Ultimatum Bargaining with Rational Inattention

A seller bargains with a rationally inattentive buyer (Sims 2003) over a good of random quality. After observing quality, the seller makes a take-it-or-leave-it offer. The buyer pays attention to the seller's product and offer at a cost proportional to expected entropy reduction. Because attention is free off-path, multiple equilibria emerge, many of which are efficient. A trembling-hand-like refinement (Selten 1975) rules out efficiency, delivering complete disagreement when attention is expensive and a unique equilibrium with trade when attention is cheap. In this equilibrium, the buyer overpays for low-quality goods, underpays for high-quality goods, and earns a strictly positive payoff.