wo friends want to have a tennis match against each other. The question is whether to play aggressively or defensively (which will depend on their ability). Both players privately observe their ability, and this is explained by their probability of winning if both play aggressively: p_H or P_L, which have corresponding probabilities q and 1 q, where 0 < pL < p_li < 1. If a player plays attacking and the rival plays defensive, he wins with probability fyp_i such that p_i < Fyn < 1, j E {H, L}. If a player plays defensive and his rival plays attacking, his probability of winning drops to op₃ where 0 < Op_i < p_i. If both play aggressive, probability of winning is p_i for a i-type player. Finally, if both players play defensive, there is no winner (payoff is 0, the match takes too long). Reward from winning is R and loss from losing is L, such that R > 0 > L.

1. Under which conditions there is a symmetric BNE where both players play aggressive regardless of type.
2. Find the conditions to support a symmetric BNE in which both players play aggressive only if their type is high.