Subgame perfection in recursive perfect information games
研究了具有完美信息和确定性转移的序贯多人博弈，证明了对于任意正数ε，该类博弈都存在子博弈完美ε-均衡，并给出了构造性证明和有限算法。
Abstract We consider sequential multi-player games with perfect information and with deterministic transitions. The players receive a reward upon termination of the game, which depends on the state where the game was terminated. If the game does not terminate, then the rewards of the players are equal to zero. We prove that, for every game in this class, a subgame perfect $$\varepsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ε</mml:mi> </mml:math> -equilibrium exists, for all $$\varepsilon > 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ε</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . The proof is constructive and suggests a finite algorithm to calculate such an equilibrium.