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Game Theory and Strategic Trading

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Probability tells you what to expect from a world that is not paying attention to you. Trading is not that world. The price you quote is seen before it is traded against, the counterparty who lifts your offer chose to, and the competitor quoting beside you is solving the same problem you are. This course covers the reasoning that starts where expected value stops.

It runs from the basics of a payoff matrix through equilibrium and mixed strategies, into private information, adverse selection and the winner's curse, and finishes on bet sizing and the games that trading firms actually play in interviews. Every idea is worked with numbers, and the closing section maps the whole thing onto the market making games you will be asked to play.

Expected value, conditional probability and variance are assumed. If those need shoring up first, start with Fundamentals of Probability and Statistics.

What Is a Strategic Game2 questionsThe shift from computing an expected value against nature to computing one against a counterparty who is choosing at the same time.Free previewDominance and Iterated Elimination2 questionsThe strongest kind of answer in a game is one that does not require you to guess what the other side will do.Free previewBest Response and Nash Equilibrium2 questionsWhat equilibrium actually promises, which is less than most people assume, and what to do when a game has more than one.Free previewZero-Sum Games and Minimax2 questionsWhat you can guarantee yourself against an opponent who is trying to hurt you, and how much of trading is actually zero-sum.
Why Pure Strategies Fail2 questionsSome games have no stable pair of fixed choices, and in those games being predictable is the only mistake you can reliably be punished for.Mixed-Strategy Equilibrium2 questionsTurning 'randomise' into a specific number, using the one condition that determines it: your mix is chosen to make them indifferent.The Ace-Queen Betting Game2 questionsA complete solution to the bluffing game trading firms actually play in interviews, worked from the setup to the bluff frequency.Commitment and Repeated Play2 questionsWhy binding yourself to a worse option can pay, and what changes when the same game runs every day against the same people.
Games with Private Information2 questionsWhen one side knows something the other does not, every action becomes evidence about who you are dealing with.The Winner's Curse2 questionsWinning is bad news, because you win exactly when you were the most optimistic person in the room.Adverse Selection and the Spread2 questionsThe bid-ask spread derived from first principles, as the equilibrium answer to not knowing who you are trading with.Reading Your Counterparty2 questionsHow much to move your price after a fill, and why the most common error in a make-a-market exercise is moving it too far.
Expected Value Against an Optimiser2 questionsWhy the expected value of a quote is not the expected value of the instrument, and how to compute the one that matters.The Kelly Criterion2 questionsHow much of the bankroll to stake when the bet is repeated, derived from the only objective that survives compounding.Bet Sizing Under Uncertain Edge2 questionsKelly assumes you know your edge. You do not, and the correction for that is larger than most people expect.Auctions and Mechanism Basics2 questionsWhy the rules of an auction change what bidding honestly means, and where a trader meets each format.
The Market Making Game as a Game2 questionsEvery idea in this course, mapped onto the exercise firms actually run in the room.Playing an Unfamiliar Game2 questionsA procedure for a game you have never seen, which is the situation every one of these interviews is designed to create.

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