Global Games

Games of incomplete information where players observe noisy signals of an underlying state, often producing unique equilibrium.

Ask the Game theory assistant 1 min read · Updated September 9, 2026

Definition

Players receive private signals $x_i = \theta + \varepsilon_i$ where $\theta\in\mathbb{R}$ is the underlying state and $\varepsilon_i$ are i.i.d. noise with small support. Equilibrium thresholds $x^*$ solve indifference given posterior beliefs.

Carlsson-van Damme (1993): in $2\times 2$ games with strategic complementarities, the global game selects a unique equilibrium as noise vanishes.

Intuition

Introducing tiny amounts of private information can break the multiplicity of coordination games.

The global-game selection (the "risk-dominant" action) emerges naturally from higher-order uncertainty.

Worked example

In a currency-attack model, traders observe noisy signals about fundamentals; the unique threshold equilibrium explains contagion and self-fulfilling crises (Morris-Shin 1998).

Bank runs, debt crises, and R&D investment have been studied as global games.

The math

As signal noise $\sigma\to 0$ , the equilibrium converges to a unique threshold generally selecting the risk-dominant action.

Laplacian belief: at the critical signal, players are uniform about the state — the "global-game" prior.

Where it is used

Macro-finance (currency crises, bank runs), political economy (revolutions), and industrial organization (entry).

Connects to the uniqueness of equilibrium in supermodular games.

More in Game theory

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