Fig. 1: Generalized payoff matrix for multi-strategy multiplayer games, reducible to two-strategy or two-player formats.

a Payoff matrix for n-strategy (k + 1)-player games: with n strategies and k co-players, the matrix size is \(n\times {\mathbb{C}}(k+n-1,\, k)\). b Payoff matrix for 2-strategy (k + 1)-player games⁴⁶: with n = 2 strategies and k co-players, the matrix size is \(2\times {\mathbb{C}}(k+1,\, k)\). c, Payoff matrix for n-strategy 2-player games³³: with n strategies and k = 1 co-players, the matrix size is \(n\times {\mathbb{C}}(n,\, 1)\). d, Payoff matrix for 2-strategy 2-player games²⁹: with n = 2 strategies and k = 1 co-players, the matrix size is \(2\times {\mathbb{C}}(2,\, 1)\).