Given the game like Prisoner's dilemma (infinitely undiscounted) and each person has 3 actions in every period: confess defect and kill, and the payoff matrix have 2 NE as (D,D),(K,K).
Can I still use the property that if in any stage NE is played, then that kind of strategy is SPNE.
It seems work for me to prove that any sequence like dd,kk,kk,kk,dd....randomly combination of dd,kk, is SPNE.
Is that correct? Can I generalize that property?