Sequential games

Definition

Sequential games are strategic interactions where players make decisions one after another, rather than simultaneously. In these games, the order of play is crucial because the decisions made by earlier players can influence the choices available to those who act later. This setup allows for deeper strategic reasoning and planning, particularly through techniques like backward induction.

5 Must Know Facts For Your Next Test

1. In sequential games, players have the opportunity to react to previous players' moves, which can lead to different outcomes than in simultaneous games.
2. The analysis of sequential games often requires constructing a game tree that visually represents all possible actions and outcomes.
3. Backward induction helps players determine their best responses by considering what future players will do in reaction to current choices.
4. Common examples of sequential games include chess and bargaining situations where one player makes an offer that the other can accept or reject.
5. The concept of subgame perfection is essential in sequential games, ensuring that players' strategies are optimal not just for the whole game but also for every possible subgame.

Review Questions

• How does the order of play in sequential games affect strategic decision-making compared to simultaneous games?
  • In sequential games, the order of play significantly impacts strategic decision-making since players can observe and react to the actions of those who move before them. This allows later players to adjust their strategies based on earlier moves, often leading to more informed and potentially advantageous decisions. In contrast, simultaneous games do not allow for this level of adaptation since all players choose their actions without knowing what others will do.
• Discuss how backward induction is applied in sequential games and why it is important for determining optimal strategies.
  • Backward induction is applied in sequential games by analyzing possible future outcomes starting from the last possible moves and working backwards to identify optimal strategies at each decision point. This method is crucial because it allows players to anticipate the reactions of others based on future choices and helps them make more informed decisions. By considering how later players will respond to their actions, earlier players can select strategies that maximize their chances of achieving favorable outcomes.
• Evaluate the implications of subgame perfection in sequential games and how it enhances the stability of strategies within these games.
  • Subgame perfection implies that a player's strategy must be optimal not only for the entire game but also for every possible subgame that could arise during play. This enhances the stability of strategies because it ensures that if a game reaches any point in its sequence, players will still have rational and strategic responses based on prior moves. It prevents players from making threats or promises that would not hold true in subsequent stages of the game, leading to more credible strategies and ultimately more predictable outcomes.

Related terms

Backward induction: A method used in sequential games where players analyze the game by starting from the end and determining optimal strategies moving backward to the initial decision.

Extensive form game: A representation of a game that shows the sequence of moves, choices available at each move, and the outcomes, often illustrated using a tree structure.

Nash equilibrium: A concept where each player's strategy is optimal given the strategies of all other players, meaning no player has anything to gain by changing their own strategy unilaterally.