Sequential Game

Definition

A sequential game is a type of game in game theory where players make decisions one after another, rather than simultaneously. This structure allows players to observe the previous actions of others before making their own choices, which can significantly influence the strategies they adopt. The strategic implications of these games are often analyzed through extensive form representations, such as game trees, and can lead to concepts like subgame perfect equilibrium where players optimize their strategies at every possible decision point.

5 Must Know Facts For Your Next Test

1. In sequential games, players can use the knowledge of prior moves to inform their own decisions, which can lead to different outcomes compared to simultaneous games.
2. The extensive form representation allows for a clearer understanding of complex strategic interactions in sequential games.
3. Backward induction is often used to solve sequential games, where players reason backward from the end of the game to determine optimal strategies.
4. Subgame perfect equilibrium is a refinement of Nash equilibrium that requires strategies to be optimal not just for the entire game but for every subgame as well.
5. Examples of sequential games include chess and bargaining scenarios, where one player's move directly influences the options available to the next player.

Review Questions

• How does the structure of a sequential game influence player strategy compared to simultaneous games?
  • In a sequential game, the structure allows players to observe the actions taken by others before making their own decisions. This observation creates an opportunity for strategic thinking, as players can adjust their strategies based on what they see. In contrast, in simultaneous games, players must make decisions without knowing what others will do, which often leads to different strategic considerations and potential outcomes.
• Discuss the importance of subgame perfect equilibrium in evaluating strategies within sequential games.
  • Subgame perfect equilibrium plays a crucial role in assessing strategies in sequential games because it ensures that players' strategies are optimal at every possible decision point throughout the game. This concept refines the Nash equilibrium by focusing on every subgame rather than just the overall game. As a result, it helps identify strategies that not only work in theory but are also feasible in practice when players must react to earlier moves.
• Evaluate how extensive form representations contribute to our understanding of sequential games and their strategic implications.
  • Extensive form representations are vital for analyzing sequential games because they visually depict the order of moves and potential outcomes in a clear manner. By using game trees, we can trace each player's decision-making process and see how earlier choices influence later options. This graphical approach enhances our understanding of strategy formulation, allowing for deeper insights into player behavior and potential equilibria. Consequently, it becomes easier to apply concepts like backward induction and subgame perfect equilibrium in practical scenarios.

Related terms

Extensive Form Game: A representation of a game that shows the sequential nature of player decisions using a tree-like diagram, illustrating the order of moves and possible outcomes.

Nash Equilibrium: A situation in a game where no player can benefit by changing their strategy while the other players keep theirs unchanged; applicable in both simultaneous and sequential games.

Game Tree: A visual representation of the sequential moves in a game, showing the possible choices available to players at each decision point and the resulting payoffs.