We show by an example that the sunspot equilibria of a competitive economy are not equivalent to the correlated equilibria if sunspots generate transfers between (extrinsic) states of nature (through a contingent commodities market). Nevertheless, we prove that the sunspot equilibrium allocations of a standard overlapping generations economy coincide with the (strategic form) correlated equilibrium allocations of a natural market game mimicking the economy.
Forges, F., & Peck, J. (1995). Correlated Equilibrium and Sunspot Equilibrium. Economic Theory, 5(1), 33-50. https://doi.org/10.1007/BF01213643 (Original work published 1995)