Business Finance

Game Theory

Risk & Decision ScienceDifficulty: ★★☆☆☆

I think in mathematical models of business systems - game theory, optimization, Bayesian decision frameworks.

You run a $3M ARR product. Your only competitor just cut their Pricing 25%. Sales is losing deals and begging you to match. But if you both keep cutting, you destroy each other's Profit. If you hold while they cut, you bleed customers. The spreadsheet gives you Revenue projections for each scenario - but the right answer depends on what the other side does next, and what they think you'll do. This is not a forecasting problem. It is a strategic interaction, and you need a different framework.

TL;DR:

Game Theory models decisions where your outcome depends on other players' choices - not just your own. Use it to predict competitor moves, structure Vendor Negotiations, design incentives that survive contact with rational self-interest, and recognize when the winning move is to change the game itself.

What It Is

Game Theory is the mathematical study of strategic interaction - situations where your best move depends on what someone else does, and their best move depends on what you do.

You already know about Utility Functions (how individuals score outcomes) and incentives (the rules that make actions attractive or unattractive). Game Theory combines both: each player has a Utility Function, each faces incentives, and the outcome depends on everyone's choices simultaneously.

The core components:

  • Players: the decision-makers (you, a competitor, a vendor, an employee)
  • Actions: what each player can choose (cut price, hold price, walk away)
  • Expected Payoffs: what each player gets for each combination of actions
  • Information: what each player knows about the other's options and Utility Functions

You map these into a table of Expected Payoffs - rows are your choices, columns are theirs, each cell shows what both sides get. Then you look for patterns: does either side have a Dominant Strategy? Where does the system settle into equilibrium?

Why Operators Care

Every P&L decision that involves another rational actor is a game. If you optimize your own numbers in isolation, you are solving the wrong problem.

Pricing: Your Competitive Pricing does not exist in a vacuum. Cutting price only works if competitors don't match. If they always match, you have just shrunk the entire market's Revenue for zero Market Share gain.

Vendor Negotiations: Every negotiation has a surplus to split. Knowing your Outside Option and estimating theirs determines the acceptable price range. Without this framework, you either overpay or blow up deals you should have closed.

Hiring: When you and a competitor both chase the same candidate, the winner depends on Total Compensation offers, but also on timing, information, and each side's risk appetite. Bidding wars follow game-theoretic patterns - and winner's curse is real.

Incentive design: You set Commissions, bonuses, and promotion criteria. Your employees are rational players who will find the Dominant Strategy in whatever structure you build. If that strategy conflicts with what you actually want, Goodhart's Law kicks in and your metric improves while your business gets worse.

The P&L impact is direct: game-theoretic mistakes show up as Profit destruction from Pricing wars, overpaying vendors, losing talent bids, and incentive structures that reward the wrong behavior.

How It Works

Step 1: Map the game

Identify the players, their available actions, and the Expected Payoff for each combination. Write it as a table.

Example - you and a competitor both sell a $200/month product to a shared market of 1,000 customers:

Competitor Holds $200Competitor Cuts to $150
You Hold $200You: $100K/mo, Them: $100K/moYou: $60K/mo, Them: $105K/mo
You Cut to $150You: $105K/mo, Them: $60K/moYou: $75K/mo, Them: $75K/mo

(Payoffs assume: if one side is cheaper they grab 700 of 1,000 customers; if equal, they split 500/500.)

Step 2: Find Dominant Strategies

A Dominant Strategy is a choice that produces a better Expected Payoff regardless of what the other side does.

Check your options:

  • If they hold: you get $105K by cutting vs. $100K by holding. Cutting wins.
  • If they cut: you get $75K by cutting vs. $60K by holding. Cutting wins.

Cutting is your Dominant Strategy. By symmetry, it is theirs too.

Step 3: Find the equilibrium

The equilibrium is where both players choose their best response to each other's choice - neither wants to unilaterally change. Here, both cut to $150, earning $75K/mo each.

Notice the trap: the equilibrium ($75K each) is worse for both players than mutual holding ($100K each). This structure - where individual incentives drive both players to an outcome neither prefers - appears constantly in business. Pricing wars, feature arms races, and excessive Marketing Spend all follow this pattern.

