Sequential games

Definition

Sequential games are a type of game in game theory where players make decisions one after another, rather than simultaneously. In these games, the order of moves matters and players can take into account the previous actions of others when deciding their next move. This structure allows for strategies that can exploit the timing of decisions, leading to various outcomes based on the knowledge and expectations players have about each other's actions.

5 Must Know Facts For Your Next Test

1. In sequential games, players can use previous moves to inform their future decisions, making the analysis of strategies more complex than in simultaneous games.
2. The concept of information sets is crucial, as it helps to determine what players know about others' past actions when making decisions.
3. Subgame perfect equilibrium is an important solution concept specifically for sequential games, ensuring that players' strategies are optimal at every possible point in the game.
4. These games often model real-world situations where timing and order of actions play critical roles, such as in negotiations or competition between firms.
5. Games with incomplete information add another layer of complexity, as players may not fully know the preferences or strategies of others when making their sequential moves.

Review Questions

• How do sequential games differ from simultaneous games in terms of player decision-making?
  • In sequential games, players make decisions one after another, allowing them to observe and react to the actions taken by previous players. This contrasts with simultaneous games, where all players choose their actions at the same time without knowledge of others' choices. The ability to see prior moves in sequential games creates opportunities for strategic planning and manipulation based on the behavior of opponents.
• Discuss the importance of subgame perfect equilibrium in evaluating strategies within sequential games.
  • Subgame perfect equilibrium is a refinement of Nash equilibrium specifically designed for sequential games. It requires that players' strategies not only be optimal in the overall game but also at every possible subgame that could arise. This means that even if a player makes an unexpected move earlier in the game, their strategy should still remain optimal for all subsequent stages. This concept helps ensure that strategies are coherent and viable under all possible circumstances.
• Evaluate how incomplete information impacts strategic interactions in sequential games and what implications this has for player behavior.
  • Incomplete information introduces uncertainty into sequential games, as players may not fully understand the preferences, payoffs, or strategies of their opponents. This lack of knowledge can significantly affect decision-making processes, as players must consider not only their own actions but also what they believe about others' types and potential moves. Such dynamics lead to more complex strategies and may result in bluffing or signaling behaviors that would not occur in complete information settings. As a result, understanding how incomplete information shapes behavior is crucial for predicting outcomes in real-world scenarios like negotiations or auctions.

Related terms

Extensive Form:

A representation of a game that illustrates the sequential nature of decisions using a tree structure, showing the choices available at each decision point.

Strategy: A comprehensive plan that outlines how a player will act throughout a game, considering both their own choices and the anticipated responses of other players.

Backward Induction: A method used in extensive-form games to determine optimal strategies by analyzing the game from the end back to the beginning, revealing optimal moves at each decision point.