Equilibrium in bargaining model with non-uniform distribution for reservation prices

We consider a game-theoretic bargaining model of bilateral monopoly under uncertainty. Each player has a private information about its own reservation price. The reservation prices are random variables with linear probabilistic density functions. Seller and buyer submit sealed offers and if the buyer's offer is higher than seller's offer a bargain is enacted and the good is sold. The Bayes equilibrium is derived in analytical form. The comparison of solutions in the typical states of the market is made.