To start off, let's define what 'network effect' is. In simplest terms, it refers to a phenomenon where a product or service acquires additional value as more people use it. Simply put, the bigger the crowd that's using it, the more advantageous it becomes for individual users.

Consider the behemoth of social networks, Facebook. When a few people in your circle were on the platform, it seemed intriguing but not essential. However, as more friends, family, and colleagues joined, the platform's value enlarged. Now you could connect, share, and collaborate with numerous people, making the platform indispensable. This is the network effect in action!

Next, we delve into the formula that underpins the network effect. Its simple math, yet extraordinarily powerful. The value of the network is proportionate to the square of its users. Essentially, doubling the number of users quadruples the value of the network. This exponential growth implies that the network effect is often the engine for scalability and viral expansion in marketplaces.

But remember, the network effect isn't limited to social media or telecom companies alone. Observe e-commerce giants like Amazon or Alibaba. The more sellers these platforms attract, the more varied products they can offer, which in turn ropes in more customers. This continuous cycle magnifies their marketplace's value, all thanks to the network effect.

However, it's important to establish desired standards and rules while cultivating the network effect. The reason is simple. The product or service's value can erode if the user base contains too many disruptive elements. Therefore, quality assurance and user regulations play a crucial role in maximizing the network effect.

In conclusion, understanding the network effect and implementing strategies around it can offer a competitive edge. When applied properly, this phenomenon has the power to amplify a marketplace's success, creating a winning environment for both providers and consumers in a business ecosystem.

To put this in layman terms, it’s like throwing a party. If just a handful of people show up, the party isn’t that great and everyone leaves early. But as more people arrive, the event becomes more exciting and the party really takes off. That’s the network effect in a nutshell!