This topic covers the basic concepts of game theory, including the definition of a game, players, strategies, payoffs, and the types of games studied in game theory.
Introduction to Game Theory
Key concepts, definitions, and examples for a quick yet comprehensive overview.
1. What Is Game Theory?
- Definition – The mathematical study of strategic interaction among rational decision‑makers (players).
- Goal – Predict outcomes when each participant’s payoff depends on the choices of others.
- Fields of Application – Economics, political science, biology, computer science, psychology, engineering, and everyday life (e.g., negotiations, auctions, sports).
2. Basic Terminology
| Term |
Meaning |
| Player |
An individual or entity that makes a decision. |
| Strategy |
A complete plan of action covering every possible situation a player may face. |
| Pure Strategy |
A deterministic choice (e.g., “cooperate” or “defect”). |
| Mixed Strategy |
A probabilistic combination of pure strategies (e.g., 70 % cooperate, 30 % defect). |
| Payoff |
Numerical reward (utility) a player receives from a particular outcome. |
| Game |
The formal description of players, strategies, and payoffs. |
| Normal‑Form (Strategic) Representation |
Matrix/table showing payoffs for each strategy profile. |
| Extensive‑Form Representation |
Decision tree that captures the order of moves, chance events, and information sets. |
| Information Set |
The set of decision nodes a player cannot distinguish between when making a move. |
| Dominant Strategy |
A strategy that yields a higher payoff than any other, regardless of opponents’ actions. |
| Nash Equilibrium (NE) |
A profile of strategies where no player can improve their payoff by unilaterally deviating. |
| Pareto Efficiency |
An outcome where no player can be made better off without making another worse off. |
| Zero‑Sum Game |
One player’s gain equals the other’s loss; total payoff sums to zero. |
| Cooperative vs. Non‑Cooperative |
Cooperative: players can form binding agreements; Non‑cooperative: only self‑enforcing strategies matter. |
3. Classic Example: The Prisoner’s Dilemma
|
Partner Cooperates |
Partner Defects |
| You Cooperate |
(3, 3) |
(0, 5) |
| You Defect |
(5, 0) |
(1, 1) |
- Dominant strategy: Defect (higher payoff regardless of partner’s move).
- Nash equilibrium: (Defect, Defect) → (1, 1).
- Pareto‑optimal outcome: (Cooperate, Cooperate) → (3, 3) – better for both but not stable without enforcement.
4. Types of Games
| Category |
Description |
Typical Example |
| Simultaneous‑move |
Players choose actions without knowing others’ choices. |
Prisoner’s Dilemma, Rock‑Paper‑Scissors |
| Sequential‑move |
Players act one after another; later players observe earlier moves (or part of them). |
Chess, Stackelberg competition |
| Static vs. Dynamic |
Static: single‑period interaction; Dynamic: multiple periods, possibly with discounting. |
One‑shot auction vs. repeated bidding |
| Complete vs. Incomplete Information |
Complete: all payoff functions known; Incomplete: some private information (types). |
Standard games vs. signaling games |
| **Perfect vs. Imperfect |
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