Step 4: Look for ways to change the game

The real power of Game Theory for an Operator is not just predicting the equilibrium - it is recognizing when you can restructure the game itself:

  • Change the Expected Payoffs: Build a competitive moat through differentiation so price cuts don't steal your customers. This literally changes the numbers in the table.
  • Change the information: Signal commitment to hold Pricing (long-term contracts, public price guarantees). If the competitor believes you will not cut, their best response may shift to holding too.
  • Change the Time Horizon: A single interaction and an ongoing relationship have different equilibria. If you will compete with this rival for years, retaliating against price cuts becomes credible - which makes mutual price-holding a stable equilibrium. Most business relationships are ongoing: you negotiate with the same vendors yearly, compete with the same rivals quarterly, manage the same team daily.
  • Strengthen your Outside Option: In Bargaining, your Outside Option sets your floor. Every dollar you invest in making that option credible translates directly into Leverage at the table.

When to Use It

Use Game Theory when:

  • Your outcome depends on a specific competitor, vendor, or partner's choice - not just general market conditions
  • You are in a negotiation and need to estimate the other side's walk-away point
  • You are designing incentives (Commissions, bonuses, Pricing tiers) and want to predict how rational agents will actually behave
  • You are deciding whether to enter a Pricing war, bidding war, or feature war
  • You see a pattern where everyone is doing something that makes everyone worse off

Do not over-apply it when:

  • The other side's behavior does not meaningfully change your outcome (they are too small, or there are too many competitors to model individually)
  • You have enough Market Share that you are setting the game, not playing it
  • The decision is purely one-sided with no strategic response - just use Expected Value and a decision tree

Minimum information you need:

  1. 1)Who are the relevant players? (Usually 2-3, not 50)
  2. 2)What actions can each player take? (Keep it to 2-4 per player)
  3. 3)What is the approximate Expected Payoff for each combination?
  4. 4)Is this a single interaction or does the relationship continue over a real Time Horizon?
  5. 5)What does each side know about the other's options and Utility Function?

Worked Examples (2)

Vendor Negotiation Using Outside Options

You need a data enrichment service for your sales pipeline. Vendor A quotes $60K/year. Your Outside Option is building in-house: $90K upfront Implementation Cost amortized over 3 years ($30K/year) plus $15K/year maintenance = $45K/year effective cost. The enrichment service adds $200K/year in Revenue through better Close Rate. Vendor A's Outside Option: their next best client is worth $35K/year to them.

  1. Determine each side's walk-away point. Your ceiling is $45K/year - at any price above this, building in-house is cheaper (you net $200K - $45K = $155K by building, so you will not pay more than $45K for the same capability). The vendor's floor is $35K/year - below this, their next client is a better deal for them.

  2. Calculate the surplus. Surplus = your ceiling minus vendor's floor = $45K - $35K = $10K/year. This is the total additional value available to split through negotiation. It is small because your build option is only slightly more expensive than their alternative client is valuable to them.

  3. Assess their opening quote. At $60K/year, the vendor is quoting $15K above your ceiling. At $60K you net $200K - $60K = $140K, but building in-house you net $200K - $45K = $155K. No rational Buyer pays $60K when they can solve the problem for $45K. Their quote is outside the negotiation range entirely.

  4. Counter at $40K/year - this sits inside the acceptable range ($35K to $45K) and signals you have a credible build option. Likely equilibrium: $38K-$43K. At $40K, you save $5K/year versus building it yourself, and they earn $5K above their Outside Option. Both sides are better off than their alternative.

Insight: In Vendor Negotiations, surplus = Buyer ceiling minus vendor floor. Your ceiling is set by your Outside Option (what it costs you to solve the problem without them) - not by the total Revenue the solution generates. The $200K in Revenue is irrelevant to the negotiation range because you capture that Revenue either way, whether you build or buy. Every dollar you spend making your Outside Option credible - getting a competing bid, scoping the build cost in detail, running a pilot internally - directly tightens the negotiation range in your favor.

