Game Theory

Game Theory in Job Interviews

Google, Amazon, Airbnb, Uber, Jane Street, Two Sigma-all ask about game theory in interviews. Not as a math puzzle, but as a way of thinking about strategic systems. Nash Equilibrium in a product is the question: "what's stable for users?" Mechanism design is "how to create incentives that don't require coercion?" Auction design is "how does Google make $237 billion per year?" This lesson translates theory into interview language.

**Google PM/SWE interviews:** "Explain the Google Ads auction mechanism" is a standard question in ads teams. Knowing GSP vs VCG, Quality Score as an IC tool-the difference between an L5/L6 candidate
**Quant finance:** Jane Street, Citadel, Two Sigma ask Nash questions directly-matrix games, mixed strategies, minimax in trading contexts. Here both formulas and intuition
**Product strategy:** matching markets, two-sided platforms, chicken-and-egg problems-questions for Director/VP level. The right answer draws on Gale-Shapley, network effects, and mechanism design

Предварительные знания

Game Theory in Tech: Pricing and Markets

Nash Equilibrium Questions

At FAANG and quant interviews, Nash Equilibrium appears in two forms: as a direct question ("find the equilibrium in this matrix") and as hidden structure in a product or system design problem ("why aren't users switching to our better product?"). The key skill is seeing the game-theoretic structure when nobody names it explicitly.

Direct questions: • "Find the Nash Equilibrium in this 2×2 matrix" • "Is this an equilibrium? Verify it." • "Is there a dominant strategy here?" Product questions: • "Two streaming services keep cutting prices-where does this end?" • "Why do engineers create technical debt?" • "Why do companies compete so hard for engineers, even overpaying?" Architecture questions: • "How is a distributed system designed with no central arbiter?" • "Why does TCP congestion control work without a coordinator?"

Interview question	Game structure	Correct answer
"Price war in the ride-sharing market"	Prisoner's Dilemma	Dominant strategy: cut prices; equilibrium is Pareto-inferior
"Why do companies overpay engineers?"	Matching market	Stable matching via Gale-Shapley; candidates propose-benefits employers
"How does Google make advertisers reveal the truth?"	Mechanism design, IC	Second-price auction-truthful bidding dominates; VCG mechanism
"Why do standards get adopted slowly?"	Coordination game	Multiple NE; network effects create lock-in; first-mover wins

The formula for a successful Nash answer: 1. Identify players and strategies. 2. Write out the payoff matrix or describe the structure. 3. Find each player's best response to every strategy of the other. 4. NE = intersection of best responses. 5. Check Pareto optimality-and explain the gap.

In interviews, Nash Equilibrium only comes up for 2×2 matrix games

Nash thinking applies to any strategic situation: product design, system architecture, pricing, HR. Interviewers often specifically test the ability to see game structure in real problems.

FAANG interviewers in product/PM roles ask: "how will user behavior change?" and "what will competitors do?"-that's Nash thinking without matrices. Translating a real situation into a game structure is more valuable than knowing formulas.

An interviewer asks: "Two competitors decide how much to spend on advertising. Each can spend a lot or a little. If both spend a lot, profits fall; if both spend little, they split the market peacefully." What is the structure of this game?

Mechanism Design and Auction Questions

Mechanism design questions appear in three interview contexts: product ("how to make users rate services honestly?"), engineering ("how to design an API so clients don't abuse it?"), and analytical ("why does Uber use surge pricing?"). They all require the same answer: incentive compatibility.

Incentive Compatibility (IC): "Honest behavior is the best strategy for an agent, regardless of what others do" IC questions: • Why are Airbnb ratings unreliable? (no IC-both sides fear bad reviews) • How can an honest marketplace be built? (IC via escrow, reputation, mandatory reviews) • Why does Google use Quality Score in auctions? (IC-incentive for ad quality) Revenue Maximization: • Why have a reserve price at an auction? (information rent) • Why do SaaS companies use per-seat pricing? (price discrimination)

The formula for answering a mechanism design question: 1. Identify agents and their incentives. 2. Describe the current "game"-why agents behave dishonestly. 3. Propose a mechanism change-how to make honesty the dominant strategy. 4. Check IC-is there still an incentive to deviate? 5. Note trade-offs: implementation complexity, possible workarounds.

Mechanism design in interviews is only for product managers

Engineers, architects, and data analysts all build systems where users/clients adapt strategically. Understanding IC is critical for API design, rate limiting, credit scoring, and recommendation systems.

Any system with multiple agents and incentives is a mechanism. An engineer building a rate limiter must anticipate: how will clients try to bypass limits? That's mechanism design thinking.

