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.