Nash Calculator: finding best responses in a payoff matrix

A payoff matrix gives each player a score for every pair of choices. The useful question is whether either player would change their choice if the other held still. I built Nash Calculator as a wxWidgets desktop tool for exploring that question in two-player games. You enter one payoff grid per player, choose the number of strategies, and calculate a pure or mixed result.

Pure strategies

For each of player 2’s choices, the calculator finds player 1’s highest payoff. It then does the reverse: for each of player 1’s choices, it finds player 2’s highest payoff. Ties remain in contention. A cell that is a best response for both players is a pure-strategy Nash equilibrium, so the result shows its strategy indices and payoff pair. If no cell qualifies, the calculator says so.

This best-response marking follows the idea in A note on determining pure-strategy equilibrium points of bimatrix games.

The mixed calculation

The mixed path repeatedly removes rows or columns that its strict payoff comparison marks as dominated. It then uses best-response payoff totals to produce a probability for each strategy in the reduced dimensions. When a player’s total is zero, it assigns equal probabilities instead. The displayed probabilities have two decimal places.

This path was informed by An Efficient Algorithm for Finding Mixed Nash Equilibria in 2-Player Games, but the current implementation does not check the resulting probabilities against the full mixed-equilibrium conditions. I treat that output as an estimate for exploring a game, not a general proof of equilibrium.

The C++ project is on GitHub.