Situations in which agents exert effort or make investments to improve their bargaining position are ubiquitous: potential buyers search the internet for information on how to bargain with car salesmen, companies and individuals hire lawyers or other experts when selling or buying valuable assets, parties in a troubled marriage find divorce lawyers to negotiate on their behalf, just to name a few.
We study a model of surplus division with costly effort or investments in the bilateral trade environment.
The effort determines the probability with which either agents gets to make an offer and thereby the surplus they are able to secure, however, it may also signal their private information, something that the rival can use to his advantage.
We characterize the equilibria of the game and show that the seller's payoff can be non-monotonic in the share of high value buyers. The seller faced with an entry decision might, therefore, find it propitious to enter a market mostly populated with low value costumers.
We also develop a model in which the probability of the agents getting an offer is exogenously given|rather then determined by their decisions but can vary with the type.
The latter model is easier to use, yet captures some important features of the more involved model.