game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

, a Markov strategy is a

strategy Strategy (from Greek στρατηγία ''stratēgia'', "troop leadership; office of general, command, generalship") is a general plan to achieve one or more long-term or overall goals under conditions of uncertainty. In the sense of the " a ...

that depends only on the current state of the game, rather than the full history of past actions. The state summarizes all relevant past information needed for decision-making. For example, in a repeated game, the state could be the outcome of the most recent round or any summary statistic that captures the strategic situation or recent sequence of play. A profile of Markov strategies forms a

Markov perfect equilibrium A Markov perfect equilibrium is an equilibrium concept in game theory. It has been used in analyses of industrial organization, macroeconomics, and political economy. It is a refinement of the concept of subgame perfect equilibrium to extensive f ...

if it constitutes a

Nash equilibrium In game theory, the Nash equilibrium is the most commonly used solution concept for non-cooperative games. A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed) ...

in every possible state of the game. Markov strategies are widely used in dynamic and stochastic games, where the state evolves over time according to probabilistic rules. Although the concept is named after

Andrey Markov Andrey Andreyevich Markov (14 June 1856 – 20 July 1922) was a Russian mathematician best known for his work on stochastic processes. A primary subject of his research later became known as the Markov chain. He was also a strong, close to mas ...

due to its reliance on the

Markov property In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process, which means that its future evolution is independent of its history. It is named after the Russian mathematician Andrey Ma ...

—the idea that only the current state matters—the strategy concept itself was developed much later in the context of dynamic game theory.

References

Strategy (game theory) {{Gametheory-stub