Game theory is a mathematical concept used to analyze strategic decision making. It has been applied in various fields, including economics, political science, and psychology.

In game theory, players strategize to achieve the best possible outcome. The methods used to solve game theory have evolved over time, and this article will explore some of the most common ones.

1. Dominant strategy

The dominant strategy is a method of solving game theory by analyzing each player’s optimal move regardless of what their opponents do. If there is a dominant strategy for each player in a game, it can be solved quickly and efficiently. However, in most cases, there is no dominant strategy.

2. Nash equilibrium

Nash equilibrium is one of the most widely used methods for solving game theory problems. It identifies a stable outcome when all players have chosen their best possible actions given what they know about their opponents’ strategies. In other words, it is a situation where no player can improve their position by changing their strategy unilaterally.

## The steps involved in finding Nash equilibrium are:

• Identify all players
• List all possible strategies for each player
• Determine each player’s payoffs for each combination of strategies
• Identify all pure-strategy Nash equilibria (situations where every player has chosen their best response)
• If there are no pure-strategy Nash equilibria, look for mixed-strategy Nash equilibria (strategies that are played with some probability)

3. Minimax theorem

The minimax theorem is another method used to solve game theory problems. It assumes that both players are rational and will act to minimize the maximum loss they could face in a worst-case scenario.

### The steps involved in finding the minimax solution are:

• Identify all players
• List all possible strategies for each player
• Determine each player’s payoffs for each combination of strategies
• Determine the maximum payoff for each row (player 1’s moves) and the minimum payoff for each column (player 2’s moves)
• The minimax solution is the choice of strategies that guarantees the highest minimum payoff for player 1 and the lowest maximum payoff for player 2.

4. Correlated equilibrium

In correlated equilibrium, players receive signals (such as cards or other random events) that guide their actions. The signals are correlated in such a way that both players benefit from following them.

### The steps involved in finding correlated equilibrium are:

• Identify all players
• List all possible strategies for each player
• Determine each player’s payoffs for each combination of strategies
• Create a correlation device that assigns a probability distribution to the set of signals given to both players.
• If there exists a correlation device such that no player wants to deviate from his strategy, then this is a correlated equilibrium.

In conclusion, these are some of the most common methods used to solve game theory problems. Each method has its own strengths and weaknesses, and choosing the appropriate one depends on the problem at hand. By identifying dominant strategies, Nash equilibria, minimax solutions, and correlated equilibria, we can analyze strategic decision-making in various fields more effectively.