Dynamic Games

Definition

Dynamic games are a class of games where players make decisions at different points in time, taking into account the actions and reactions of other players over the course of the game. These games are characterized by the sequential nature of decision-making and often utilize extensive form representation, allowing for strategies that evolve as the game progresses. The concepts of equilibrium, beliefs, and information updates become crucial in understanding how players interact within these dynamic frameworks.

5 Must Know Facts For Your Next Test

1. In dynamic games, players consider not only their current choices but also how their decisions will impact future interactions and outcomes.
2. Subgame perfect equilibrium is a refinement of Nash equilibrium specifically applicable to dynamic games, ensuring that players' strategies are optimal at every possible stage of the game.
3. Players in dynamic games often update their beliefs about other players’ strategies as they observe actions taken during the game, which can influence their own strategy choices.
4. Dynamic games can involve both complete and incomplete information, affecting how players form expectations and respond to one another's actions.
5. The structure of dynamic games allows for complex strategies, including threats, promises, and commitment tactics that can shape the course of play.

Review Questions

• How do dynamic games differ from static games in terms of decision-making and strategy formulation?
  • Dynamic games differ from static games primarily in that they allow players to make decisions over time, considering how past actions affect future outcomes. In static games, players choose their strategies simultaneously without knowledge of others' choices. Conversely, in dynamic games, the sequential nature means that players can adapt their strategies based on the observed actions of others, leading to more complex interactions and potential strategy refinements over multiple rounds.
• Discuss the importance of subgame perfect equilibrium in evaluating strategies within dynamic games.
  • Subgame perfect equilibrium is crucial in dynamic games as it ensures that players' strategies are optimal not just at the beginning of the game but at every possible stage or subgame. This concept requires that players consider future moves and responses, making it a more stringent condition than Nash equilibrium. By applying backward induction, players can identify credible threats and commitments that shape their strategies effectively throughout the game.
• Evaluate how beliefs and updating impact decision-making processes in dynamic games with incomplete information.
  • In dynamic games with incomplete information, players must constantly update their beliefs based on observed actions and signals from other participants. This belief updating influences how they perceive potential strategies employed by opponents, leading to adjustments in their own tactics. Perfect Bayesian equilibrium provides a framework for understanding this process, emphasizing that players not only react to observable actions but also infer hidden information about others’ types or intentions, which ultimately impacts their decision-making trajectories.

Related terms

Extensive Form Game: A representation of a game that depicts players' choices at various decision points, often using a game tree to illustrate possible moves and outcomes.

Nash Equilibrium: A situation in a game where no player can benefit by changing their strategy while the other players keep their strategies unchanged.

Backward Induction: A method used in extensive form games to determine optimal strategies by analyzing the game from the end back to the beginning.