The problem
In a two-population matching queue with nonzero matching times, agents observe the system and choose whether to join or balk. The natural state is multidimensional, which makes direct strategic analysis difficult.
The structural result
The analysis shows that one dimension can be omitted when characterizing subgame-perfect Nash equilibrium. This reduction leads to threshold-based equilibrium strategies and makes the strategic system more tractable.
Design implication
Numerical analysis studies pricing and social welfare. A targeted intervention on one side can outperform more diffuse policies under some system conditions.
The useful theorem is not only an equilibrium formula—it is the discovery of which part of the state actually matters strategically.