Hey friends 👋🏼 Startups are games. This newsletter is about empowering brains (with startup game theory) & hearts (with intros + celebrations). Today, we do the former: this multi-part article will be about running our first startup simulations. 😎

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Founders play multiple games in parallel, e.g., hiring, distribution, fundraising, PR, among others.

While not everybody plays all of them, there is one that everybody plays: the fundamental game of startups.

Last week, we introduced an important hypothesis that will make it possible to run simulations.

This week, we’re going to set up a simulation to address one of the biggest questions for early-stage ventures:

“How to optimally balance distribution versus product to win?”

This is part 1 of answering this question.

Teaser: I haven’t met a single founder who gets this right.

We’ll study the following simple situation:

You’re an early-stage startup in a mature market, competing only against a big incumbent and another startup.

Recalling the definition & framework of the fundamental game, we now have to make the actors, state space, game dynamics, starting conditions, and action space explicit.

We’re refining the 3 players we mentioned above & their strategic profiles using the following names:

Each company will only care about 2 pieces of information:

For the sake of clarity, as time can be converted into money and reciprocally, we will only speak about time in this example.

Furthermore, we assume a market of 100’000 prospects fixed.

Note: we’re furthermore assuming that each prospect uses one and only one solution (so it’s a zero-sum setup assuming the “no solution” is a player).

The way customers decide on a product is based on the notion of comparative function, i.e., a function that compares 2 solutions A & B. The customer then picks the one that has the higher value.

To make things smooth & simple while still being very realistic, we’re assuming to be in a situation where the homogeneous efficient customers hypothesis (HECH) condition holds. In a nutshell, it says that the switching costs are equal between any two solutions. This implies that comparative functions L_c are the same (for more details, see customer decision-making frameworks).

From the customer perspective, then, because of HECH, customers only care about the best product & its price, i.e, they care only about product quality and price.

Finally, regarding the perceived product value V_c, we want it to scale rapidly at the start, but then slow down due to diminishing returns (e.g., bureaucracy, 80-20, etc). We also want to reflect that incumbent products often feel outdated (the original skeleton was built years ago, and it shows) compared to startup products (which are more modern). For that, we add a 25% handicap to incumbent products.

Regarding allowed actions, we restrict ourselves to the case where startups can only do the following two things:

There are countless ways to improve a product or acquire users, each with distinct maths & structure. For now, we focus on the most common, the simplest, yet also one of the most important classes: linear actions.

We define linear actions as those that are such that 1 unit of time always returns a constant output, independently of the date. In our example, this means a constant number of phone calls with prospects or a constant delta in product improvement, whether you spent that unit of time today or in 3 months.

We’re going to call such actions linear (as their returns scale linearly with time).

We now distinguish between 2 families of strategies a startup can consider

For the sake of simplification, this toy example will only feature “pure” strategies, i.e., all players will repeatedly invest a fixed percentage of their monthly resource into both acquisition and product, respectively, every month.

With the setup defined, we assign pure linear strategies to each actor as follows.

The slow incumbent (25% product, 75% acquisition):

The balanced PMF seeker (50% product, 50% acquisition):

The all-in product startup (70% product, 30% acquisition):

I’m running out of characters! (Already at 1300 chars 🥲)

(I want these to be readable in 5’ to be more pleasant for you guys 🫶🏼)

In Part 2, we’re going to simulate the slow incumbent, balanced PMF seeker, and all‑in product startup under HECH, tracking customer flows and bank dynamics.

What is going to happen, you think? Have linear strategies been working for you in your startup? If yes, how? If not, why? What has your intuition been telling you? 🤔

The game gets easier the more players join.

👉 Share this with one sharp friend — the bigger the network, the faster we all win. ⚡

(P.S. If you’ve got feedback or want me to analyse a specific situation, just hit reply — I read every message 😎)