Game Theory & Social Choice

Strategic play, voting, and the paradoxes of collective choice.

Minimax Theorem — Every finite zero-sum game has a value — and a mixed strategy achieves it.
Braess' Paradox — Add a road, slow everyone down — selfish routing degrades with more options.
Arrow's Impossibility — No ranked voting rule is fair, decisive, and non-dictatorial — pick at most two.

Further Topics

Nash Equilibrium (pure strategies) — Profiles where no player gains by switching alone.
Dominant & Dominated Strategies — Strict dominance and iterated elimination of dominated strategies.
The Prisoner's Dilemma — A dominant strategy for each can leave both worse off.
Mixed-Strategy Nash Equilibrium — Randomize over best responses; indifference fixes the probabilities.
Pareto Efficiency — When can everyone be made better off — and why equilibria can waste.
Extensive-Form Games & Backward Induction — Game trees, solved by rolling back optimal moves from the leaves.
Subgame-Perfect Equilibrium — Backward induction rules out non-credible threats in sequential games.
Repeated Games & the Folk Theorem — How patience and the threat of punishment sustain cooperation.
Nash Bargaining Solution — Maximize the product of gains over disagreement to split a surplus.
The Shapley Value — Fair allocation as average marginal contribution over join orders.
The Core — Allocations no coalition can profitably abandon.
Stable Matching / Gale–Shapley — Blocking pairs, stability, and the deferred-acceptance algorithm.
Condorcet Paradox — Pairwise majority rule can cycle, so no Condorcet winner exists.