Commission Structure as a Game Between Sales Reps

You manage 4 sales reps sharing a territory. The pipeline receives 100 inbound per month. Current Commissions: 10% of Revenue on closed deals, no rules about how pipeline is allocated. Average deal size: $10K. Overall Close Rate: 20%. You notice reps grabbing the easiest pipeline and ignoring the rest. Pipeline Volume looks healthy, but conversion is falling.

  1. Map the game. Each rep's Dominant Strategy is to grab the highest-probability pipeline first. A 40% probability deal has an Expected Payoff of 0.40 x $10K x 10% = $400 in Commissions. A 5% probability deal pays 0.05 x $10K x 10% = $50. Rationally, every rep ignores the hard deals.

  2. Identify the failure mode. With 4 reps all chasing the same top pipeline, the best 30 get fought over (wasted effort from overlap) and the bottom 70 get abandoned. Effective Pipeline Volume drops from 100 to roughly 40 actually worked. Team Revenue: 40 x 25% blended Close Rate x $10K = $100K/month. Total Commissions cost: $100K x 10% = $10K/month. P&L contribution: $100K - $10K = $90K/month.

  3. Redesign the incentives to change the game. Assign pipeline via round-robin (removes the cherry-picking action from the game entirely). Add a bonus for working all assigned pipeline to completion, regardless of outcome. New structure: 8% Commissions + $200 per fully-worked deal.

  4. Project the new equilibrium - including the full Cost Structure. Each rep gets 25 inbound. All 100 get worked. Team Revenue: 100 x 20% x $10K = $200K/month. New Commissions cost: $200K x 8% = $16K/month. New bonus cost: 100 x $200 = $20K/month. Total comp: $36K/month, up from $10K - comp nearly quadrupled. But Revenue doubled from $100K to $200K. Net P&L contribution: $200K - $36K = $164K/month, up from $90K. That is $74K/month better - $888K/year in additional Profit.

Insight: The reps were not lazy - they were playing rationally under bad rules. The old Commissions structure had a Dominant Strategy (grab easy pipeline, ignore the rest) that produced a bad equilibrium for the P&L. Redesigning the game changed the Dominant Strategy to one aligned with business goals. But always model the full Cost Structure of the new incentive design: Revenue doubled while total comp nearly quadrupled ($10K to $36K). The redesign is still strongly net positive ($74K/month), but an Operator who only tracks the Revenue lift without modeling the comp increase is solving half the problem.

Key Takeaways

  • Your outcome depends on other players' choices. Optimizing your own numbers in isolation gives you the wrong answer whenever a competitor, vendor, or employee can react to your move.

  • Look for Dominant Strategies - yours and theirs. If both sides have one and the equilibrium it produces is bad for everyone, you need to change the game structure, not just play harder within it.

  • The most powerful Operator move in Game Theory is often restructuring the game itself: changing Pricing models, strengthening your Outside Option, redesigning incentives, or converting a single interaction into an ongoing relationship over a longer Time Horizon where reputation matters.

Common Mistakes

  • Assuming the other side will not react. You model a price cut as if competitors hold still, or a hiring offer as if the candidate has no other options. They will respond. Always ask: 'what does the other side do after my move, and what do they think I will do after that?'

  • Ignoring Time Horizon dynamics. Most business relationships are ongoing - you negotiate with the same vendors yearly, compete with the same rivals quarterly, manage the same team daily. A move that wins a single interaction (squeezing a vendor to their absolute floor) can destroy value over a longer Time Horizon (they deprioritize your account, cut service quality, or refuse to renew).

  • Confusing total value with surplus. If a vendor's service generates $200K/year in Revenue for you but your Outside Option costs $45K/year, your ceiling is $45K - not $200K. The surplus is the gap between your ceiling and their floor. Anchoring on total value created instead of the negotiation range is the most common error in Vendor Negotiations, and it leads you to accept prices far above what you should pay.

