**Does Luigi Measure Up Game Theory?**

Game theory is a mathematical study of decision-making in situations where two or more individuals have conflicting interests. In recent years, it has become increasingly popular to apply game theory to analyze video games. One of the games that has been receiving attention from game theorists is “Luigi’s Mansion 3,” a puzzle-adventure game developed by Nintendo.

## The Game of Luigi’s Mansion 3

In this game, players take on the character of Luigi as he explores a haunted hotel to rescue his friends from the clutches of King Boo. The game features a variety of puzzles and challenges that players must solve to progress through the levels. The game also includes several boss battles against ghosts and other creatures.

One aspect of the game that has drawn attention from game theorists is the use of cooperative play between Luigi and his companions. In some levels, players control both Luigi and one of his companions simultaneously, and they must work together to solve puzzles and overcome obstacles.

## The Nash Equilibrium

One concept from game theory that has been applied to “Luigi’s Mansion 3” is the Nash equilibrium. This concept refers to a situation in which each player in a game chooses their best possible strategy given their opponent’s strategy.

In “Luigi’s Mansion 3,” players must work cooperatively with their companion characters to progress through certain levels.

The Nash equilibrium can be applied here because each player must choose their best possible strategy based on what they expect their companion to do. For example, if Luigi expects his companion to push a block in a certain direction, he must choose his own actions accordingly to achieve the Nash equilibrium.

## Mixed Strategy Equilibrium

Another concept from game theory that applies to “Luigi’s Mansion 3” is the mixed strategy equilibrium. This concept refers to a situation in which each player chooses a random strategy from a set of possible strategies.

In “Luigi’s Mansion 3,” players must use a variety of strategies to overcome obstacles and progress through levels. The mixed strategy equilibrium can be applied here because players must choose randomly from their available strategies to keep their opponents guessing.

For example, if Luigi always uses the same strategy to defeat a boss, the boss will eventually learn his moves and be able to counter them. By choosing randomly from his available strategies, Luigi keeps the boss guessing and increases his chances of success.

## Conclusion

Overall, “Luigi’s Mansion 3” provides an interesting case study for game theorists looking to apply their concepts to video games. The game’s cooperative play and variety of challenges make it an ideal subject for analysis using game theory concepts such as the Nash equilibrium and mixed strategy equilibrium. As video games continue to evolve, it will be interesting to see how game theorists continue to apply their concepts in new and innovative ways.