Previous work shows that reputation results may fail in repeated games with long-run players with equal discount factors. Attention is restricted to extensive-form stage games of perfect information. One and two-sided reputation results are provided for repeated games with two long-run players with equal discount factors where the first mover advantage is maximal. If one of the players is a Stackelberg type with positive probability, then that player receives the highest payoff, that is part of an individually rational payoff profile, in any perfect equilibria, as agents become patient. If both players are Stackelberg types with positive probability, then perfect equilibrium payoffs converge to a unique payoff vector; and the equilibrium play converges to the unique equilibrium of a continuous time war of attrition. All results generalize to simultaneous move stage games, if the stage game is a game of strictly conflicting interest.