Add Game Theory Algorithms

[VesperAkshay]

Feature description

Description:

We aim to enhance our repository by including a comprehensive list of game theory algorithms. This addition will provide valuable resources for users interested in understanding and implementing these algorithms in various applications.

Proposed Algorithms to Add:

1. Minimax Algorithm: A decision-making algorithm for two-player games to minimize the maximum possible loss.

2. Alpha-Beta Pruning: An optimization technique for the minimax algorithm that reduces the number of nodes evaluated by eliminating branches that won't affect the final decision.

3. Nash Equilibrium: A solution concept in non-cooperative games where no player can benefit by changing their strategy while others keep theirs unchanged.

4. Monte Carlo Tree Search (MCTS): A heuristic search algorithm used for decision-making processes, particularly in games like Go.

5. Dynamic Programming in Games: Techniques like backward induction for solving extensive-form games by solving subproblems in a bottom-up manner.

6. Evolutionary Game Theory: Analyzes strategies in populations of agents using concepts like replicator dynamics and Nash equilibria.

7. Fictitious Play: A learning process where players assume their opponents will continue to play the same mixed strategies over time.

8. Shapley Value: A method for distributing payoffs fairly among players based on their contributions in cooperative games.

9. Correlated Equilibrium: A generalization of Nash equilibrium where players coordinate their strategies based on signals from a mediator.

10. Zero-Sum Games: Algorithms designed for games where one player's gain is balanced by the losses of another, often solved using linear programming.

Tasks:

• Create documentation for each algorithm, including explanations, pseudocode, and examples.
• Implement code examples for each algorithm in the appropriate programming language(s) used in the repo.
• Ensure that all new content follows the existing coding standards and documentation style.

Benefits:

Adding these algorithms will provide users with a richer resource for understanding game theory and its applications, fostering learning and development in this area.

[tianyizheng02]

If you wish to contribute, please simply open a PR with your algorithm. You don't need to open an issue to get approval or to get assigned to work on it. If you wish to contribute a game theory algorithm, please don't create a new directory for it; place your algorithm under maths/ instead, and we may consider moving game theory algorithms to a separate directory once we have enough of them to justify doing so.

As a side note, some of your proposed "algorithms" aren't really algorithms. For instance:

• "Nash equilibrium" is just a concept in game theory, not an algorithm in itself. You could maybe contribute an algorithm that computes the Nash equilibrium if it exists, but you should reference the name of that algorithm if you do.
• "Dynamic programming in games" is just dynamic programming (which we already have a directory for) applied to games. Simply contribute new dynamic programming algorithms instead, whether they're applied to games or not is tangential.
• "Evolutionary game theory" is just a subfield of game theory, also not an algorithm.
• "Zero-sum games" is just a type of game studied in game theory, also not an algorithm. Please do not contribute implementations of games, they won't/shouldn't be considered "algorithms" for the purposes of this repo.