This talk explores equilibrium concepts in stopping games with underlying diffusion processes. We address key challenges in classical existence results for equilibria, focusing on two common approaches: (1) equilibria in general randomized stopping times, which are too broad to allow for explicit solutions and fail to respect subgame perfection, and (2) equilibria in first-entry times, which rely on overly restrictive conditions.

As an alternative, we introduce the concept of Markovian randomized stopping times, providing a unifying framework to overcome these limitations. We establish general existence theorems for Markovian equilibria across a wide range of stopping games. This approach has two key advantages: (1) it enables explicit solutions in diverse scenarios, and (2) it offers clear game-theoretic interpretations, enhancing its relevance for both theory and applications.

The talk is based on joint work with: Boy Schultz and Kristoffer Lindensjö.