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 means that later players can observe the actions of those who went before them, allowing for strategic responses based on earlier choices. The order of moves and the ability to react to previous actions are crucial features that distinguish sequential games from static games.

5 Must Know Facts For Your Next Test

1. In sequential games, players have the advantage of being able to observe previous actions, which can lead to different strategies compared to simultaneous games.
2. The concept of perfect information refers to a scenario in sequential games where all players are fully aware of all previous actions taken in the game.
3. Sequential games can be represented in extensive form, where each player's decision points are laid out in a tree-like structure, showing possible outcomes based on choices made.
4. Backward induction is often used to find optimal strategies in sequential games, allowing players to anticipate others' moves and make informed decisions.
5. The notion of commitment plays a significant role in sequential games; a player’s ability or inability to commit to a certain action can influence the strategies and outcomes of the game.

Review Questions

• How does the ability to observe previous actions impact the strategy choices of players in a sequential game?
  • In a sequential game, players make their decisions with the knowledge of earlier moves made by other players. This observation allows them to adjust their strategies accordingly, potentially leading to more advantageous outcomes. For example, if one player makes a move that signals aggression, subsequent players may choose more defensive strategies or react differently based on that initial action, demonstrating how strategic planning evolves as the game progresses.
• Compare and contrast sequential games with simultaneous games in terms of information availability and strategic decision-making.
  • Sequential games differ from simultaneous games primarily in terms of information availability. In sequential games, players act one after another with full knowledge of previous actions, enabling them to tailor their strategies based on what has transpired. In contrast, simultaneous games require players to make decisions without knowing their opponents' choices, leading to greater uncertainty and often requiring different strategic approaches such as mixed strategies. This fundamental difference affects how players assess risks and potential payoffs in each type of game.
• Evaluate the importance of backward induction in finding equilibrium strategies in sequential games and its implications for real-world decision-making.
  • Backward induction is crucial for solving sequential games as it allows players to anticipate future moves and determine optimal strategies by analyzing potential outcomes from the end back to the beginning. This method not only helps in identifying Nash equilibria within these games but also has significant real-world implications, such as in negotiations or competitive business strategies. By understanding how others might react based on prior actions, individuals can craft more effective plans that take into account both immediate and future consequences, enhancing decision-making efficiency.

Related terms

Nash Equilibrium: A situation in a game where no player can benefit from changing their strategy while the other players keep theirs unchanged.

Extensive Form Game: A representation of a game that shows the order of play and the possible moves at each decision point, often depicted using a tree structure.

Backward Induction: A method used to solve sequential games by analyzing the game from the end to the beginning, determining optimal strategies for each player.