Game Theory

Players, strategies and payoffs, the grid they form, and why the numbers written in it have to be utilities rather than money.

The one prediction that needs no guess about what anyone believes, iterated until it stops, and the famous game where it gives a single unwelcome answer.

Best responses, the profile at which every player is giving one, how to read equilibria off a grid, and the games where none exists.

Randomising to avoid being predicted, the indifference condition that fixes the probabilities, Nash's existence theorem, and why a harsher penalty does not reduce the crime.

Games with several equilibria, the mixed equilibrium that is worse than all of them, and the arguments from outside the model that pick a winner.

Security levels, the gap between maximin and minimax, von Neumann's theorem closing it with mixing, and the one class of games with an unambiguous prediction.

Strategy sets that are intervals, best responses that are functions, the Cournot equilibrium solved from a parabola, and why price competition drives profit to zero.

Game trees, a strategy as a complete contingent plan, backward induction, and the first-mover advantage priced out in a quantity-setting duopoly.

Subgame perfection removes equilibria that rest on threats nobody would carry out, and shows why destroying your own options can be worth paying for.

Why a known last round destroys cooperation, how a discount factor prices the future, and the patience threshold above which the prisoner's dilemma reverses.

Repetition sustains almost any payoff above the minmax, so a result that explained cooperation ends up explaining everything, and the empirical reply is a tournament.

Equilibrium accepts every division of a gain, so Nash imposed four properties on the answer instead, and they pin down exactly one split.

Model the haggling instead of the outcome, and impatience alone fixes a unique split, reached immediately, that no laboratory subject plays.

Give each player a private type and a belief about everyone else's, then price a second-price bid, a first-price bid, and the cost of winning.

The scorecard laid out honestly, the three models built to fit the failures, and the discipline that stops the theory absorbing every anomaly into the payoffs.