Contract Net Task Allocation

The task allocation problem consists of:
- T: tasks
- A: agents
- c_i : 2 ^T -> Reals. cost to agent i to do a subset of tasks.
- (t₁, t₂,..., t_|A|): an initial allocation of tasks to agents.
The standard contract net protocol does not specify how much an agent should bid. An simple option is to have the agents bid their marginal cost since Adam Smith tells us that they will eventually converge to it.
MC_add(T^contract | T_q) = c_q(T^contract + T_q) - c_q(T_q) : The cost for agent q to add some tasks in contract.
MC_remove(T^contract | T_r) = c_r(T^r) - c_q(T_r - T^contract) : The cost for agent r to remove some tasks as given in contract.