Suppose that player B rather than player A gets to move...

Suppose that player $\mathrm{B}$ rather than player A gets to move first in the sequential game described in this chapter. Draw the extensive form of the new game. What is the equilibrium for this game? Does player B prefer to move first or second?

Key Concepts

Extensive Form Game

An extensive form game represents a strategic situation using a tree structure that outlines the order of moves, the points at which players make decisions, the available actions at each decision node, and the outcomes or payoffs associated with each terminal node. This format is especially useful for sequential games where the sequence and timing of moves are crucial to understanding the players’ strategies.

Sequential Game

Sequential games are those in which players make decisions one after another rather than simultaneously. Each player, when making a decision, is typically aware of the earlier moves, allowing strategies to be contingent on previous actions. This sequentiality is fundamental in analyzing how the order of moves might affect the strategy and outcome.

Subgame Perfect Equilibrium

A subgame perfect equilibrium is a refinement of the Nash equilibrium concept specifically designed for dynamic games with a sequential structure. It requires that players' strategies form a Nash equilibrium in every subgame of the original game. This concept helps eliminate non-credible threats and is typically derived using backward induction for a consistent resolution at every stage of the game.

Backward Induction

Backward induction is a method used to solve sequential games by analyzing the game tree from the terminal nodes backward to the initial node. By determining the optimal strategy at each decision node, players can anticipate and plan for future moves, ensuring that their overall strategy is optimal at every stage. This process is essential for establishing a subgame perfect equilibrium in sequential settings.

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