Strategic Exit and Unilateral Control

Alexander Kangas

Papers from arXiv.org

Abstract: 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 $(1+p)U_X+(4-p)U_Y+5(p^2-3p-1)E[\tau]=0$ 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.

Date: 2026-07, Revised 2026-07
References: Add references at CitEc
Citations:

Downloads: (external link)
https://arxiv.org/pdf/2607.21898 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2607.21898

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().