Two agents work in a team. They simultaneously choose effort e; at cost c(e;), yielding output y(e1 + e2). Utility is linear, so an agent's utility equals the share of the output they receive minus the cost of effort. Assume c is differentiable, strictly convex with c (0) = 0 and lime- c(e) = co. Assume y is differentiable and concave. 2.1. Write down the FOC for the first-best effort, et. Now, suppose we identify which agent produces the most output. Given (e1, e2), agent 1 wins with probability p(e1, e2) and agent 2 wins with 1 - p(e1, e2). Suppose we give the winner share s of the output, while the loser gains share 1 - s. Assume p is increasing in e1, differentiable and p(e1, e2) = 1 - p(e2, e1). 2.2. Write down the FOC for the agent's problem. Derive an expression for s in order to implement the first-best. 2.3. Suppose y = (e1 + e2), c(e) = ez/2 and p = , where r 2 1 reflects the responsive- ness of the signal to effort. Which shares (s, 1 - s) implement the first-best