Game Theory Interview Questions

Game theory questions in quant interviews come in five recurring flavors: backward-induction puzzles, Nash and minimax equilibria, Nim-style counting games, optimal-stopping games against a deck or die, and information games built on adverse selection.
The common thread: assume your opponent plays perfectly, then find the strategy neither side wants to leave.

Last updated 2 July 2026 · sub-areas, difficulty mix and firm attributions on this page are compiled directly from the 94 game-theory problems in the QuantVault bank; firm tags are candidate-reported, not employer-verified, and no individual author is named in our source data.

Core sub-areas
Backward induction · equilibria & minimax · Nim-style games · optimal stopping · adverse selection
Typical difficulty
Skews medium-to-hard — 5 easy, 49 medium and 40 hard across the 94-problem set
Who leans on it
Trading-heavy interview loops — problems here carry candidate tags from Jane Street, Citadel, Optiver, DRW, Two Sigma and others
Practice pool
94 problems in the bank · 19 free to open with the full worked solution

Where game theory shows up: mostly in brain-teaser phone rounds and trader onsites, where “let's play a game” doubles as a market-instinct test — the same reasoning prices a two-sided quote against informed flow. For how it sits inside specific funnels, see the Jane Street interview questions guide and the Citadel interview questions guide.

Practice game theory questions interactively → Browse the full problem bank All interview topics

The surfaceThe game theory sub-areas quant interviews test

Five families cover essentially every game-theory question in the bank. Each row pairs a sub-area with the recurring question shape and a representative type — a flavor drawn from real problems, not a leaked wording — so you can see where the difficulty actually lives.

The game theory sub-areas tested in quant interviews, with the recurring question shape and a representative question type for each.
Sub-areaRecurring shapeRepresentative type (flavor, not a real question)
Backward induction & sequential gamesSolve the last move first, fold values backA duel, pirate-style vote or pursuit game where the right first move only makes sense once you have solved the endgame.
Nash equilibria & minimaxFind the profile no one gains by leaving; mix to make the opponent indifferentA restricted rock-paper-scissors or number-assignment duel where the answer is a probability mix, not a single move.
Nim-style counting gamesIdentify the losing positions and always hand one to your opponentA take-turns counting game to a target where the winner controls an arithmetic ladder of losing positions.
Optimal stopping & game valuePrice the option to continue; stop when the current draw beats itA keep-or-redraw card game, or a die you may reroll a capped number of times — the threshold falls out of a short backward recursion.
Information & adverse selectionCondition on what the other side's willingness to trade tells youA take-it-or-leave-it price or noisy-signal decision where the counterparty accepting is itself bad news.

What's confirmed vs. what varies: the sub-areas and the difficulty mix above come straight from the problem set, so they are stable. Which firm asks which flavor is candidate-reported through problem tags — treat the firm attributions as directional, and expect trading tracks to weight the stopping and adverse-selection families more heavily than research tracks.

The patternsSignature game theory question patterns

Three moves generate most correct answers in this topic. Each worked box below is a 60–90 second micro-example in the interview's actual cadence — the reasoning template, applied to a generic setup rather than any firm's wording.

Backward induction — own the losing positions

Takeaway: never search a take-turns game forward — classify positions as winning or losing from the end, and play to hand your opponent a losing one every turn.

Shape. Two players alternately add 1, 2 or 3 to a running total; whoever says the target number \(N\) wins. Who wins, and how?

1. Solve the endgame. Standing on \(N-1\), \(N-2\) or \(N-3\) with the move is winning — you finish immediately. Standing on \(N-4\) is losing: every move you make lands your opponent in the winning band.

2. Fold back. The same argument repeats every four numbers, so the losing positions are exactly the totals congruent to \(N \bmod 4\).

3. Play the invariant. If the starting total is a losing position for your opponent, take it and keep restoring the congruence each turn; whatever they add, you top it up to 4. The move: find the invariant from the end, then never let go of it.

Mixed strategies — randomize to make the opponent indifferent

Takeaway: in a mixed equilibrium you do not solve for your own payoff — you solve for the probabilities that make the other player's options pay exactly the same.

Shape. A zero-sum matching game: if you both pick A you win 3, if you both pick B you win 1, on any mismatch you lose 1. What is optimal play?

