Sequential games

Definition

Sequential games are strategic interactions where players make decisions one after another, with later players having knowledge of the earlier players' choices. This structure allows players to plan their strategies based on the observed actions of others, making it essential for understanding strategic behavior in dynamic situations. The key characteristic of sequential games is that they involve a clear order of play, which distinguishes them from simultaneous games.

5 Must Know Facts For Your Next Test

1. Sequential games can be represented using extensive form, which allows for a visual depiction of the order of moves and decision points.
2. Backward induction is a common method used to solve sequential games, where players reason backward from the end of the game to determine optimal strategies.
3. In sequential games, the concept of subgame perfection helps ensure that players' strategies are optimal not just for the overall game but for every possible subgame.
4. Information asymmetry can play a significant role in sequential games, as players may not know all details about others' strategies or payoffs.
5. Real-world examples of sequential games include negotiations, pricing strategies in business, and certain political strategies.

Review Questions

• How does backward induction help players strategize in sequential games?
  • Backward induction helps players strategize in sequential games by allowing them to think backward from the end of the game to identify optimal actions at each stage. By considering how later moves will respond to earlier actions, players can devise strategies that maximize their outcomes based on expected responses. This reasoning process ensures that decisions made at every point are aligned with achieving the best possible payoff by anticipating future choices.
• Discuss how perfect information influences player decisions in sequential games compared to those with imperfect information.
  • Perfect information significantly impacts player decisions in sequential games because it allows each player to know all previous moves made by others, leading to more informed strategic choices. In contrast, when players operate under conditions of imperfect information, they must make decisions based on incomplete knowledge, which can lead to uncertainty and potentially suboptimal strategies. This difference underscores the importance of information in shaping outcomes and strategies within sequential game frameworks.
• Evaluate the role of subgame perfection in determining stable outcomes in sequential games and provide an example.
  • Subgame perfection plays a critical role in determining stable outcomes in sequential games by ensuring that players' strategies remain optimal not only for the entire game but also for every possible subgame. This concept eliminates non-credible threats and encourages players to commit to strategies that are sustainable throughout the game. For example, in a bargaining scenario where one player must offer concessions to reach an agreement, subgame perfection would require that any proposed offer must be rationally acceptable at all points in the negotiation process to avoid breakdowns in discussions.

Related terms

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

Perfect Information: A scenario in a game where all players have complete knowledge of all previous actions taken by other players when making their decisions.

Extensive Form Games: A way to represent games using a tree structure that shows the order of moves, possible actions at each decision point, and the payoffs for each outcome.