Game theory is a branch of mathematics that studies decision-making in strategic situations. It’s a field that has found applications in many areas, including economics, political science, and psychology. One of the most important concepts in game theory is the idea of a complete strategy.
What Is a Complete Strategy?
In game theory, a complete strategy is a plan of action that specifies what a player will do in every possible situation. It’s a way for players to communicate their intentions to each other and to coordinate their actions.
For example, consider the classic game of rock-paper-scissors. A complete strategy for this game would specify which move to make in each possible scenario.
If your opponent plays rock, you should play paper. If they play paper, you should play scissors. And if they play scissors, you should play rock.
Why Are Complete Strategies Important?
Complete strategies are important because they help players avoid confusion and misunderstandings. In many strategic situations, there are multiple ways to achieve your goals, but some strategies may be more effective than others depending on what your opponent does.
By having a complete strategy, you can be confident that you’re making the best possible moves given the information available to you. You don’t have to worry about second-guessing yourself or improvising on the fly.
- Types of Complete Strategies
There are several types of complete strategies in game theory:
Pure Strategies
A pure strategy is a complete plan of action that specifies exactly what move to make in every possible scenario. For example, if you always choose rock in rock-paper-scissors, that’s a pure strategy.
Mixed Strategies
A mixed strategy is a complete plan of action that specifies probabilities for each move in every possible scenario. For example, if you choose rock with a probability of 1/3, paper with a probability of 1/3, and scissors with a probability of 1/3, that’s a mixed strategy.
Sequential Strategies
A sequential strategy is a complete plan of action that specifies what to do at each stage of the game, based on the moves made by other players. Sequential strategies are often used in games where players take turns making moves.
Simultaneous Strategies
A simultaneous strategy is a complete plan of action that specifies what move to make without knowing what the other players will do. These strategies are often used in games where all players make their moves at the same time.
Conclusion
In conclusion, a complete strategy is an important concept in game theory that helps players coordinate their actions and avoid misunderstandings. There are several types of complete strategies, including pure strategies, mixed strategies, sequential strategies, and simultaneous strategies. By understanding these concepts and using them effectively, you can improve your chances of success in strategic situations.