A strategy profile that is a Nash equilibrium in every subgame, including those outside the realized play path. In finite sequential games, backward induction constructs such profiles by solving continuation games before earlier decisions. When a stage is an all-pay contest, its solution can involve mixed strategies.
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Subgame Perfect Equilibrium (SPE) is a refinement of Nash Equilibrium used in game theory, specifically in the context of extensive-form games, which can be represented by a tree-like structure. In an SPE, the strategy profile is not only a Nash Equilibrium in the game as a whole but also remains a Nash Equilibrium in every subgame of that game.