Game Trees

Game Theory · Axiom Academy

Unit 3: Sequential Games - Understanding the extensive form representation of strategic interactions A game tree contains five essential components: Initial node: The starting point where the game begins (also called the root) Decision nodes: Points where a player must choose an action Branches: Lines representing available actions from each decision node Terminal nodes: End points where the game concludes Payoffs: Numerical outcomes assigned to each terminal node Watch as we construct a basic game tree to see how these components fit together: 2. Decision Nodes and Player Assignments At each decision node, we must specify which player is making the choice. This is crucial because different players have different preferences and objectives. The order of play matters significantly. In a two-player game: The first mover (Player 1) chooses at the initial node The second mover (Player 2) observes Player 1's action and responds Additional rounds may alternate between players Each player anticipates future responses when choosing their action Let's see how players are assigned to nodes in a sequential entry game: 3. Actions, Branches, and Payoffs Each branch emanating from a decision node represents a distinct action available to the player at that node. The labels on these branches describe the strategic choices. For a game with n players, each terminal node has an n -tuple of payoffs: The first coordinate is Player 1's payoff The second coordinate is Player 2's payoff

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