The Deferred Acceptance (DA) algorithm is stable and strategy-proof, but can produce matchings that are Pareto-inefficient for students, and thus several alternatives have been proposed to correct this inefficiency that only involve consented priority violations. However, we show that these...

We study games with incomplete information and characterize when a feasible outcome is Pareto efficient. Outcomes with excessive randomization are inefficient: generically, the total number of action profiles across states must be strictly less than the sum of the number of players and the...