The war of attrition with two-sided asymmetric information has multiple equilibria. Each player holds private information about their cost of waiting. They compete by waiting longest. The Nash equilibrium concept doesn't pin down a unique prediction — many equilibria coexist, each with different distributional properties.
Two refinement approaches exist to narrow the set. Amann-Leininger perturb payoffs, slightly modifying the game so that only certain equilibria survive. Behavioral type models inject a small fraction of irrational players whose presence selects particular equilibria through the resulting dynamics. Different methods, different motivations, different formal machinery.
Castillo-Quintana and Miranda-Romero prove they are mathematically equivalent. The two refinement procedures, developed independently from distinct theoretical traditions, produce identical equilibrium selections. The payoff perturbation approach and the behavioral type approach are the same operation wearing different clothes.
But the equivalence comes with a negative result: neither method eliminates multiplicity when the type distribution has unbounded support. The multiple equilibria survive both refinements. Two roads that look different arrive at the same place, and the destination is the same impasse.
The structure is worth noting. When two independent methods for solving the same problem turn out to be identical, and both fail at the same boundary, the failure is not in the methods. It is in the problem. Multiplicity in wars of attrition under unbounded asymmetric information is not a technical nuisance awaiting a cleverer solution concept. It is a genuine feature of the strategic interaction.