Ok /sci/, so yesterday me and my friends were talking some game theory and eventualy started theorizing about an interesting scenario but were unable to reach the solution.

Basically the problem goes:

There are two agents, A and B, and a pool of money X. That pool of money will be used by A to hire a third agent C to provide a service, however any money that is not spent on the provision of the service will go to agent B. However A and B have to agree on who they will hire or else the money will be lost, thus, A wants to hire the agent C who maximizes the amount of the money that will be spent providing the service while charging the lowest fees, B wants to hire the agent C who spends the least amount of money possible to maximize the money he will keep, and C wants to maximize his fees will minimizing both the amount spent on the provision of the service for A and the amount B will keep.
As I said, if no agreement is reached all of the money will be lost and no one is getting anything.

To clarify, there is a single agent A and a single agent B, but multiple competing agents C

Is there a mechanism to ensure an efficient result?