1. Check for a pure equilibrium. Every cell tempts someone to deviate — if your choice were predictable, the opponent mismatches you at will — so the equilibrium must be mixed.

2. Impose indifference. Let the opponent pick A with probability \(q\). Your two options pay \(3q-(1-q)=4q-1\) and \(-q+(1-q)=1-2q\); setting \(4q-1=1-2q\) gives \(q=\tfrac13\). By the symmetric argument your own A-frequency is \(p=\tfrac13\).

3. Read off the value. At \(q=\tfrac13\) both options pay \(\tfrac13\), so the game is worth \(+\tfrac13\) to you per round. The move: equalize the opponent's payoffs, then the value falls out for free.

Optimal stopping — the threshold is the continuation value

Takeaway: value the option to continue first; the optimal rule is always “stop exactly when what you hold beats the expected value of playing on.”

Shape. Draw a number uniformly from 1–100. You may keep it, or discard it and accept one fresh draw. What is the game worth?

1. Price the fallback. A forced second draw is worth its mean, \(50.5\). That number — not 50 — is your continuation value.

2. Derive the rule. Keep the first draw exactly when it exceeds \(50.5\), i.e. on 51 or above; redraw otherwise. The threshold is the continuation value, never a round number you guessed.

3. Price the game. With probability \(\tfrac12\) you keep an average of \(75.5\); with probability \(\tfrac12\) you fall back to \(50.5\). Total: \(\tfrac12(75.5)+\tfrac12(50.5)=63\). The move: work backward from the last decision — capped-reroll and multi-stage card games just iterate this step.

Free practiceGame theory practice questions by sub-area

All 19 free problems from the 94-problem game-theory set, grouped by the sub-areas above — every link opens the full worked solution, so you can check your reasoning line by line. One honesty note: the free pool is 14 medium and 5 hard; the bank's five easy game-theory problems sit in the paid tier, so treat a clean medium here as your warm-up.

Backward induction & sequential games

Nash equilibria & minimax

Nim-style counting games

Optimal stopping & the value of a game

Information & adverse selection

The planHow to prepare for game theory questions

Five techniques to make reflexive, in the order they pay off. Each maps onto one of the practice groups above, so you can drill it immediately after reading.

  1. Make backward induction your first instinct. Whenever a game has a last move, solve it first and fold values back — duels, pirate votes and pursuit games all crack this way. If you catch yourself simulating forward, stop and restart from the end.
  2. Internalize the indifference principle. When no pure strategy is stable, the equilibrium mix is whatever makes your opponent's options pay the same. Practice setting up the two-line indifference equation until it takes under a minute.
  3. Hunt invariants in take-turns games. Nim-style questions reduce to a modular-arithmetic ladder of losing positions; find the ladder, then articulate the strategy as “always return the total to the ladder.”
  4. Price the option to continue. In keep-or-redraw and capped-reroll games, compute the continuation value first and stop exactly when your current holding beats it — interviewers listen for that phrase, not for the final number alone.
  5. Treat “want to trade?” as information. In pricing games, a counterparty who accepts your offer is disproportionately one who knows you mispriced — build that conditioning in before you quote. Then run the free practice set and take the interactive game theory playlist on a clock.

FAQGame theory interview questions — frequently asked

How important is game theory for quant interviews?

A reliable second-tier topic: it appears less often than probability or expected value, but trading firms lean on it because optimal play against a thinking adversary is the job in miniature. One clean game-theory round can carry outsized signal, since most candidates prepare it far less than probability.

What game theory topics should I focus on?

Backward induction, mixed-strategy indifference and optimal stopping cover most of what gets asked. Round it out with Nim-style losing-position arguments and a working feel for adverse selection — the idea that the other side agreeing to trade is itself information.

How hard are game theory interview questions?

Mostly medium-to-hard: of the 94 problems in this set, 49 are medium, 40 are hard and only 5 are easy. The difficulty rarely comes from computation — it comes from finding the right framing, after which the arithmetic is usually short.

Are these real quant interview questions?

They are representative, not verbatim. The problems are curated from our bank to match the game-theory shapes candidates report, rewritten for clarity with worked solutions we author ourselves — we never claim any wording is a leaked question.