For those cognizant of the commercial financing atmosphere, SBA 7A lenders are a term that resonates with a perception of an economic panacea. Despite this, there's a ubiquitous lack of comprehensive understanding about these entities. Today, we intend to dissect and elucidate the concept of SBA 7A lenders, their modus operandi, and their intrinsic role in the economic sphere.

SBA 7A lenders are accredited entities that offer loans under the Small Business Administration’s (SBA) 7A loan program. The SBA is a U.S. government agency that provides support to small businesses, and the 7A loan is one of their primary offerings. The SBA 7A loan program is designed to aid small businesses that might otherwise struggle to secure financing. However, the SBA does not directly provide loans. Instead, it guarantees a portion of the loan, reducing the risk for lenders - the essence of the 7A program.

Applying game theory to this milieu, the SBA effectively modifies the payoff matrix for the lenders. This is done by shifting some of the risks associated with the loan to the SBA, thus making the ‘loan default’ outcome less detrimental to the lender. Consequently, lenders are more inclined to lend to small businesses.

Diving deeper into the labyrinth of the SBA's 7A loan program, it is important to understand its symbiotic relationship with lenders. It operates by forming an alliance with banks, credit unions, and other lending institutions that are willing to underwrite loans to small businesses. These entities, referred to as SBA 7A lenders, provide the actual loans which are subsequently guaranteed by the SBA.

The intricate, yet sophisticated, mechanism of how SBA 7A lenders operate, is guided by stringent regulations detailed in the SBA Standard Operating Procedure (SOP). The SOP delineates the intricate aspects of credit underwriting, loan closing, and servicing policies. It also encompasses the critical procedures for liquidating collateral and pursuing collection on the guaranteed portion of the loan if a borrower defaults. This is a key facet of the SBA 7A lender's role, as they’re tasked with the initial loan processing, servicing, and, if necessary, liquidation activities.

The SBA 7A lenders are generally found in every state across the United States, as well as in U.S territories. They primarily exist to stimulate economic activity by providing an influx of capital to businesses that may otherwise not qualify for traditional loans. These lenders, therefore, play a pivotal role in fostering business development and consequently job creation.

In the context of chronology, the SBA 7A lender's involvement begins once a small business owner decides to apply for an SBA loan. The lender will then evaluate the application based on both SBA eligibility requirements and its lending policies. If approved, the SBA guarantees a part of the loan, and the lender proceeds to finalize the loan terms and disburse the funds to the borrower.

The role of SBA 7A lenders is pivotal to the functioning of the U.S economy. Considering the Keynesian theory, which emphasizes the effect of aggregate demand in the short run, these loans contribute to the stimulation of economic activity. By providing small businesses the opportunity to access capital, they indirectly play a role in job creation, innovation, and the overall growth of the U.S economy.

To encapsulate, SBA 7A lenders are a sophisticated cog in the machine of the U.S. economy. They bridge the gap between high-risk small businesses and the much-needed capital access. Their existence and functionality are cemented by the complex intertwining of economic theory, governmental policies, and the inherent entrepreneurial spirit that drives small businesses.