Dynamic game

Definition

A dynamic game is a type of strategic interaction where players make decisions at different points in time, taking into account the actions of others and the evolving nature of the game. In these games, the timing of moves can affect players' strategies and payoffs, leading to complex outcomes that are often modeled using backward induction or subgame perfection. Players must consider not only their current choices but also how their actions will influence future decisions and the overall trajectory of the game.

5 Must Know Facts For Your Next Test

1. Dynamic games can involve both sequential and simultaneous moves, requiring players to adapt their strategies based on previous actions.
2. The concept of discounting future payoffs is crucial in dynamic games, as players must weigh immediate benefits against long-term consequences.
3. Dynamic games often lead to strategic behavior like commitment, where players can signal intentions to influence others' future decisions.
4. The ability to observe other players' actions in real-time can change how strategies are formulated in dynamic games compared to static games.
5. Examples of dynamic games include auctions, bargaining scenarios, and many economic interactions where timing and sequence matter.

Review Questions

• How does a dynamic game differ from a static game in terms of player strategy and decision-making?
  • In a dynamic game, players make decisions over time and consider how their current actions will influence future moves by themselves and others. This contrasts with static games, where all players choose their strategies simultaneously without considering future implications. The sequential nature of dynamic games allows for strategies that can evolve as the game progresses, which is not possible in static settings.
• Discuss the importance of backward induction in solving dynamic games and provide an example of its application.
  • Backward induction is crucial for finding equilibria in dynamic games by reasoning backward from the game's end. It allows players to determine optimal strategies based on expected future moves. For example, in a two-stage bargaining game, one player may offer a deal knowing that if rejected, they will have to make a less favorable offer in the next stage. By analyzing outcomes backward, players can craft more effective initial offers.
• Evaluate the role of commitment strategies in dynamic games and how they can affect player behavior and outcomes.
  • Commitment strategies play a significant role in dynamic games by allowing players to credibly signal their intentions or capabilities, thus influencing opponents' decisions. For instance, in a dynamic pricing game, a firm might commit to a low price for an extended period to deter competitors from entering the market. Such commitments can reshape the strategic landscape, leading to more favorable outcomes for the committing player by altering expectations and reactions from others.

Related terms

Subgame Perfect Equilibrium:

A refinement of Nash equilibrium applicable in dynamic games, where players' strategies constitute a Nash equilibrium in every subgame.

Backward Induction: A method used to solve dynamic games by analyzing the game from the end to the beginning, allowing players to anticipate future moves.

Repeated Game: A situation where the same game is played multiple times, allowing players to build strategies based on past actions and outcomes.