Payoffs, Strategies, and the Game Matrix
Core vocabulary and reading skills for two-player payoff matrices, framed for game designers.
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Questions Covered in This Set
10 cards to master
What are the three ingredients of a game in game theory?
Players (decision-makers), strategies (available choices), and payoffs (numbers showing how much each player likes each outcome).
What is a payoff?
A utility number standing in for how desirable an outcome is to a player — higher is better. It can be gold, points, territory, or any measure of what the player actually wants.
What is a payoff matrix (normal form)?
A grid representing a simultaneous-move game: row player's strategies as rows, column player's as columns, each cell holding a pair of payoffs.
In a cell written (3, 5), which number belongs to whom?
The first number (3) is the row player's payoff; the second (5) is the column player's payoff.
When can a game be written in normal form?
When players choose simultaneously — or in ignorance of each other's choice, which is equivalent.
In the Prisoner's Dilemma loot table, why is Steal a red flag for a designer?
Steal beats Share in every column (5>3 and 1>0), so it dominates — the choice isn't really a choice.
What does it mean if your row payoffs are identical across all columns?
The other player's choice is irrelevant to you — you've designed a solitaire game with extra steps.
What's wrong with a matrix where one cell dwarfs all others?
Players beeline for it and the rest of the matrix becomes decoration; there's no real tension.
What are three designer questions to ask of a matrix?
Is any row better no matter what the opponent does? Are payoffs interesting or lopsided? Does tension come from interaction rather than luck?
What makes the two-door coordination game (2,2)/(0,0)/(0,0)/(3,3) interesting?
No row dominates — whether Left is good for you depends entirely on the other player's choice, creating genuine interaction.