Games Without Saddle Points

GamesWithoutSaddlePoints is a Java implementation of a simple, formula-based method to compute Nash Equilibria for 2×2 and 3×3 payoff matrices in two-player non-zero-sum games without saddle points.

The program returns the ratios of optimal mixed strategies for each player. For 3×3 games, it also includes a one-time pure strategy dominance check to reduce matrix size when possible.

Features

• 2×2 Nash Equilibrium (Mixed Strategy): Uses standard closed-form formulas to compute optimal mixed strategies for both players.

• 3×3 Nash Equilibrium (Mixed Strategy): Computes strategy ratios via formula-based logic; includes support for reducing the game matrix using pure strategy dominance (checked once).

• No Saddle Point Assumption: Designed for games without pure strategy saddle points.

How It Works

• Input: Two separate 2D arrays representing Player A and Player B's payoff matrices.
• Output: Ratios representing the players' optimal mixed strategies.

In 3×3 games, if a row or column is strictly dominated, it will be removed once before computing equilibria.

Getting Started

Requirements

• Java 8 or later
• No external dependencies

Compilation & Execution

1. Compile:

   javac start.java

2. Run:

   java start

Example (2×2)