  Tackling complex team problems requires understanding each team member's
skills in order to devise a task assignment maximizing the team performance.
This paper proposes a novel quantitative model describing the decentralized
process by which individuals in a team learn who has what abilities, while
concurrently assigning tasks to each of the team members. In the model, the
appraisal network represents team member's evaluations of one another and each
team member chooses their own workload. The appraisals and workload assignment
change simultaneously: each member builds their own local appraisal of
neighboring members based on the performance exhibited on previous tasks, while
the workload is redistributed based on the current appraisal estimates. We show
that the appraisal states can be reduced to a lower dimension due to the
presence of conserved quantities associated to the cycles of the appraisal
network. Building on this, we provide rigorous results characterizing the
ability, or inability, of the team to learn each other's skill and thus
converge to an allocation maximizing the team performance. We complement our
analysis with extensive numerical experiments.
