Sequential games

Definition

Sequential games are a type of game in game theory where players make decisions one after another, rather than simultaneously. This structure allows for strategic interactions where players can observe the actions of previous players before making their own decisions, leading to a more dynamic understanding of strategies and outcomes. Such games often involve the analysis of how players can optimize their choices based on the responses of others in the sequence.

5 Must Know Facts For Your Next Test

1. In sequential games, the order of play is crucial, as it allows players to respond to previous actions, which can affect their own decision-making.
2. The concept of subgame perfect equilibrium is central to sequential games, where players choose strategies that are optimal not just for the overall game but also for every possible subgame.
3. Players in sequential games often use strategies that incorporate beliefs about how other players will act based on their observed choices.
4. Examples of sequential games include chess and bargaining scenarios, where each player's move directly influences subsequent decisions.
5. Understanding sequential games is important in many fields such as economics, political science, and negotiation theory because they highlight the importance of timing and information.

Review Questions

• How does the structure of sequential games impact players' strategic decision-making?
  • The structure of sequential games significantly impacts strategic decision-making because players have the advantage of observing previous actions before making their own choices. This allows them to adapt their strategies based on what others have done, creating a dynamic environment. Players can incorporate their expectations about other players' reactions into their plans, which often leads to more complex and nuanced decision-making compared to simultaneous games.
• What is subgame perfect equilibrium and why is it essential in analyzing sequential games?
  • Subgame perfect equilibrium is an important concept in analyzing sequential games as it ensures that players' strategies are optimal at every point in the game, not just at the beginning. This means that each player's strategy must be credible and lead to optimal outcomes even when considering any potential subgame that might arise after certain moves. It helps identify strategies that can withstand scrutiny and predicts outcomes more accurately in strategic interactions.
• Evaluate how knowledge of past actions influences future decisions in a sequential game context, using an example.
  • In a sequential game context, knowledge of past actions plays a crucial role in shaping future decisions because it allows players to make informed choices based on observed behavior. For example, consider a negotiation scenario where one party makes an initial offer; the other party can then adjust their counteroffer based on this initial move. If they perceive the first offer as too low, they may decide to offer a higher counterproposal. This illustrates how players' strategies evolve based on what has been previously communicated and how understanding these dynamics can lead to more favorable outcomes.

Related terms

Extensive form: A representation of a game that shows the sequential nature of player decisions, typically illustrated through a tree structure.

Backwards induction: A method used to solve sequential games by analyzing the game from the end back to the beginning, determining optimal strategies for players based on future actions.

Nash equilibrium: A concept in game theory where no player can benefit by changing their strategy while the other players keep theirs unchanged, applicable in both simultaneous and sequential games.