Game Theory in Growth Strategy: Pricing, Positioning and Strategic Interactions

Introduction: Why I Think About Growth as a Game

When building growth strategy in a competitive market, I do not just think about what works in isolation. I think about how others will respond. Competitors, platforms and even customers behave strategically. That is why I often use concepts from game theory to model pricing, campaign rollouts, offer timing and more.

Game theory gives me a structured way to think through interactions where multiple actors are trying to optimise their own outcome. It is not theoretical fluff. It is a method for predicting and planning in dynamic, reactive environments.

The Setup: Strategic Interdependence

Most growth decisions are made in an environment of strategic interdependence. Your outcome depends not just on your choice, but on the choices of others.

For example, if two eCommerce brands both run steep discounting campaigns during a seasonal window, neither benefits. If one discounts and the other holds price, one wins and one loses. If both hold, margins stay healthy. This is a classic setup for a prisoner's dilemma, one of the foundational games in game theory.

Nash Equilibrium: Where No One Wants to Move First

A Nash equilibrium occurs when each player's strategy is the best they can do, given what the other player is doing. No one has an incentive to change unilaterally.

Suppose we have two brands, A and B, choosing whether to discount or hold price. The payoffs could look like this:

	B Discounts	B Holds Price
A Discounts	(3, 3)	(5, 1)
A Holds Price	(1, 5)	(4, 4)

In this case:

If both discount, they split market share but lose margin (3, 3)
If one discounts and the other does not, the discounter wins (5, 1) or (1, 5)
If both hold, margins remain (4, 4)

The Nash equilibrium is (4, 4), because if either player switches from that strategy unilaterally, they lose. This outcome is stable.

The Maths Behind It

Formally, a Nash equilibrium exists when for all players $i$ :

u_i(s_i^*, s_{-i}^*) \geq u_i(s_i, s_{-i}^*) \quad \forall s_i \in S_i

Where $u_i$ is player $i$ 's utility, $s_i^*$ is their equilibrium strategy, and $s_{-i}^*$ represents all other players' equilibrium strategies. In plain English: no one can do better by changing their strategy alone.

Dominant Strategies: What to Do Regardless of the Other

A dominant strategy is one that is best no matter what the other player does.

In practice, very few marketing games have dominant strategies. Most are conditional. But dominant strategies do exist in highly asymmetrical situations. For example:

If you have vastly lower cost of delivery, you might always undercut price
If you control the search channel, you might always bid aggressively on branded terms

I map this using payoff matrices. Each cell in the matrix shows the result of a strategic pair. I often build these in spreadsheets or Python to simulate scenarios.

Practical Example: eCommerce Shipping Wars

Consider two fashion retailers competing on shipping:

	B: Free Shipping	B: Paid Shipping
A: Free Shipping	(2, 2)	(4, 1)
A: Paid Shipping	(1, 4)	(3, 3)

If Retailer A has fulfilment costs 30% lower than B (due to warehouse location), free shipping becomes a dominant strategy for A. They win in both scenarios where they offer free shipping.

Zero Sum vs Non Zero Sum Games

A zero sum game means one player's gain is another's loss. The total payoff is constant.

Example: bidding on the same ad slot. If your ad shows, mine does not.

A non zero sum game allows for cooperative gain. Both players can improve simultaneously. For example, growing the overall category via joint education or industry events.

Growth hacking is full of both kinds. Referral programmes, loyalty schemes and industry events are non zero sum. Bidding, price wars and exclusive deals are often zero sum.

The Zero Sum Formula

In a zero sum game with two players:

u_A + u_B = 0

Any gain for A is an equal loss for B. This makes pure competition scenarios easy to model but hard to win sustainably.

Modelling Competitor Reactions

I build reaction functions to anticipate competitor response. For example, in dynamic pricing, I might assume a competitor updates their price based on a trailing window of my price.

I model:

P_C(t+1) = f(P_M(t), D(t), E(t))

Where:

$P_C$ is competitor price
$P_M$ is my price
$D$ is demand
$E$ is environmental noise (e.g. inflation, platform change)

This helps me plan not just what to do, but what happens next.

Practical Example: SaaS Pricing Response Model

For a B2B SaaS client, I modelled competitor response to our price reduction:

P_{competitor}(t+1) = \alpha \cdot P_{us}(t) + (1-\alpha) \cdot P_{competitor}(t)

With $\alpha = 0.3$ , meaning competitors adjust 30% toward our price each period. This let us simulate a 6 month pricing trajectory and identify the equilibrium point before we committed to the reduction.

Practical Example: Pricing Defence in Subscription SaaS

A SaaS client faced a new entrant offering a similar product at half price. They were considering matching the offer. I modelled this as a dynamic game.

We assumed that:

The new entrant would raise prices over time
Price sensitive users were likely to churn, but power users cared more about feature set
Aggressive pricing could trigger a race to the bottom

Instead of price matching, we segmented users by sensitivity, added value to the high end plan, and let the competitor absorb the low margin base.

The result: churn stabilised, average revenue per user increased by 18%, and the competitor eventually narrowed their offer to a single freemium tier.

Game theory guided that outcome.

Strategic Tools I Use

Payoff matrices: simple grids to visualise strategy pairs
Backward induction: in multi stage games, work backwards from end goals
Best response functions: model what the optimal reaction is to each possible move
Mixed strategy equilibria: when players randomise across options (e.g. ad timing or discount cadence)

These tools allow me to build growth plans that anticipate pressure, avoid traps, and exploit strategic blind spots.

Backward Induction Example

When planning a product launch into a competitive market, I work backwards:

Where do I want to be in 12 months? (Market position, pricing, share)
What will competitors do when they see my launch?
How should I structure my launch to account for their response?
What is my opening move?

This prevents the common mistake of optimising for week one without considering month six.

Why This Matters in Growth

In competitive markets, growth is not just about doing the right thing. It is about predicting and shaping the response environment. Game theory gives me that lens.

I use it to:

Decide when to lead, and when to let others move first
Build resilience into pricing strategy
Avoid zero sum waste
Identify stable, high margin equilibria

Most importantly, it helps me move from guessing to simulating.

Final Thought: Strategy Is a Multiplayer Game

If you are launching into a space where others already operate, or you want to defend position without reacting blindly, I can help you map the game, play to your strength, and grow with strategy, not just tactics.