Explicit formulas are given for the asymptotic value limλ → 0v(λ) and the asymptotic minmax lim w(λ) of finite λ-discounted absorbing games together with new simple proofs for the existence of the limits as λ goes to zero. Similar characterizations for stationary Nash equilibrium payoffs are obtained. The results may be extended to absorbing games with compact metric action sets and jointly-continuous payoff functions.
