Distributed Strategic Learning for Wireless Engineers

Proposition 2.3.2.1 ([81]). In any two-by-two game, assuming players’ aspirations are different from their respective payoffs (${\tilde{R}}_j\left(\text{a}\right)\ne M_j$ for all j and a) and below their respective maximin, the process X_t converges to an S2RP with probability 1 (the set formed by all S2RPs is asymptotically reached with probability 1). If the initial state is completely mixed, then every S2RP can be asymptotically reached with positive probability.

Proposition 2.3.2.2 ([81]). In any two-by-two game, assuming players’ aspirations are different from their respective payoffs and above their respective maximin:

•  If there is any S2RP, then the process X_t converges to an S2RP with probability 1 (the set formed by all S2RPs is asymptotically reached with probability ...