Other meanings of Strategy
Game Theory
In game theory, a strategy is a complete plan of action that specifies what a player will do in every possible situation they might encounter. It is a central concept that underpins the analysis of strategic interactions, where the outcome for each participant depends on the choices of others. Strategies can be pure (deterministic) or mixed (probabilistic), and they form the basis for solution concepts such as Nash equilibrium. The term was formalized in the mid-20th century by mathematicians like John von Neumann and John Nash, building on earlier work in economics and mathematics.
A strategy in game theory is a rule that tells a player which action to take at every possible decision point in the game. A pure strategy is a deterministic choice, meaning the player always selects the same action in a given situation. In contrast, a mixed strategy assigns a probability distribution over pure strategies, allowing for randomization. For example, in rock-paper-scissors, a player might choose each option with probability 1/3. 1
Strategies can also be classified as behavioral (specifying actions based on information sets) or contingent (depending on opponents' past moves). In extensive-form games, a strategy must specify actions even for branches that are never reached, which is crucial for backward induction. 2
The most influential solution concept is the Nash equilibrium, introduced by John Nash in 1950. A set of strategies (one per player) forms a Nash equilibrium if no player can improve their payoff by unilaterally changing their strategy, given the others' choices. 3 Nash proved that every finite game has at least one equilibrium in mixed strategies, a result that revolutionized economics and social sciences.
Other concepts include dominant strategies (best regardless of opponents), minimax (maximizing the minimum payoff), and correlated equilibrium (where players receive signals from a shared source). These refinements help analyze games with incomplete information or sequential moves. 4
Strategic thinking is applied in economics to model oligopoly competition, auctions, and bargaining. In biology, evolutionary game theory uses strategies to explain animal behavior and the evolution of cooperation, as in the hawk-dove game. In computer science, algorithms for multi-agent systems and artificial intelligence rely on game-theoretic strategies, such as in poker-playing programs.
Political science uses strategies to analyze voting systems and international conflicts, while military theory has long employed strategic concepts. The 2005 Nobel Prize in Economics was awarded to Robert Aumann and Thomas Schelling for their contributions to game theory, highlighting its broad impact. 5
One subtlety is that in games with perfect information, a strategy can be represented as a decision tree, but in games with imperfect information, strategies must be defined over information sets, not just histories. 2 Another niche concept is the trembling hand equilibrium, which considers the possibility of small mistakes by players, refining Nash equilibrium.
Historically, the idea of mixed strategies was anticipated by the 18th-century mathematician Pierre-Rémond de Montmort in his analysis of card games. 6 Also, in evolutionary biology, an evolutionarily stable strategy (ESS) is a strategy that, if adopted by a population, cannot be invaded by any alternative. This concept, introduced by John Maynard Smith, has been used to explain ritualized combat in animals.
Strategies are fundamental to game theory, providing a framework for analyzing strategic interactions in economics, biology, and beyond.
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