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A currency peg holds if few speculators attack and collapses if enough do. With everyone sure of the fundamentals, either outcome can be self-fulfilling. In the benchmark model, give each trader a slightly noisy read of the economy and the ambiguity gives way to one threshold.

Global games

Coordination games can have many equilibria, and stories about crises often lean on that: the attack succeeds because everyone expects it to. The Morris-Shin currency-attack benchmark shows how private noise can select one threshold equilibrium, pinned by fundamentals and the model’s payoff and information structure.

From earlier lessons

Two quick ones before we start.

In a Bayesian game each player conditions its action on...

A coordination game with strategic complements typically has...

Predict, then play

The peg falls if the fraction attacking exceeds the economy’s fundamental strength $\theta$ ; attacking costs $c$ . Each speculator sees a slightly noisy signal of $\theta$ and attacks if it looks weak enough. Set the cost and see which economies collapse.

Why did that happen?

Take a guess, then reveal the reason

With everyone perfectly informed of the same fundamental, there is a middle range where both “all attack” and “none attack” are equilibria, and the outcome seems arbitrary. Private noise breaks the symmetry: no one is quite sure what others saw, so each must reason about the whole distribution of signals. That reasoning ties every player to a single switching point. A cheaper attack lowers the bar for finding it worthwhile, so the threshold at which the regime survives moves up, and more economies fall.

The math

The regime collapses if the mass of attackers reaches the fundamental $\theta$ ; attacking costs $c$ and pays off only if the regime falls. Under complete information, for intermediate $\theta$ there are two equilibria (everyone attacks, or no one does). The benchmark assumes a diffuse uniform prior over $\theta$ and independent additive private noise that becomes arbitrarily small: each speculator observes $x_i=\theta+\varepsilon_i$ . These assumptions generate the Laplacian belief used below.

Definition, global game

A global game is a coordination game where each player observes a payoff-relevant state with idiosyncratic error. In the canonical currency-attack model, under its monotonicity and signal assumptions, small private noise yields a unique equilibrium in threshold strategies: attack iff your signal is below a cutoff. The noise prevents players’ information from being common knowledge, which pins down higher-order beliefs. Other global games need not have this exact threshold or uniqueness result.

At the switching signal, the marginal speculator’s belief about the fraction of others attacking is uniform on $[0,1]$ (the Laplacian property), so it puts probability $1 - \theta^*$ on the regime falling. Setting that equal to the cost $c$ gives the fundamental threshold

\theta^* = 1 - c.

The regime falls exactly when $\theta < \theta^*$ . With $c = \tfrac12$ , $\theta^* = \tfrac12$ . Lower the cost and $\theta^*$ rises, so crises become more common: strong fundamentals no longer guarantee safety once they dip below $1-c$ .

Work it out

Find the crisis threshold

Consider the marginal speculator, the one whose signal sits exactly at the switching cutoff. A key property of the global-games limit is that this agent’s posterior over the fraction $\ell$ of others who attack is uniform on $[0,1]$ . Its best estimate of the fundamental is its own signal, $\theta^*$ , and the regime falls when $\ell \ge \theta^*$ , an event of probability $1 - \theta^*$ .

Attacking pays $1$ if the regime falls and costs $c$ either way, so the marginal agent is indifferent when $1 - \theta^* = c$ , giving the fundamental threshold $\theta^* = 1 - c$ . At $c = \tfrac12$ this is $\tfrac12$ . Halve the cost to $c = \tfrac14$ and the threshold becomes $\tfrac34$ . Calling that “three-quarters of economies” additionally requires fundamentals to be uniformly distributed on $[0,1]$ ; the strategic result itself is the cutoff, not a population frequency.

Key idea

In this benchmark currency-attack model, small private noise selects one threshold equilibrium from a coordination game’s many complete-information equilibria. The regime falls when fundamentals drop below 1 minus the cost of attacking.

Check yourself

Check yourselfapply

Attacking becomes cheaper (c falls from 1/2 to 1/4). What happens to the crisis threshold?

Check yourselfanalyse

In the benchmark currency-attack model, what does adding small private noise do to the set of equilibria?

Check yourselfbrings back: supermodular games

Global games build on coordination with strategic complements. How does the crisis story relate to that structure?

Sources

Carlsson, H., and van Damme, E. (1993). Global games and equilibrium selection. Econometrica, 61(5), 989-1018.
Morris, S., and Shin, H. S. (1998). Unique equilibrium in a model of self-fulfilling currency attacks. American Economic Review, 88(3), 587-597.