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Economics & Markets

Game Theory: Discrete & Continuous

Model #0689Category: Economics & MarketsDepth to apply:

By Updated 3 sources

4 min read

Contents

  1. 1. Core Idea
  2. 2. How to See It
  3. 3. How to Use It
  4. 4. Founders & Leaders
  5. 5. Connected Models
  6. 6. One Key Quote
  7. 7. Summary & Further Reading
Economics & Markets
Section 1

Core Idea

In discrete games, players choose from a finite set of actions (e.g. cooperate or defect, enter or stay out). In continuous games, they choose from a continuum (e.g. price, quantity, effort). Continuous games often yield smooth best-response functions and equilibria found by calculus; discrete games yield payoff matrices and corner solutions. Many real situations are hybrid: e.g. discrete "in or out" plus continuous "how much." For founders, the takeaway is to match the model to the decision: if the lever is "how much" (price, spend, capacity), think continuous; if it's "yes or no" or "which option," think discrete. Mix both when the strategy has both dimensions.

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Section 2

How to See It

Pricing
You're seeing Discrete & Continuous when you set a price (continuous) but also decide whether to be in a segment or channel (discrete). The combined choice is a hybrid game.
Strategy
You're seeing it when entry and exit are discrete ("do we enter this market?") while scale and investment are continuous ("how much do we invest?"). Model both layers.
Negotiation
You're seeing it when the deal has binary clauses (walk away or not) and continuous terms (price, duration). Best response in the continuous part can be derived; the discrete part is threshold logic.
Section 3

How to Use It

Separate the discrete and continuous parts of the decision. For the continuous part, use marginal reasoning and best-response curves where possible. For the discrete part, use thresholds and payoff comparison. When they interact (e.g. "enter if expected profit > 0, then choose quantity"), solve the continuous subgame first, then the discrete choice.
Decision filter
"Is this a "how much" question (continuous) or a "which one" / "yes or no" question (discrete)? Model each with the right tool, then combine."
As a founder
In pricing and capacity decisions, treat level as continuous and use marginal logic; in market or product choices, treat as discrete and use payoff matrices or thresholds. When both appear (e.g. "which markets and how much in each"), solve the continuous allocation conditional on the discrete choices.
Section 5

Founders & Leaders

John MaloneChairman, Liberty Media; cable and media strategist
Malone repeatedly combined discrete moves (which assets to buy or sell, which regulations to fight) with continuous ones (how much to bid, how much to invest). Founders can copy the split: decide the discrete strategic moves first, then optimise the continuous variables (price, scale) within each branch.
Section 7

Connected Models

Reinforces
Game Theory
Discrete and continuous games are both game-theoretic; they differ in the strategy set. Same players and payoffs; different mathematical machinery (matrices vs calculus) and often different equilibrium characterisation.
Reinforces
Marginal Cost/Benefit
In continuous games, equilibrium often satisfies marginal conditions (e.g. marginal revenue = marginal cost). The discrete vs continuous lens tells you when to use marginal analysis (continuous) vs payoff comparison (discrete).
Leads-to
Optimization
Continuous strategy choices are often solved by optimisation (first-order conditions). Discrete choices are solved by comparison. Combining them is two-stage optimisation: optimise within each discrete scenario, then choose the scenario.
Section 8

One Key Quote

"Games may be defined by whether strategies are finite (discrete) or drawn from a continuum. The solution methods differ; the principle of equilibrium applies to both."
— John von Neumann & Oskar Morgenstern, Theory of Games and Economic Behavior
Section 11

Summary & Further Reading

Discrete games: finite actions; use payoff matrices and thresholds. Continuous games: continuous choices; use calculus and best-response functions. Many decisions are hybrid — separate the discrete and continuous parts, solve each, then combine.
01
Theory of Games and Economic Behavior — von Neumann & Morgenstern (1944)
Book
Foundational treatment of discrete and continuous strategy sets.
02
Game Theory: Analysis of Conflict — Roger Myerson (1991)
Book
Unified treatment of discrete and continuous games in economics.
03
Microeconomic Theory — Mas-Colell, Whinston, Green
Book
Nash equilibrium in discrete and continuous games; applications.

Why this matters next

mental modelsScale

Game Theory: Discrete & Continuous applied the Scale mental model

mental modelsMarginal Cost/Benefit

Game Theory: Discrete & Continuous applied the Marginal Cost/Benefit mental model

mental modelsCost

Game Theory: Discrete & Continuous applied the Cost mental model

mental modelsGame Theory

Game Theory: Discrete & Continuous applied the Game Theory mental model

mental modelsNash Equilibrium

Game Theory: Discrete & Continuous applied the Nash Equilibrium mental model

mental modelsMechanism Design

Game Theory: Discrete & Continuous applied the Mechanism Design mental model

Frequently asked questions

What is Game Theory: Discrete & Continuous?

Game Theory: Discrete & Continuous is a mental model used for better thinking and decision-making.

How do you apply Game Theory: Discrete & Continuous?

To apply Game Theory: Discrete & Continuous, identify situations where this framework is relevant, then use it as a lens to evaluate your options and decisions. The model is most useful when combined with other complementary mental models.

What category does Game Theory: Discrete & Continuous fall under?

Game Theory: Discrete & Continuous falls under the Economics & Markets category of mental models. Other models in this category can be found on the Economics & Markets hub page.

Why is Game Theory: Discrete & Continuous important?

Game Theory: Discrete & Continuous is important because it provides a structured way to think about problems that would otherwise be approached with intuition alone. Understanding this model helps you avoid common reasoning errors and make better decisions.

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