Sequential game

Definition

A sequential game is a type of game in game theory where players make decisions one after another, with each player being aware of the previous players' choices. This format allows players to strategize based on the actions taken by others, leading to different outcomes compared to simultaneous games where all decisions are made at the same time. In sequential games, the order of moves can significantly influence the strategies and payoffs of the players involved.

5 Must Know Facts For Your Next Test

1. Sequential games can be analyzed using extensive form representation, which illustrates players' choices at different stages.
2. In sequential games, later players can adapt their strategies based on earlier actions, leading to a dynamic interplay between choices.
3. The concept of perfect information applies to sequential games where all players are fully aware of prior moves made by others.
4. Sequential games often lead to strategic commitments, where earlier players can set the stage for future actions by making certain decisions.
5. Backward induction is commonly used in sequential games to find the optimal strategies by reasoning backwards from the potential end results.

Review Questions

• How does the structure of a sequential game impact player decision-making compared to simultaneous games?
  • In a sequential game, players make decisions one after another, which allows them to observe and react to the choices made by previous players. This structure contrasts with simultaneous games, where all players must make decisions without knowledge of others' actions. The ability to adjust strategies based on prior moves can lead to different outcomes and potentially more favorable results for players who move later.
• Discuss how backward induction is applied in solving sequential games and its significance in determining optimal strategies.
  • Backward induction involves analyzing a sequential game by starting from the end and determining optimal moves at each stage moving backwards. This method is significant because it helps identify the best strategies for players, considering that later players have the advantage of knowing prior moves. By employing backward induction, players can foresee potential outcomes and strategically commit to decisions that maximize their payoffs.
• Evaluate the implications of perfect information in sequential games and how it influences strategic interactions among players.
  • In sequential games characterized by perfect information, all players are fully aware of previous actions taken by others, which dramatically influences their strategic interactions. This transparency allows for more informed decision-making as players can consider past moves when crafting their own strategies. The presence of perfect information can lead to more predictable behaviors and equilibrium outcomes, as players anticipate each other's responses based on the known history of moves.

Related terms

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

Extensive Form Game: A representation of a sequential game that uses a tree diagram to show the different possible moves and outcomes.

Backward Induction: A method used in sequential games to determine optimal strategies by analyzing the game from the end back to the beginning.