Game theory is a branch of mathematics that deals with the study of decision-making in strategic situations. It is widely used in economics, political science, psychology, and other fields where decision-making is an integral part of the system.

The basic premise of game theory is that every decision-maker is rational and tries to maximize their own payoff. In this article, we will discuss the four principles of game theory.

Principle 1: Rationality

The first principle of game theory is rationality. According to this principle, every player in a game is rational and tries to maximize their own payoff.

This means that players will always choose the strategy that gives them the highest expected payoff. Rationality also assumes that players have perfect information about the game and the strategies available to them.

Example:

Consider a simple game between two players: Player A and Player B. Each player has two strategies: cooperate or defect.

If both players cooperate, they each receive a payoff of 3. If one player cooperates and the other defects, the defector receives a payoff of 5 while the cooperator receives a payoff of 1. If both players defect, they each receive a payoff of 2.

If both players are rational, they will choose to defect because it gives them a higher expected payoff than cooperation (5 vs 3). This shows how rationality plays an important role in decision-making in games.

Principle 2: Dominant Strategy

The second principle of game theory is dominant strategy. According to this principle, if one player has a dominant strategy – a strategy that gives them a higher payoff regardless of what their opponent does – then they should always choose that strategy.

In the same example as before, it turns out that both players have a dominant strategy – defecting. No matter what Player B does, Player A will always receive a higher payoff by defecting.

Similarly, no matter what Player A does, Player B will always receive a higher payoff by defecting. Therefore, both players should choose to defect.

Principle 3: Nash Equilibrium

The third principle of game theory is Nash equilibrium. According to this principle, a Nash equilibrium is a set of strategies where no player can improve their payoff by unilaterally changing their strategy.

In the same example as before, the Nash equilibrium is for both players to choose the strategy of defecting. If either player changes their strategy to cooperate, they will receive a lower payoff than if they had continued to defect. Therefore, neither player has an incentive to change their strategy unilaterally.

Principle 4: Zero-Sum Game

The fourth principle of game theory is zero-sum game. According to this principle, in a zero-sum game, one player’s gain is another player’s loss. That is, the sum of all payoffs in the game is zero.

Consider a simple game between two players: Player A and Player B. Each player has two strategies: heads or tails.

If both players choose heads or both players choose tails, nothing happens and they each receive a payoff of 0. If one player chooses heads and the other chooses tails, the player who chose heads receives a payoff of 1 while the other receives a payoff of -1.

This is an example of a zero-sum game because the sum of all payoffs in the game is zero (1 + (-1) = 0). In such games, players are often more aggressive because they know that their opponent’s loss is their gain.

In conclusion, these four principles are fundamental to understanding and analyzing games from different fields using mathematical models. By understanding the principles of rationality, dominant strategy, Nash equilibrium, and zero-sum game, we can make better decisions and predict outcomes in strategic situations.