Sequential games

Definition

Sequential games are a type of game in game theory where players make decisions one after another, with each player's choice depending on the previous actions taken by others. This structure allows players to consider the potential responses of their opponents when formulating their strategies. Unlike simultaneous games where players choose their actions at the same time, sequential games introduce an element of strategy that hinges on timing and foresight.

5 Must Know Facts For Your Next Test

1. Sequential games can be modeled using extensive form representations, where players' decisions are depicted as branches of a tree.
2. In sequential games, players must anticipate and respond to the choices of others, leading to strategic planning based on prior actions.
3. The concept of backward induction is often used in sequential games, where players analyze possible future actions to determine the best current action.
4. These games can be analyzed to find subgame perfect equilibria, where strategies are optimal at every point in the game.
5. Sequential games are common in negotiation scenarios where one party makes an offer and the other party responds based on that offer.

Review Questions

• How does the structure of sequential games impact strategic decision-making compared to simultaneous games?
  • The structure of sequential games greatly impacts strategic decision-making because players must consider previous actions taken by others when formulating their responses. This means that players can develop strategies based on observed behavior, allowing for deeper levels of tactical planning. In contrast, simultaneous games require players to make choices without knowledge of others' actions, often leading to more uncertainty and less informed decisions.
• Discuss the role of backward induction in solving sequential games and how it aids in determining optimal strategies.
  • Backward induction is a crucial method for solving sequential games as it involves analyzing the game from the end back to the beginning. By anticipating future decisions and outcomes, players can determine what actions would be optimal at each stage of the game. This process helps players identify not just their best response but also predicts how opponents will react to those responses, leading to more strategically sound decisions throughout the game.
• Evaluate the significance of subgame perfect equilibrium in sequential games and its implications for negotiation tactics.
  • Subgame perfect equilibrium is significant in sequential games as it ensures that strategies remain optimal at every decision point within the game. This concept is particularly important in negotiations, where parties must maintain credibility throughout discussions. By committing to strategies that are rationally optimal at each stage, negotiators can build trust and improve their chances of reaching favorable agreements. Thus, understanding subgame perfect equilibria enables negotiators to formulate consistent and effective tactics that account for potential reactions from counterparts.

Related terms

Nash Equilibrium:

A situation in which each player's strategy is optimal given the strategies chosen by other players, resulting in no player having an incentive to deviate from their chosen strategy.

Perfect Information: A scenario in which all players are fully aware of all past actions taken by other players, allowing them to make informed decisions.

Extensive Form Game: A representation of a sequential game using a tree structure that illustrates the various possible moves and their outcomes at each stage of the game.