Finite Mixed Extension of Dyadic Games and their Fair Solutions

A dyadic game being a result of binarization of the strategic behaviour may have either non-fair or impracticable equilibria if the game is not solved in pure strategies. Therefore, a novel approach is suggested for solving such dyadic games. The number of game rounds is the key parameter, which determines a respective finite mixed extension of the game. The finite mixed extension implies using only those non-pure mixed strategies whose nonzero probabilities are fractions with a definite denominator. The finiteness allows consistently realizing such probabilities, whereupon the respective players’ payoffs tend to those theoretically calculated. Compared to the classic equilibrium conception, the suggested approach is more efficient in fair solutions, where the fairness includes both the payoffs equalization and the payoffs sum maximization.