An interviewer says: "On a marketplace, sellers inflate prices because the recommendation algorithm shows them anyway. How can this be fixed through incentive design?" Which mechanism is correct?

Auction Design in Interviews

Auction questions are a classic at FAANG interviews, especially in ad product teams (Google, Meta, Amazon) and marketplaces. Typical questions: "Explain how Google Ads works", "Why use a second-price auction instead of first-price?", "How is a reserve price set?", "What is GSP and how does it differ from VCG?"

Second-price auction (Vickrey): • Winner pays the second-highest bid • Truthful bidding (bid = true value) is a dominant strategy • Why: shading the bid risks losing; overbidding risks winning at a loss GSP (Google/Bing): • Multiple positions with different CTRs • Ranking by bid × Quality Score • Payment = (next bid_score) / own Quality Score • Not strictly IC, but has a "locally envy-free" equilibrium Revenue Equivalence: • First and second price yield the same expected revenue • Fails with: affiliated values, asymmetry, risk aversion Reserve price: • Increases expected revenue with a single bidder • Optimal: r* = arg max r*(1-F(r*)) (Myerson)

Question	Key answer	Why it matters
Why second-price?	Truthful bidding dominates-no need for strategic calculation	Simpler behavior, fewer manipulations
Why Quality Score?	IC: incentivizes relevant ad creation	Google earns more from clicks-incentive alignment
When is first-price better?	With asymmetric bidders or risk aversion	Revenue Equivalence breaks down
What is a reserve price?	Minimum sale price-increases revenue	Threat of not selling forces higher bids

Google AdWords is a Vickrey (second-price) auction for multiple slots

Google uses GSP (Generalized Second Price)-not pure VCG. GSP is not strictly IC, but has a practically workable "locally envy-free" equilibrium and is simpler to implement.

Saying "it's a Vickrey auction" in an interview with an ads team is a common mistake. The correct answer: "GSP extends the second-price idea to multiple positions with Quality Score, which adds an additional incentive for quality." That's depth.

An interviewer asks: "Why does Google use a Quality Score auction instead of a pure bid auction?" What is the best answer?

Strategic Questions and Product Thinking

The most interesting interview questions aren't "find the NE in this matrix"-they're "how do you enter a two-sided market?", "why aren't users switching to our platform?", "how do you design pricing?" These are strategic games disguised as product problems. Game theory provides a framework for a structured answer.

Step 1: Identify players and strategies → Who is making decisions? What can they choose? Step 2: Describe payoffs → What does each player maximize? Where is the conflict of interest? Step 3: Find Nash Equilibrium → What's stable? Who doesn't want to deviate? Step 4: Assess efficiency → PoA: how much worse is NE than the social optimum? Step 5: Propose a mechanism → How can the rules be changed so IC directs agents toward a better outcome?

Another important class of questions is **information asymmetry**. "How can a buyer know the real quality of goods on a marketplace?" (signaling: high-quality sellers offer warranties because it's cheap for them). "Why does insurance require a medical exam?" (adverse selection: without screening, only sick people buy coverage). These questions test understanding of incomplete information games.

Answering game theory questions requires knowing all the formulas and theorems

Interviewers test structured thinking, not formula recall. The ability to reframe a problem as a game, find the NE, and propose a mechanism is worth more than deriving the optimal reserve price.

Even without Myerson's formula, the explanation is straightforward: "a reserve price increases revenue because it creates a threat of not selling-buyers with high values are forced to bid more." That's deeper than just stating r* = 0.5 for U[0,1].

An interviewer asks: "We have a new freelance platform. Contractors won't sign up without orders; clients won't sign up without contractors. What is the right move?" What is the best answer?

Key Ideas

**Nash questions:** identify players → payoff matrix → best responses → NE → Pareto comparison
**IC mechanism:** honesty as a dominant strategy-the answer to "how can abuse be prevented?"
**Auction design:** second price = IC, GSP = locally envy-free, reserve = revenue, Quality Score = quality incentive
**Two-sided platforms:** chicken-and-egg = two NE; subsidize the valuable side first to escape (0,0)

Вопросы для размышления

Take any product used daily (Telegram, GitHub, Notion). Try to describe it as a mechanism: who are the players, what are the strategies, is it IC? Where are the ratings, where is the market design?
"Why do engineers create technical debt, knowing it will hurt the team?"-answer through game theory: what's the game structure, what's the Nash Equilibrium, how can the mechanism be fixed?
If a bidding system were being designed for a freelance platform from scratch-what type of auction should be chosen and why? How could Quality Score be incorporated for contractors?

Связанные уроки

alg-21-dp