Game theory is a branch of mathematics that deals with decision-making in competitive situations where the outcome of one participant’s decision depends on the decisions of others. It is a study of how people behave in strategic situations.
In game theory, strategies refer to the plans and actions that players take to achieve their objectives. A strategy is a set of rules or guidelines that govern the player’s decisions and actions throughout the game. The objective is to maximize one’s own payoff or minimize one’s losses.
There are two types of strategies in game theory: pure strategies and mixed strategies.
A pure strategy is a specific course of action that a player takes in a game. It involves choosing one option from a set of options without any randomization or probability involved. For example, in rock-paper-scissors, choosing “rock” every time as your move is a pure strategy.
A player can have multiple pure strategies available to them, but they can only choose one at any given time during the game. The goal is to choose the best possible pure strategy that maximizes their payoff.
A mixed strategy, on the other hand, involves randomizing between different pure strategies based on some probability distribution. This means that instead of always choosing one particular option, players assign probabilities to each option and choose randomly according to those probabilities.
For example, if you were playing rock-paper-scissors and chose each move with equal probability (1/3), then that would be an example of a mixed strategy.
Mixed strategies can be used when there are no dominant pure strategies available or when it’s difficult to predict what your opponent will do next.
How Are Strategies Determined?
Determining the best strategy involves analyzing all possible outcomes based on various choices made by all players. Game theorists use mathematical models to analyze these outcomes and determine optimal solutions for each player.
One popular tool used to analyze strategies is the Nash equilibrium. Named after John Nash, a Nobel Prize-winning mathematician, a Nash equilibrium is a state in which each player is doing the best they can given the choices of others.
Examples of Strategies in Game Theory
One classic example of game theory is the prisoner’s dilemma. In this scenario, two criminals are arrested and given separate interrogations.
They are offered a plea bargain: If one confesses and implicates the other, they will get a reduced sentence while the other gets a harsher sentence. If both confess, they both get harsher sentences than if neither confesses.
The strategies available to each prisoner are to either confess or remain silent. If both prisoners remain silent, they will each receive lighter sentences than if one or both confess.
Another example is the game of chicken. In this game, two drivers speed towards each other on the same road and must decide whether to swerve or keep driving straight ahead.
If both drivers swerve, they avoid a collision but lose face. If only one driver swerves and the other keeps going straight, then the driver who swerved loses face while the driver who kept going straight wins.
The strategies available in this game are to either swerve or not swerve. The outcome depends on what each player thinks their opponent will do.
Strategies play a vital role in game theory as players aim to maximize their payoff by making informed decisions based on their opponent’s actions and reactions. Understanding pure and mixed strategies and how to determine them can help players make better decisions in competitive situations.