<p>I have a Principal agent problem where principal knows about the information about the agent which is critical to both the parties. Principal is a business tycoon who has an inside information about the performance of equity and debt instruments. Agents are the investors who are going to put in more money in share if the environment is less risky and more into debt when output . <span class="math-container">$ 0&lt;x_1&lt;1 $</span> informs about the volatility and help in deciding how much share to invest and <span class="math-container">$0&lt;x_2&lt;1 $</span> tells about output and help in deciding about investment in debt instrument.</p>
<p>Principal announces <span class="math-container">$$ 0&lt;x_1&lt;1 $$</span> and <span class="math-container">$$0&lt;x_2&lt;1 $$</span> and agent put in value based on expectation developed on principal's claim.</p>
<p>I have a non-binding incentive compatibility constraint which argues that any deviation by principal to some other claim wouldn't make him better off -</p>
<p><span class="math-container">$$ x_1 E(x_1) + x_2 E(x_2) &gt; x'_1 E(x'_1) + x'_2 E(x'_2) $$</span></p>
<p>How to check if incentive constraint will hold? Do I take derivative?</p>
<p>Any guidance will be helpful.</p>

CC BY-SA 4.0
2022-11-15T18:48:08.770Z
Your notations are a bit confusing. In general the variable denoting the type should be different from the variable denoting the announcement. You seem to denote both with the same variable. Also, a bit more context on the problem would help.
Herr K.
CC BY-SA 4.0
2022-11-16T05:40:24.290Z
Thanks @HerrK. I have edited and try to explain my problem. Hope it helps. Please just let me know if I have to take first derivative. How can I show that telling truthfully about the environment is the best principal can do?
Elina Gilbert
CC BY-SA 4.0
2022-11-16T21:49:56.953Z
It's still not fully clear to me. Can you explain the payoff function in the last inequality? Whose payoff is it? What does $x_1 E(x_1)$ mean? Shouldn't the expectation be conditioned on the announcement somehow?
Herr K.
<contract-theory><principal-agent><incentives>
Incentive compatibility constraint with continuous types
Elina Gilbert
# Incentive compatibility constraint with continuous types

(Asked by: username_0 on 2022-11-15)

I have a Principal agent problem where principal knows about the information about the agent which is critical to both the parties. Principal is a business tycoon who has an inside information about the performance of equity and debt instruments. Agents are the investors who are going to put in more money in share if the environment is less risky and more into debt when output . $ 0 informs about the volatility and help in deciding how much share to invest and $0 tells about output and help in deciding about investment in debt instrument.

Principal announces $$ 0 and $$0 and agent put in value based on expectation developed on principal's claim.

I have a non-binding incentive compatibility constraint which argues that any deviation by principal to some other claim wouldn't make him better off -

$$ x\_1 E(x\_1) + x\_2 E(x\_2) > x'\_1 E(x'\_1) + x'\_2 E(x'\_2) $$

How to check if incentive constraint will hold? Do I take derivative?

Any guidance will be helpful.

**Tags:** contract-theory, principal-agent, incentives

> **Comments:**
> **username_1**: Your notations are a bit confusing. In general the variable denoting the type should be different from the variable denoting the announcement. You seem to denote both with the same variable. Also, a bit more context on the problem would help.  
> **username_0**: Thanks @HerrK. I have edited and try to explain my problem. Hope it helps. Please just let me know if I have to take first derivative. How can I show that telling truthfully about the environment is the best principal can do?  
> **username_1**: It's still not fully clear to me. Can you explain the payoff function in the last inequality? Whose payoff is it? What does $x_1 E(x_1)$ mean? Shouldn't the expectation be conditioned on the announcement somehow?  

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## 0 answers

