ix-game

name	ix-game
description	Game theory — Nash equilibria, Shapley value, auctions, evolutionary dynamics
disable-model-invocation	true

Game Theory

Model strategic interactions between rational agents.

When to Use

When the user needs to analyze competitive/cooperative scenarios, design auctions, compute fair allocations, or model population dynamics.

Capabilities

• Nash Equilibria — Support enumeration, fictitious play, dominant strategies
• Cooperative Games — Shapley value, Banzhaf index, core membership
• Auctions — First-price, second-price (Vickrey), English, Dutch, all-pay
• Evolutionary — Replicator dynamics, ESS detection, Hawk-Dove, Rock-Paper-Scissors
• Mechanism Design — VCG mechanism, Myerson optimal reserve
• Mean Field — Large-population game dynamics, logit equilibrium

Programmatic Usage

use ix_game::nash::{BimatrixGame, support_enumeration};
use ix_game::cooperative::{CooperativeGame, shapley_value};
use ix_game::auction::{second_price_auction, english_auction};
use ix_game::evolutionary::{replicator_dynamics, is_ess};
use ix_game::mean_field::{MeanFieldGame, find_equilibrium};

Classic Examples

• Prisoner's Dilemma: [[3,0],[5,1]] vs [[3,5],[0,1]]
• Matching Pennies: [[1,-1],[-1,1]] vs [[-1,1],[1,-1]]
• Hawk-Dove: use hawk_dove_matrix(v, c) helper