How are extensive-form games shown with game trees?

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A colorful payoff matrix for a normal form game in game theory, showing strategy options-support, oppose, evade-for both party A and party B. Each cell contains cartoon figures representing each party's action and lists percentage payoffs for A and B. The bottom-right cell is labeled saddlepoint, highlighting the equilibrium. — game theory Table 1
The normal-form table illustrates the concept of a saddlepoint, or entry, in a payoff matrix at which the expected gain of each participant (row or column) has the highest guaranteed payoff.

In game theory, extensive-form games are used to model games that progress step by step, one move at a time. These games are represented visually using a "game tree," which maps out the structure of the interaction.1

In this representation:
* Vertices: Each turn or decision point in the game is represented as a vertex (or node) of the tree.1
* Branches: Each branch extending from a vertex represents the specific choices available to the player at that point in the game.1

By tracing these branches, the tree illustrates the sequence of moves and the resulting paths of play, allowing for a clear analysis of the decision-making process throughout the game.1