Assignment Task
Question
In this question, we’ll consider a version of the authority model where the principal works with two
- agents, each on a separate project.
- There is one principal who is in charge of two projects, ???? = 1, 2. The principal hires one agent for
- each project; we identify the agent associated with project ???? as Agent ????.
- Each Agent ???? separately chooses effort ????????
- to produce an idea for his own project ????. Each Agent ????’s
- effort cost is 1
- . At the same time, the Principal ???? chooses effort levels ????1
- and ????2
- to devote to each
- project. Her total effort cost is 1
- .
- The probability that Agent ???? produces an idea for Project ???? equals his effort ????????
- . The probability that
- ???? produces an idea for Project ???? equals ????????
- .
- For Project 1: if the Principal’s idea is implemented, then the Principal and Agent 1 both receive 1.
- If Agent 1’s idea is implemented, then the principal receives 0 < ????1 < 1>
- For Project 2: as long as either the Principal’s or Agent 2’s idea is implemented, then both players
- receive project values of 1 each.
- Notice that this means neither agent cares whose idea (his own versus the principal’s) is implemented for their project. The principal does not care whose idea is implemented for project 2, but
- prefers to implement his idea over Agent 1’s idea for project 1.
- ????’s total payoff is the sum of his project values from both projects, minus her effort cost 1
- Agent ????’s payoff is his project value from his own project, minus his effort cost ????
- The timing of the game is:
- 1. Each ????????
- chooses effort level ????????
- . At the same time, ???? chooses ????1
- 2. Each player’s attempt (to generate an idea) either succeeds or fails.
- 3. For each project, ???? chooses which idea (if both are successful) to implement
- 4. Payoffs are realized.
- We’ll go through the problem set-by-step.
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