One-shot deviation principle

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The one-shot deviation principle (also known as single-deviation property^[1]) is the principle of optimality of dynamic programming applied to game theory.^[2] It says that a strategy profile of a finite multi-stage extensive-form game with observed actions is a subgame perfect equilibrium (SPE) if and only if there exist no profitable single deviation for each subgame and every player.^[1][3] In simpler terms, if no player can increase their expected payoff by deviating from their original strategy via a single action (in just one stage of the game), then the strategy profile is an SPE. In other words, no player can profit by deviating from the strategy in one period and then reverting to the strategy.

Furthermore, the one-shot deviation principle is very important for infinite horizon games, in which the principle typically does not hold,^[4] since it is not plausible to consider an infinite number of strategies and payoffs in order to solve. In an infinite horizon game where the discount factor is less than 1, a strategy profile is a subgame perfect equilibrium if and only if it satisfies the one-shot deviation principle.^[5]