Coordination on a Grid: Posterior Ties, Entropy, and Multiplicity
This paper studies categorical information in coordination games and shows that reporting resolution is a distinct informational primitive. Coarse reporting creates exact posterior ties and makes multiplicity more pervasive, while finer reporting lowers ties and shrinks the equilibrium interval. On a fixed coarse grid, higher measurement accuracy can instead concentrate mass on a few reports and widen multiplicity. Tie incidence then yields a natural entropy measure of uncertainty over posterior-relevant reports, under which the apparent Morris-Shin jump near complete information disappears.