In the dynamic landscape of entrepreneurship, the banking sector plays an indispensable role, especially for startups. Banks provide the financial backbone for new businesses, enabling them to navigate the choppy seas of initial growth, investment, and expansion. It is, therefore, essential for startups to grasp the nuances of banking and make an informed decision when choosing a banking partner.

Historically, traditional banks have been the go-to financial institutions for startups. However, in recent years, upstarts in the banking sector - neobanks - are gaining traction amongst startups. These fully digital banks provide user-friendly interfaces, ease of operation, and considerable cost-effectiveness - features that are making them increasingly popular amongst the tech-savvy, efficiency-focused startup community.

In the quintessential chicken-and-egg conundrum, startups need capital to grow, but they need to show growth to attract capital. Traditional banks, with their risk-averse approach and stringent criteria for lending, often pose a significant challenge for startups in need of funds. Neobanks, on the other hand, are emerging as more startup-friendly, offering products and services tailored to their unique needs.

On the downside, the relative novelty of neobanks brings its own set of uncertainties. Regulatory frameworks, long-term stability, and lack of physical presence are areas of concern for businesses considering this route. Moreover, in spite of their innovative approach, neobanks are yet to prove their mettle in offering comprehensive financial solutions that encompass more complex transactions and services that established businesses require.

The choice between traditional banks and neobanks also has geographical implications. In countries with advanced banking systems, traditional banks are evolving to match the digital offerings of neobanks, providing a blend of stability and innovation. In contrast, in emerging markets where banking infrastructure is less developed, neobanks offer a leapfrog opportunity, bypassing traditional banking systems altogether.

In light of these factors, the decision on a banking partner for startups is far from straightforward. Both traditional banks and neobanks have their unique strengths and weaknesses. The startup's industry, stage of growth, geographical location, and specific requirements play a major role in this decision.

Startups in the tech sector or those with a digital-first approach might lean towards neobanks, valuing their alignment with a technology-driven philosophy. On the other hand, startups in traditional industries or those dealing with substantial amounts of cash or complex transactions might prefer the stability and comprehensiveness of traditional banks.

An astute understanding of game theory can provide insights in this regard. The Nash equilibrium suggests that the optimal choice for a startup would be the one where, given the choice of the other player (in this case, the bank), they cannot benefit by choosing differently. This implies taking into account the bank's preferences and strategies while making their decision. A bank's willingness to invest in a startup, its risk appetite, product offerings, geographical presence, and financial stability would all factor into this analysis.

In conclusion, the banking industry's evolution, driven by digital disruption, presents a plethora of choices for startups. The decision on a banking partner will be a key determinant of a startup's financial agility, resilience, and, ultimately, its success. Startups, therefore, need to approach this choice not as a mere operational necessity but as a strategic decision with far-reaching implications. It is, indeed, a game of strategic interaction - a delicate dance between the nascent business and its financial partner - that would sculpt its path to growth and prosperity.