Dynamic game

Definition

A dynamic game is a type of game in which players make decisions at various points in time, and the outcome of their choices can depend on the history of play. This concept is crucial for understanding how strategies evolve over time, as players anticipate future moves and adjust their current actions accordingly. In these games, the sequence of actions and the ability to react to previous moves play significant roles in determining the strategies players will adopt.

5 Must Know Facts For Your Next Test

1. Dynamic games involve players making decisions at different stages, allowing for more complex interactions compared to static games.
2. The history of actions taken in a dynamic game influences current decisions, making it essential for players to consider past moves while strategizing.
3. Players may use strategies like threats or promises based on anticipated future responses from their opponents in dynamic games.
4. Dynamic games can be modeled using extensive form representations, which clearly show the sequence of moves and possible outcomes.
5. An important concept in dynamic games is the idea of equilibrium, where players reach a stable strategy profile that takes into account future decisions.

Review Questions

• How does the concept of history influence player decision-making in dynamic games?
  • In dynamic games, the history of previous actions impacts current decision-making significantly. Players consider what has happened before when determining their next moves, leading them to strategize based on past behavior and potential future reactions. This historical context creates a layered approach to strategy, where players may adjust their plans based on observed tactics from others, making each move more strategic and calculated.
• Discuss how subgame perfect equilibrium differs from regular Nash equilibrium in the context of dynamic games.
  • Subgame perfect equilibrium is a refinement of Nash equilibrium specifically designed for dynamic games. While a Nash equilibrium only requires that no player has an incentive to deviate from their strategy given others' strategies at any point, subgame perfect equilibrium demands that this holds true in every subgame as well. This means players must formulate their strategies considering not just the overall game but also how they would respond optimally at every point along the way, leading to more robust strategic planning.
• Evaluate the role of backward induction in solving dynamic games and its implications for strategic thinking.
  • Backward induction plays a critical role in solving dynamic games by allowing players to analyze potential outcomes starting from the end of the game and working backward. This method helps identify optimal strategies by considering how future decisions will affect earlier ones. By applying backward induction, players are encouraged to think strategically about how their current actions will influence subsequent moves by themselves and others, ultimately refining their approach to achieving desired outcomes within the game's framework.

Related terms

Extensive Form Game: A representation of a game that illustrates the sequential nature of players' decisions using a tree structure, showing possible moves, outcomes, and payoffs.

Subgame Perfect Equilibrium:

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

Backward Induction: A method used to solve dynamic games by analyzing the game from the end to the beginning, determining optimal strategies based on future consequences.