Practice

medium

You and a competitor both spend $50K/month on Marketing Spend, splitting a shared pipeline of 200 inbound evenly (100 each). If you increase to $80K and they hold at $50K, you capture 140. If both increase to $80K, you split evenly again at 100 each. Inbound convert at 15% Close Rate with an average deal of $8K. Build the payoff table (Revenue minus Marketing Spend) and determine whether increasing spend is a Dominant Strategy. Then explain what an Operator should actually do.

Hint: Calculate monthly Profit (Revenue minus Marketing Spend) for all four scenarios: both hold, you increase alone, they increase alone, both increase. Then check whether increasing is better for you regardless of what the competitor does.

Show solution

Revenue per inbound: 15% x $8K = $1,200. Both hold $50K: 100 x $1,200 - $50K = $70K each. You increase to $80K, they hold: 140 x $1,200 - $80K = $88K for you; 60 x $1,200 - $50K = $22K for them. They increase, you hold: $22K for you, $88K for them. Both increase: 100 x $1,200 - $80K = $40K each. Check: if they hold, $88K (increase) vs. $70K (hold) - increasing wins. If they increase, $40K (increase) vs. $22K (hold) - increasing wins. Yes, increasing is a Dominant Strategy for both sides. But the equilibrium ($40K each) is worse than mutual holding ($70K each). This is a Marketing Spend arms race. The Operator's move: invest in differentiation or a competitive moat so your Pipeline Volume converts regardless of spend parity, breaking the symmetry of the payoff table.

hard

You are renegotiating a SaaS contract. The vendor quotes $120K/year for renewal. Your Outside Option: migrate to a competing product for $40K in switching costs plus $90K/year ongoing. The vendor's Outside Option: lose your account and fill the slot with a smaller customer worth $70K/year. The software generates $500K/year in value for your Operations. What is the surplus, what is your target price, and what should your opening offer be?

Hint: Your ceiling is the total Amortized Cost of your Outside Option over a reasonable Time Horizon - that is the maximum you would rationally pay. The vendor's floor is their Outside Option. Surplus is the gap between your ceiling and their floor. Be careful: the $500K in value does not set your ceiling. Your alternative does.

Show solution

Your Outside Option: $40K switching cost amortized over 3 years = $13.3K/year + $90K/year = $103.3K/year effective cost. This is your ceiling - above $103.3K, migrating is cheaper. Vendor's Outside Option: $70K/year. This is their floor. Surplus: $103.3K - $70K = $33.3K/year. Acceptable range: $70K (vendor's floor) to $103.3K (your ceiling). The vendor's quote of $120K is $16.7K above your ceiling - do not accept it. At $120K you overpay versus migrating. Opening offer: $75K/year (just above their Outside Option, signals you will walk). Target: $85K-$90K. At $85K you save $18.3K/year versus migrating; they get $15K above their Outside Option. You hold the Leverage because their quote exceeds your walk-away point - they need to come down $16.7K just to reach your ceiling, and further to reach a price where both sides capture meaningful surplus.

Connections

Game Theory extends the individual decision-making you learned in Utility Function and incentives to situations with multiple rational actors. Where Utility Function taught you how a single person scores outcomes, Game Theory shows what happens when two or more players with different Utility Functions interact under a shared set of incentives. This concept is the foundation for several downstream ideas: Dominant Strategy (the core solution concept you use to predict behavior), Zero-sum Game (the special case where one player's gain is exactly another's loss), Outside Option and Bargaining (negotiation modeled as a game of surplus-splitting), auction theory and Bid Shading (competitive bidding as strategic interaction), Shapley value (fair Allocation of value when multiple players cooperate), and Goodhart's Law (what happens when the incentive game produces an equilibrium you did not intend). If you design Pricing, negotiate contracts, or set Commissions, you are designing games - the only question is whether you model them deliberately or let the equilibrium surprise you.

Disclaimer: This content is for educational and informational purposes only and does not constitute financial, investment, tax, or legal advice. It is not a recommendation to buy, sell, or hold any security or financial product. You should consult a qualified financial advisor, tax professional, or attorney before making financial decisions. Past performance is not indicative of future results. The author is not a registered investment advisor, broker-dealer, or financial planner.