More Rambling Thoughts on Strategic Network Formation...

A continuation/elaboration on yesterday's post...basically I am trying to developed a decision calculus that will serve as a micro-foundation for my more traditional network formation model...

Question: Why do banks form credit networks?
Banks basically want to do two things:

1. Make lots of money, and
2. Generate liquidity

With this in mind, I am thinking of inter-bank network formation as a strategy banks use to achieve these ends.  Banks make money by lending money (ie., by forming links with other banks, firms, etc): banks essentially trade money now for more money later.  This is my working justification for why the number of direct links should be included in the bank's pay-off function.  Now in order to achieve its other objective, liquidity generation, a bank may want to establish lines of credit with other banks.  I am tempted to say that, all things equal, small banks should exhibit some type of preference to link with banks that have lots of links already.  This could be for one of two reasons, either because number of links is viewed as a proxy for something useful, or because lots of links implies greater access to the rest of the network which would affect interest rate charged on the line of credit.  This is my working justification for including indirect links (at least those of its immediate neighbors) in the bank's pay-off function.

In an effort to try and make things more concrete, lets follow (Gai and Kapadia, 2010) and suppose that we have N banks B1, ...Bn and that each Bi has two types of assets and two sources of liabilities...

• Assets:
• Inter-bank assets Ai,IB: these are liquid assets that flow into Bi in the form of loan payments made by other banks in the network that owe Bi money.  The number of inter-bank assets Ai,IB represents the in-degree score for Bi. 
• Durable assets Ai,M: these are illiquid assets that the Bi owns. (Gai and Kapadia, 2010) think of them as morgtages.  Durable assets have a resale price of q.
• Liabilities:
• Inter-bank liabilities Li,IB: these are the liabilities that flow out of Bi in the form of loan payments made to the banks in the network to whom Bi owes money.  The number of these inter-bank liabilities Li,IB represents the out-degree of Bi.
• Customer deposits Di: These are exactly what they sound like.  (Gai and Kapadia, 2010) treat these as exogenously given. 
• Regulatory Captial Requirement K: this is the minimum amount of cash-on-hand that banks must maintain on deposit with regulatory authority.  It is the same for all banks 

Now the question is where to go from here given that I am trying to develop some type of micro-founded endogenous network formation process.  There are basically two markets going on here (possibly three if you want to endogenize the customer deposits): a credit market for for the liquid assets and a spot market for the illiquid asset (and possibly a market for customer deposits).  Banks want to loan as much money as they can (i.e., form links with other banks) in order to generate value (value for whom though? customers...) subject to the constraint that they remain solvent and that they must maintain capital regulatory requirement.

I am not sure if this is an improvement over yesterday's effort, or whether I am simply wandering further down the rabbit hole...