Stochastic Stability of Agglomeration Patterns in an Urban Retail Model

Both the paper and the candidate solution analyze the K=2 symmetric Harris–Wilson setting by comparing the potential at the symmetric split x̄=(1/2,1/2) with the two corner agglomerations, derive the same threshold equation (1+φ)^2=4^α φ, and conclude that dispersion is globally potential-maximizing (and thus stochastically stable) for φ≤φ** while agglomeration is so for φ≥φ**. The model adds a fuller derivative-based uniqueness check of interior stationary points and an explicit comparative statics proof that φ** decreases in α. The paper states the result as Proposition 3 and invokes stochastic stability via potential maximization in potential games. Aside from a likely typesetting/OCR glitch in the discriminant inside the square root in the paper’s closed form of φ** (the correct discriminant is 4^α(4^α−4), consistent with α→1 limits), the arguments align.