# Game Theory

**Type:** Concept  
**Domain:** Applied Mathematics  
**Codex URL:** /mathematics/applied/game-theory/  
**Entry status:** Live — v1.0 (2026-05-27)

## Summary
Mathematical study of strategic decision-making. Founded by von Neumann and Morgenstern (1944).

## Prisoner's Dilemma
Both betray = dominant strategy for each player individually, even though mutual silence is better for both jointly.

## Minimax theorem (von Neumann, 1928)
In finite 2-player zero-sum games, optimal strategies minimizing maximum loss always exist — predates and founds game theory.

## Repeated games
Axelrod's tournaments (1980): simple "Tit-for-Tat" strategy outperforms complex strategies.

## Cooperative game theory
Shapley value (1953) — fair division of coalition gains.

## Mechanism design
"Reverse game theory" — Hurwicz, Maskin, Myerson (2007 Nobel).

## Evolutionary game theory
Maynard Smith & Price (1973) — evolutionarily stable strategies.

## Computational complexity
Finding Nash equilibria is PPAD-complete (Daskalakis, Goldberg, Papadimitriou, 2009).

## Sources
### Tier 1
- von Neumann, J. and Morgenstern, O. (1944). *Theory of Games and Economic Behavior*.
- Fudenberg, D. and Tirole, J. (1991). *Game Theory*.
### Tier 2
- Axelrod, R. (1984). *The Evolution of Cooperation*.

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*Mathematics Codex entry v1.0 — added 2026-05-27 — thecodex.expert/mathematics/*