Game Theory: Discrete & Continuous

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.

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.

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.