<p>I'm reading this paper on credit lending cycles and trying to understand how it works for the case of one bank. This is the set-up of the model: 
There are two players, a bank and the market. There are also two states of the world: adverse and normal.</p>

<p>The banks lends across time t=0,1 and 2. The bank can be of two types: High type, which generates profitable loans with a high probability <span class="math-container">$\theta$</span> in normal times and generates profitable loans with probability 0 in adverse times. Low type, which generates profitable loans with a probability lesser than <span class="math-container">$\theta$</span> in normal times and probability 0 in adverse times. </p>

<p>The bank lends loans in period 0 and becomes aware of the state of the world in period 1 when the loans turn out good or bad. If the loan is bad the bank can either terminate the loan with a cost of -1 dollars or can decide on a credit policy ( for eg extending the term of the bad loan). The credit policy varies between [0,a] and comes with a cost c in period 2 for the bank. After the credit policy is implemented the market observes the bank's earnings and updates its reputation, which is given by p+ = Prob( H/positive earnings in period1) and p- = Prob (H/negative earnings in period 1). Having implemented the credit policy, the bank's earnings can remain unaffected with probability a, and can become negative with probability 1-a. </p>

<p>Now in such a scenario, given the utility function of the manager as shown in equation (1) of the image attached, how do I formulate the incentive compatibility problem of the manager. I should reach equation(3) from the ICC, but I'm not able to at the moment on my own. </p>

<p>image of equ (1) and (3) : <a href="https://i.sstatic.net/6hlyi.jpg" rel="nofollow noreferrer">https://i.sstatic.net/6hlyi.jpg</a></p>

CC BY-SA 4.0
2020-06-13T21:44:53.410Z
Hi, Welcome to Economics SE! we have a policy regarding homework questions where we require that you show some work before an answer is provided. More on this topic here: https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions
Kitsune Cavalry
CC BY-SA 4.0
2020-06-14T22:19:22.623Z
Hi, thanks kitsune. This isnt a homework question, I'm doing some self-study as a part of research for my dissertation. I have arrived at an answer finally. However, I still would like to have an in-depth understanding of how BNE works when both states and types are unknown to the public. ( So far I had only studied cases where either the state or the type of the player is unknown ).
Meera Unni
<banking><bayesian-game><principal-agent>
Perfect Bayesian Equilibrium for banks
Meera Unni
# Perfect Bayesian Equilibrium for banks

(Asked by: username_0 on 2020-06-11)

I'm reading this paper on credit lending cycles and trying to understand how it works for the case of one bank. This is the set-up of the model:
There are two players, a bank and the market. There are also two states of the world: adverse and normal.

The banks lends across time t=0,1 and 2. The bank can be of two types: High type, which generates profitable loans with a high probability $\theta$ in normal times and generates profitable loans with probability 0 in adverse times. Low type, which generates profitable loans with a probability lesser than $\theta$ in normal times and probability 0 in adverse times.

The bank lends loans in period 0 and becomes aware of the state of the world in period 1 when the loans turn out good or bad. If the loan is bad the bank can either terminate the loan with a cost of -1 dollars or can decide on a credit policy ( for eg extending the term of the bad loan). The credit policy varies between [0,a] and comes with a cost c in period 2 for the bank. After the credit policy is implemented the market observes the bank's earnings and updates its reputation, which is given by p+ = Prob( H/positive earnings in period1) and p- = Prob (H/negative earnings in period 1). Having implemented the credit policy, the bank's earnings can remain unaffected with probability a, and can become negative with probability 1-a.

Now in such a scenario, given the utility function of the manager as shown in equation (1) of the image attached, how do I formulate the incentive compatibility problem of the manager. I should reach equation(3) from the ICC, but I'm not able to at the moment on my own.

image of equ (1) and (3) : <https://i.sstatic.net/6hlyi.jpg>

**Tags:** banking, bayesian-game, principal-agent
> **Comments:**
> **username_1**: Hi, Welcome to Economics SE! we have a policy regarding homework questions where we require that you show some work before an answer is provided. More on this topic here: https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions  
> **username_0**: Hi, thanks kitsune. This isnt a homework question, I'm doing some self-study as a part of research for my dissertation. I have arrived at an answer finally. However, I still would like to have an in-depth understanding of how BNE works when both states and types are unknown to the public. ( So far I had only studied cases where either the state or the type of the player is unknown ).  

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## 0 answers

