Employment relations and the boundaries of the firm

What kind of economic activity is conducted through markets and what kind is conducted through firms? We approach this Coaseian question by way of an employment relation between players. Every players has an endowment of 100% of his time. He may choose to give away part of his time to other players. We will work the employment relation into characteristic functions (cooperative game theory). Here, one can proceed via Owen’s (1970) multilinear extension. However, we prefer the minimum extension. For two agents, we find (as Coase suggested) that firms spring up in response to market inefficiencies and that markets will prevail if organizational inefficiencies are profound. More specificly, cross employment (one agent employing the other and vice versa) may well happen. Also, the more productive agent is more likely to employ the less productive one than the other way around.