An extensive form game is a representation of a strategic situation that allows players to make decisions at various points in time, depicted through a tree-like structure that illustrates the sequence of moves, choices, and potential outcomes. This format helps analyze strategies in situations where timing and order of moves matter, connecting key concepts like backward induction, sequential rationality, and subgame perfect equilibrium, while also illustrating credible threats and promises as well as the iterative elimination of dominated strategies.
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Extensive form games are often represented using game trees that visually display the players, their possible actions, and the resulting outcomes.
The concept of backward induction is crucial for determining optimal strategies in extensive form games by evaluating decisions from the end of the game back to the start.
In extensive form games, a subgame is any part of the game that can be viewed as a game itself, allowing analysis of strategies in smaller segments.
Credible threats and promises in extensive form games are essential for influencing opponents' strategies and decision-making processes.
Iterative elimination of dominated strategies can simplify extensive form games by removing options that are never optimal, making it easier to identify viable strategies.
Review Questions
How does backward induction apply to extensive form games, and what does it reveal about player strategies?
Backward induction is used in extensive form games to derive optimal player strategies by analyzing the game's possible outcomes starting from the final moves. It reveals how players should react based on expected responses from their opponents at each decision point. This method ensures that players choose actions that lead to the best possible outcomes considering future possibilities.
Discuss the importance of subgame perfect equilibrium in ensuring rational play within extensive form games.
Subgame perfect equilibrium is vital because it refines Nash equilibrium by ensuring that players' strategies are optimal not just overall but also within every possible subgame. This concept guarantees that even if a player deviates from their original plan during the game, their actions will still align with optimal strategies in every scenario they might face. It emphasizes that rational play must consider all potential subgames when making decisions.
Evaluate how credible threats and promises can influence outcomes in extensive form games and relate this to strategic decision-making.
Credible threats and promises are pivotal in shaping player interactions in extensive form games as they can alter opponents' perceptions and strategies. When a threat or promise is perceived as credible, it can compel opponents to adjust their decisions to avoid unfavorable outcomes. This dynamic showcases how strategic decision-making hinges on players' beliefs about one another's future actions, thereby significantly impacting the overall game results.
Related terms
Backward induction: A method used in extensive form games to determine optimal strategies by reasoning backward from the end of the game to the beginning.
Subgame perfect equilibrium: A refinement of Nash equilibrium applicable to extensive form games where players' strategies constitute a Nash equilibrium in every subgame.
Dominated strategy: A strategy that results in a worse outcome for a player than another strategy, regardless of what the other players do.