Defense Feedback and Global-Game Selection

Georgy Lukyanov and Yaroslav Yosifov

No 26-1782, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: Global games select a unique cutoff when a player’s incentive moves monotonically with private information. We show that this logic can fail when a privately informed participant can take a costly, simultaneous, and unobserved action that defends the status quo. In a currency-attack model, the defender acts only at intermediate signals. Along the traders’ cutoff equation, this interval response creates an endogenous defense-loss term that vanishes at the endpoints of an activation component but can dominate the decreasing benchmark payoff margin in between. We establish a primitive region in which defense is inactive and uniqueness survives, and a finite-CDF overshoot condition under which two active defense cutoff roots coexist with the inactive benchmark root. Because marginal indifference need not imply global incentives, we also give sufficient conditions for a genuine monotone cutoff best response. Finally, outward-rounded interval arithmetic proves that a proper-prior parameter vector has exactly three symmetric monotone-cutoff equilibria and that this topology persists locally. The result isolates a payoff-based boundary of global-game selection: hidden intervention can restore multiplicity without public signalling or a perturbation of the information hierarchy.

Keywords: global games; regime change; active defense; private information; equilibrium multiplicity; computer-assisted proof (search for similar items in EconPapers)
JEL-codes: C72 D82 F31 (search for similar items in EconPapers)
Date: 2026-10-14
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