We propose a complete ranking of strategy-proof mechanisms in terms of the contingent reasoning they require agents to engage in to recognize their dominant strategy. 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 agents can adopt a simplifying heuristic to avoid dominated strategies. It prescribes  playing  strategies optimal against all unconditional behaviors of the others. A mechanism is as-if dominant strategy if the adoption of this heuristic is self supporting. That is, no agent can ever profit by unilaterally strategizing further.  As-if dominance is more permissive than dominance, allowing for substantially more transparent mechanisms. This is useful, as we show  transparency makes the heuristic’s prescriptions easier to follow. Our approach rationalizes the auction choice of prominent online platforms, such as eBay. Further, it provides a unified explanation for a range of experimental findings. Finally, under some conditions met in our applications, as-if dominance ensures that coarse rationality emerges from a generational learning process.

An auction equilibrium is weakly credible if the auctioneer cannot alter the auction rules in a way  that (i) no bidder alone can detect and (ii) she is sure to profit from. I show that no static multiunit auction has an efficient and weakly credible equilibrium in which losers do not pay.  Further, no auction for more than two units has an efficient and weakly credible equilibrium in dominant strategies.  Finally, I prove that an adaptation of the ascending auction proposed by Ausubel (2004)  has an efficient and weakly credible ex-post equilibrium, regardless of how many units are for sale. 

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.