You have also have another player, (lets call him M) who has been getting small positive payoffs from S. M was foolish enough to think he could outmaneuver S at his own game. In fact, M was directly responsible for putting S in a position to put down the rules of the game and was immediately given small rewards, while another player (named R) objected strongly.

In strategic interactions between S and R, S has shown himself to be completely non-altruistic and R suffered severe negative payoffs. In strategic interactions between M and R, M has shown himself to be also completely non-altruistic and R suffered negative payoffs, but not as severe as when it interacted with S.

R is now asked to support either M or S in a game in which he was eliminated. The outcome of that game will determine who gets to interact strategically with R in the future. R’s support for either player is costly (i.e. it is an acknowledgment of the rules of the game). R knows that S will not be fully eliminated under any outcome. R calculates that his expected payoff is unlikely to change under any outcome. R knows that although long ago his payoffs were strongly correlated with M, but that has ceased to be the case.

From my point of view R would not be able to play unless M is the winner.

R his reaction dose not have any value as he is out of the play and probability of entering this game while two players exist equal to 0.

So we can devide the game into 2 games first between S and M then R will find his place in the next game with the winner and as we looking for R to win we need player from first game (the one with no power or less power) specially we will found a lot of org standing beside R if he aganist M which is not exist in case of R V.s S