AI 中文总结
研究重复博弈中对手决定关系是否持续时的情况，通过战略退出将全局控制转化为局部控制，在双行动博弈及囚徒困境中得出相关恒等式，战略双边退出留下一维收益 - 持续时间关系并排除非平凡仅收益累积恒等式。
AI 中文摘要
重复博弈策略可通过平衡跨期的可控收益来施加全局收益关系。问题在于当对手在每轮观察后决定关系是否持续时会留下什么。对于每个具有有限期望持续时间的依赖历史的对手策略，当且仅当其期望阶段增量在每个可达历史处消失时，累积线性恒等式才可强制执行。战略退出因此将全局控制转化为局部控制。在具有唯一局部均衡器的双行动博弈中，控制器在每个可达历史处必须使用相同的混合行动，对双方玩家均无记忆限制。对于囚徒困境\((T,R,P,S)=(5,3,1,0)\)，幸存的恒等式为\((1 + p)U_X + (4 - p)U_Y + 5(p^2 - 3p - 1)E[\tau]=0\)。持续时间系数在\([0,1]\)上永不消失。因此战略双边退出留下一维收益 - 持续时间关系，同时排除每个非平凡的仅收益累积恒等式。
英文摘要
Repeated-game strategies can impose global payoff relations by balancing controlled rewards across time. The question is what remains when the opponent decides, after observing each round, whether the relationship continues. Against every history-dependent opponent strategy with finite expected duration, a cumulative linear identity is enforceable if and only if its expected stage increment vanishes at every reachable history. Strategic exit therefore converts global control into local control. In a two-action game with a unique local equalizer, the controller must use the same mixed action at every reachable history, without any memory restriction on either player. For the Prisoner's Dilemma with $(T,R,P,S)=(5,3,1,0)$, the surviving identities are $(1+p)U_X+(4-p)U_Y+5(p^2-3p-1)E[τ]=0$ The duration coefficient never vanishes on $[0,1]$. Hence strategic bilateral exit leaves a one-dimensional payoff-duration relation, while ruling out every nontrivial payoff-only cumulative identity.
CommentsI identified prior results that materially affect the manuscript's novelty, attribution, and contribution framing. The mathematical results remain correct, but the paper requires substantial revision and should not be posted in its current form
