1  Introduction

This book introduces the fundamental ideas of game theory—the study of strategic interaction between rational decision‑makers. The goal is to develop intuition first, mathematics second, and insight throughout.The chapters build progressively from simple ideas like dominant strategies to more advanced concepts such as sequential games, mixed strategies, and repeated interaction.

2 What is Game Theory?

Game theory studies rational interactive decision‑making. Unlike standard optimization—where a decision affects only the outcome, game theory analyzes situations where your outcome depends on the actions of others. Examples include:

  • Athletes choosing tactics in sports
  • Businesses setting prices or advertising levels
  • Governments choosing spending, taxes, or military strategies
  • Students choosing effort levels in a group project
  • Everyday strategic choices such as which route to take or whether to cooperate

Game theory separates two parts of performance:

  1. Skill — mechanical or physical ability
  2. Strategy — anticipating and responding to others’ choices

This book focuses on the strategic part and for the most part assumes that players have the skill to execute their actions.

3 Definitions

A game arises when a person is aware that his/her actions affect another individual and that the actions of the other individual(s) affect him/her. A game has the following components:

  • Players: at least two decision makers
  • Actions: choices available to each player
  • Strategies: complete plans of action
  • Payoffs: the benefits or consequences that result from the choices
  • Rules: who moves when, what they know, and how outcomes are determined.

4 Classifying Games

Games in game theory are broadly classified by the timing of players’ actions as either simultaneous or sequential. In simultaneous-move games, players choose their strategies concurrently, without observing each other’s actions, as in the classic Prisoner’s Dilemma where two suspects decide independently whether to confess or remain silent. This setup introduces strategic uncertainty, as each player must anticipate the other’s choice based on beliefs rather than direct observation. In contrast, sequential games involve players moving in a prescribed order, with subsequent players able to condition their strategies on prior observable actions, such as in the game of chess or a Stackelberg duopoly where a leader firm sets output before followers respond. Additionally, games differ in the alignment of players’ interests: zero-sum games feature complete conflict, where one player’s gains exactly equal another’s losses (e.g., poker), while non-zero-sum games allow for mutual benefit or cooperation, as in the Battle of the Sexes where players prefer coordinating on the same action despite differing preferences.

Games may also be categorized by their duration: one-shot (or normal-form) games are played exactly once, forcing players to evaluate payoffs based solely on immediate incentives, often leading to myopic behavior like defection in a single Prisoner’s Dilemma. Repeated games, however, extend over multiple periods—either finitely or infinitely—enabling strategies that condition future play on past outcomes, such as tit-for-tat in an iterated Prisoner’s Dilemma, which fosters cooperation through the threat of retaliation or promise of reciprocity. Repetition introduces the folk theorem, which posits that a wide range of payoff profiles, including cooperative ones, can be sustained as equilibria if players are sufficiently patient (high discount factor), highlighting how dynamic interaction transforms short-term conflict into long-term gains.

A critical dimension of games concerns information availability, introducing uncertainty that shapes strategic reasoning. External uncertainty arises from exogenous factors like weather affecting crop yields in a farming game, while strategic uncertainty stems from ignorance of opponents’ past moves or concurrent decisions. Games with neither—where every player observes the full history of play at each decision node—are termed perfect information games, exemplified by tic-tac-toe. Departures yield imperfect information games. Separately, complete information assumes all players know the game’s structure, strategies, and payoffs; incomplete (or asymmetric) information occurs when players possess private knowledge, such as types or valuations (e.g., in auctions where bidders know their own value but not others’), leading to Bayesian equilibria where beliefs about hidden information guide choices.