One-shot deviation principle

In game theory, the one-shot deviation principle (also known as the single-deviation property) is a principle used to determine whether a strategy in a sequential game constitutes a subgame perfect equilibrium. An SPE is a Nash equilibrium where no player has an incentive to deviate in any subgame. It is closely related to the principle of optimality in dynamic programming.

The one-shot deviation principle states that a strategy profile of a finite multi-stage extensive-form game with observed actions is an SPE if and only if there exist no profitable single deviation for each subgame and every player. In simpler terms, if no player can profit (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.

The one-shot deviation principle is very important for infinite horizon games, in which the backward induction method typically doesn't work to find SPE. 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.