Game Theory Interview Questions
Game theory is the study of optimal play when your payoff depends on what a rational adversary does next. In quant interviews it shows up as combinatorial games (Nim, counting-to-N, parity puzzles solved by backward induction), strategic equilibria (Nash, mixed strategies, iterated dominance), aucti
How to think about game theory questions
Most game-theory puzzles look like clever one-offs, but they all ask the same question: where does play settle when both sides are smart? The answer is a strategy profile so stable that no one gains by deviating — and once you learn to hunt that fixed point, coin-guessing duels, Nim piles, and auctions stop feeling like tricks.
FIND THE STABLE PROFILE
A Nash equilibrium is the spot where every player is already best-responding to everyone else, so no one's incentive points away from it. In sequential games you reach it by backward induction — solve the last move first and fold the value back; in matrix games you scan for the cell that is best down its column and across its row.
MIX TO INDIFFERENCE
When no pure profile is stable — matching pennies, bluffing, guessing a flip — the equilibrium goes mixed. The unlock: randomize so your opponent becomes exactly indifferent among their options, because only then can their own mix be optimal. You don't solve for your payoff; you solve for the probabilities that flatten theirs.
Work this set top to bottom and one move recurs — assume your opponent is as sharp as you, then find the profile neither of you wants to leave — until reaching for the equilibrium becomes reflex.
Game Theory questions (56)
- Nash Equilibrium in a Two-Player Game
- Nim Game with 1000 Stones
- Pirate Game
- Guess Two-Thirds of the Average
- Two-Pile Nim: Winning and Losing Positions
- Three-Way Duel With Rational Players
- Tic-Tac-Toe AI via Minimax
- Ultimatum Game: Optimal Split Proposal
- Collector's Sculpture Auction
- Lions and Gazelle: Backward Induction
- Chip-Taking Game Optimal Strategy
- Optimal Bid in a First-Price Auction Against a Uniform Opponent
- Card Flipping Game with Adjacent Cards
- Stone Picking Game with Optimal Position Choice
- Restricted Rock-Paper-Scissors Nash Equilibrium
- Array Increment Game: Who Wins?
- Coin Placement Game on a Circle
- Sealed-Bid Auction for a Coin-Toss Box
- Can I Win: Bitmask Game Theory
- Optimal Pick Against a Uniform Opponent
- Take-It-or-Leave-It Pricing with Adverse Selection
- Optimal Stopping for a Die Roll Game
- Paying for a Better Die
- Market Making on Country Altitude
- Optimal Offer for a Random-Value Box
- Card Game: Redraw vs. Switch Option
- Marble Piles: First-Player Winning Strategy
- First-Price Auction: Equilibrium and Optimal Reserve
- Penney's Game with Biased Coin
- Pirate Gold Division: Extending the Pattern
- ABA vs. BAB Tournament Sequence Strategy
- Optimal Calling Strategy in a Simplified Poker Game
- Minimax Card Number Assignment
- Black Box Demand Game
- Optimal Bet Sizing: Expected Value vs. Kelly Criterion
- Market Making the Population Guessing Game
- Flipping Cups on a Rotating Table
- Optimal Deck Composition Against a Guesser
- Ghost Word Game on a Trie
- Last to Discard
- Value of a Costly Signal in Market Making
- Number-Picking Game with a Handicap
- Taxman Card Game: Optimal Strategy
- Doubling Stakes with Uniform Numbers
- Guaranteed Profit from Mystery Bills
- Deterministic Poker with Perfect Information
- Optimal Card Betting With a Known Deck
- Pirate Hat Puzzle: Cooperative Parity Strategy
- Two-Way Communication via Break-and-Repair Signaling
- Choose Your Map Selection Method
- Identifying an Anti-Terrorist by Majority Query
- Optimal Stopping in the Red-Black Card Game
- Optimal Strategy for a Three-Card Game
- Prisoners and the Glass Signal
- Optimal Betting Strategy to Reach a Target
- Adaptive Coin Identification with Costly Sampling
Game Theory interview questions FAQ
What kind of game theory questions show up in quant interviews?
This page collects 56 game theory problems that recur in quant trading and research interviews, each with a full worked solution and the intuition behind it. They range from quick warmups to the harder variants firms use to separate candidates.
How hard are game theory interview questions?
The set spans 1 easy, 29 medium and 26 hard problems. Most sit at medium difficulty — a few minutes of clean reasoning — with a harder tail that rewards knowing the canonical approach rather than grinding.
How should I practice game theory for quant interviews?
Work through them by difficulty, starting just below your level, and write the solution out before checking. 13 are free to open with the full worked solution, so you can judge the quality first. Focus on the recurring patterns rather than memorizing answers — the same handful of ideas generate most variants.
Are these real quant interview questions?
They are a curated set drawn from our problem bank — the kind of game theory question that actually appears in quant interviews, rewritten for clarity with solutions we author ourselves. We don't claim any single wording is verbatim, and every problem carries a full solution.