Exit Rights, Free Movement Alliances, and Game-Theoretic War Deterrence

Article 2 — Abstract (English) This paper studies war deterrence through guaranteed exit rights in a three-stage extensive-form model. Its Stage 3 shared-cutoff result is conditional on the stated stay-on-indifference selection, capacity-valid private reservations, and a common income/security pair at the reserved best destinations for all citizens in the baseline. Aggregate capacity alone establishes none of these conditions; heterogeneous individual best-destination values in the separate finite admission analysis do not imply a common cutoff. A separate bounded finite admission analysis shows that such reservations select the citizens with strictly positive best-destination gains, while a common fixed-priority rule permits construction of one pure Nash equilibrium. Two two-citizen examples show that total capacity alone need not guarantee best-destination admission and that realized weighted labor loss can fall from 5 to 3 as exit freedom rises from 0 to 3/4, with one emigrant in each case. A mechanical check covers 1,088 specified rational cases; it is numerical evidence, not a universal or empirical result. The full continuation game and empirical identification remain open. Historical examples are illustrative and do not identify a causal deterrence effect. Article 3 — Abstract (English) This paper studies war deterrence through guaranteed exit rights in a three-stage extensive-form model. Conditional on a qualifying alliance-formation equilibrium and the stated capacity condition, the finite-citizen model gives a stepwise emigration response; the continuum cutoff remains an approximation. The shared Stage 3 cutoff additionally assumes a common income/security pair at citizens' privately reserved best destinations; the separate finite-admission analysis permits individual destinations but does not derive a common cutoff. A bounded analysis of the finite admission subgame separates a capacity-valid complete private reservation, which selects citizens with strictly positive best-destination gains, from a common fixed-priority rule, under which a greedy procedure constructs one pure Nash equilibrium. Two two-citizen examples show that aggregate capacity alone need not secure best-destination admission and that realized weighted labor loss can fall from 5 to 3 as exit freedom rises from 0 to 3/4, with one emigrant in each case. A mechanical check covers 1,088 specified rational cases; it is numerical evidence, not a universal or empirical result. The full continuation game and causal deterrence identification remain open. Changes in Version v12 (Articles 2 and 3, October 2026) This version presents the current bounded Article 2 and Article 3 models together in English and German. Article 1 remains in the historical version chain. The claims below concern specified model cases and diagnostic checks; they do not establish a general deterrence effect or empirical identification. Article 2: The Stage 3 shared cutoff is explicitly conditional on the stay-on-indifference selection, capacity-valid private reservations, and a common income/security pair at the reserved best destinations in the baseline. The finite admission analysis is kept separate from that cutoff claim. Article 3: The qualifying alliance-formation equilibrium and capacity condition are stated for the finite-citizen stepwise response. The common cutoff remains a continuum approximation under additional assumptions. Finite admission and counterexamples: Both articles distinguish complete private reservations from a common fixed-priority rule. Two two-citizen examples show why total capacity alone does not secure best-destination admission and why realized weighted labor loss can fall from 5 to 3 as exit freedom rises from 0 to 3/4. Verifier: The diagnostic verifier keeps the current B.2 calibration distinct from earlier numerical examples. Its 1,088 specified rational checks are diagnostic, not a universal proof or empirical validation. Scope: The full continuation game, causal deterrence identification, and empirical confirmation remain open. Changes in Version v10 (Article 2 formal-correction and source-verification update, July 2026) This version publishes the corrected Article 2 formal-theory branch after an adversarial proof audit (2026-07-12), together with the July 2026 source-verification update. Article 1 remains available as version v9 (record 20258846) under the same concept DOI. Critical (Theorem 2): The stage-2 peace condition dropped the aggressor's opportunity cost of forfeiting the alliance bonus. Corrected condition: peace is optimal iff Pi_A ≤ eta · m_A · Y_A (previously: iff Pi_A ≤ 0). The deterrence threshold is now defined by Pi_A(omega-bar) = eta · m_A · Y_A. The correction strengthens the mechanism: for alliance-member aggressors the forfeited alliance bonus acts as an additional deterrence channel and the threshold omega-bar decreases; the previous statement is recovered as the special case m_A = 0. Critical (existence): A new explicit assumption (A7') lambda-bar > kappa_max was added; it guarantees full mobilization of the mobile population below omega = d and is required for the Intermediate Value Theorem step. Without (A7'), a deterrence threshold in (0, d) may fail to exist for prizes close to G_crit; this is now stated as an honest scope condition. Major (uniqueness): The SPNE uniqueness claim was weakened to conditional uniqueness: peace is the unique subgame-perfect outcome among equilibria with alliance formation. The no-join coordination equilibrium in stage 1 is now explicitly acknowledged, with a payoff-dominance selection remark (Harsanyi and Selten 1988) and an explicit caveat that risk dominance may select differently. Major (Lemma A.1): The CES a-fortiori lemma was downgraded to a robustness indication: the normalization (common output and marginal product of labor at the baseline point) is now explicit, the interval-wide ordering step is documented as an open gap, a misattributed citation was removed, and the Leontief-limit claim was deleted. Notation: The CES substitution elasticity was renamed to varsigma to resolve a double use of sigma (previously also the security weight). Source verification: Existing Article 2 DOI entries were checked against Crossref; new UCDP/JPR 2026, UNHCR Global Trends 2025, free-movement backlash, EU migration-governance, and weaponized-migration sources were checked against publisher, DOI, institutional, and database records. Bibliography update: Added verified entries for Davies/Pettersson/Öberg 2026, UNHCR Global Trends 2025, Stoetzer/Kroh/Dasey 2024, Alrababah et al. 2024, EU/EPRS/MMC 2026, MPI 2026, Gerani 2026, Böhmelt 2025, and Harsanyi/Selten 1988. Manuscript update: Article 2 EN/GER now use the current UCDP baseline, UNHCR 2025 displacement frame, political absorption/backlash caveat for Stage 1, a sharper SC6 distinction between rights-based exit and coercive mobility, and an A6 governance-capacity caveat. Changes in Version v9 (May 2026) This version publishes the 2026-05-17 source-verification maintenance pass for the legacy Article 1 branch. Article 2 v8 remains available as a separate formal-theory branch under record 20102376 and the same concept DOI; future journal retargeting should be documented separately. Source verification: 28 bibliography entries were checked against Crossref/DOI metadata, DOI resolver pages, the Zenodo API, and the project bibliography. Bibliography corrections: Missing DOI URLs, issue data, official subtitles, full book-title data, and author initials were corrected or completed. Design maintenance: The Article 1 EN, GER, and combined PDFs were rebuilt with current Hyperref metadata, merge-safe destination prefixes, and no overfull/undefined/citation/rerun warnings. German text quality: The German PDF text layer was checked for real umlauts, including Freizügigkeitsallianz, Bevölkerungsabwanderung, Bürger, ökonomisch, and militärische Fähigkeiten. Previous live version v8 (May 2026) Version v8 was published on 2026-05-10 as record 20102376. It contains Article 2 EN/GER and remains available as the formalized Article 2 branch.