Decentralised bilateral trading, competition for bargaining partners and the “law of one price”

This paper analyses a model of price formation in a market with a finite number of non-identical agents engaging in decentralised bilateral interactions. We focus mainly on equal numbers of buyers and sellers, though we discuss other cases. All characteristics of agents are assumed to be common knowledge. Buyers simultaneously make targeted offers, which sellers can accept or reject. Acceptance leads to a pair exiting and rejection leads to the next period. Offers can be public, private or “ex ante public”. As the discount factor goes to 1, the price in all transactions converges to the same value.