with transfers, and provides novel rankings of mechanisms that implement stable outcomes in matching problems. Finally, we characterize minimally complex mechanisms for a range of settings, and formalize the intuition that some mechanisms are as simple as if they were (strongly) obviously strategy-proof. We explain how this extension can be valuable for high-stakes applications such as the FCC incentive auction.

We show that achieving dominant strategy incentive compatibility often requires a designer to choose a mechanism of severely limited transparency. Since both properties have been shown to affect a mechanism's performance, we propose as-if dominant strategy mechanisms to successfully balance transparency and straightforward strategic incentives.  An as-if dominant strategy mechanism is such that, as long as all agents believe others play as if they where in a direct mechanism: (i) They all have a strategy that is optimal no matter what others do, and (ii) rationality alone is enough to ensure that they always best respond to each other. We show that the auction format used by prominent online auction platforms---such as eBay---achieves maximal transparency within the set of as-if dominant strategy second-price auctions with decentralized bids. Furthermore, our approach reconciles theoretical predictions with experimental evidence in a range of settings, from matching to multi-unit auctions environments. Finally, we show that a refinement of as-if dominance is a useful technical tool to easily identify mechanisms that are solvable by iterated elimination of weakly dominated strategies. 

We study exploding offers by considering the strategic interaction between a low-tier firm and a set of workers within a large job market. Each worker has a private value for the firm and may receive offers from preferred top-tier firms according to an exogenous stochastic process. We show that more risk averse workers receive offers with shorter deadlines, and that there is a level of risk aversion beyond which a worker only receives offers that expire as soon as possible---independently of what all other firms are doing. If workers are sufficiently risk averse, the workers' expected welfare is maximized if and only if exploding offers are banned. Finally, any minimal offer length that does not ban exploding offers may lead to workers falling through the cracks. All results are robust to a range of sequentially-rational strategies for the workers. Our predictions match existing evidence and have implications for policies regulating exploding offers.