Equilibrium Game Theory Explained
Game theory is a field of mathematics that studies decision-making in strategic situations. It is used to predict the outcomes of interactions between individuals or groups, where the payoff for each participant depends on the strategy chosen by all participants. One of the most important concepts in game theory is equilibrium, which refers to a situation where no player can improve their payoff by changing their strategy.
What Is Equilibrium in Game Theory?
In game theory, an equilibrium is a state where all players have chosen their best possible strategy given the choices made by other players. This means that no player can gain an advantage by changing their strategy while all other players keep theirs unchanged.
There are two types of equilibria in game theory: Nash equilibrium and Pareto equilibrium. Nash equilibrium is when no player can improve their payoff by unilaterally changing their strategy. Pareto equilibrium is when there is no other outcome where at least one player can be made better off without making another player worse off.
How Does Equilibrium Work?
Equilibrium works through a process called backward induction. In this process, players start by assuming that all other players will play optimally. They then work backwards from the end of the game to determine what strategies they should choose at each stage of the game.
For example, consider a simple game called “Prisoner’s Dilemma”. Two suspects are arrested for a crime and held in separate cells. Each suspect has two options: cooperate with the police or remain silent.
If both suspects cooperate, they will both receive a light sentence. If one suspect cooperates and the other remains silent, the cooperating suspect will receive no sentence while the silent suspect will receive a heavy sentence. If both suspects remain silent, they will both receive a moderate sentence.
In this game, there are two Nash equilibria: both suspects remain silent or both suspects cooperate. However, the Pareto optimal outcome is for both suspects to cooperate. This is because if both suspects remain silent, they will receive a moderate sentence, which is worse than the light sentence they would receive if they both cooperate.
Applications of Equilibrium Game Theory
Equilibrium game theory has many applications in economics, political science, and other fields. It is used to study situations such as pricing strategies in markets, bargaining between labor unions and employers, and arms races between countries.
One famous example of equilibrium game theory is the “Tragedy of the Commons”. This refers to a situation where individuals acting in their own self-interest deplete a shared resource, such as a fishery or a forest. In this situation, there is no individual incentive to conserve the resource, leading to its eventual collapse.
Equilibrium game theory is a powerful tool for analyzing strategic interactions between individuals or groups. It helps us predict outcomes in situations where each participant’s payoff depends on the choices made by all other participants. By understanding equilibria in games like Prisoner’s Dilemma and Tragedy of the Commons, we can make better decisions in our personal and professional lives.