Interim

Definition

In game theory, 'interim' refers to the state of knowledge or beliefs that players have about uncertain elements before they make decisions, typically in scenarios where information is incomplete. This concept is crucial for understanding how players form strategies when they don't have complete information about other players' types or actions, which is a central aspect of Bayesian Nash equilibrium.

5 Must Know Facts For Your Next Test

1. Interim knowledge is distinct from 'ex ante' knowledge, which refers to what players know before any actions are taken.
2. In interim situations, players have subjective beliefs about the distribution of types among the other players.
3. The concept of interim is essential in defining the strategies that rational players will adopt in games with incomplete information.
4. Interim beliefs can lead to different equilibria depending on how players update their beliefs after observing actions taken during the game.
5. Players’ interim information influences their payoff structures and ultimately affects the overall outcome of the game.

Review Questions

• How does interim knowledge impact decision-making strategies in a game with incomplete information?
  • Interim knowledge significantly impacts how players formulate their strategies in games characterized by incomplete information. Players must rely on their beliefs about other players' types to make informed decisions. The strategies they choose will often reflect their expectations regarding the possible actions of other players based on this interim knowledge. Consequently, this leads to diverse strategic outcomes depending on how accurately players assess each other's types.
• Compare and contrast interim knowledge with ex ante knowledge in the context of strategic decision-making.
  • Interim knowledge differs from ex ante knowledge primarily in terms of timing and certainty. Ex ante knowledge is what players know prior to any decisions being made, which is often more concrete. In contrast, interim knowledge involves subjective beliefs about other players' types after some actions have occurred but before final outcomes are revealed. This distinction affects how players approach strategy formation; ex ante considerations might lead to different risk assessments compared to the uncertain landscape shaped by interim beliefs.
• Evaluate the role of interim beliefs in achieving a Bayesian Nash equilibrium in games with incomplete information.
  • Interim beliefs play a critical role in reaching a Bayesian Nash equilibrium as they provide the foundation upon which players base their strategies. In such games, players must consider their own type and anticipate how others will respond based on their own interim beliefs about the distribution of types. The equilibrium is achieved when no player can benefit from unilaterally changing their strategy, given these beliefs. Thus, accurately modeling interim knowledge is essential for predicting behavior and ensuring that all players optimize their outcomes in line with their expectations about others.

Related terms

Types: In game theory, types refer to the private information held by players, which can include their preferences, payoffs, and available strategies.

Bayesian Updating: This is the process by which players revise their beliefs about other players' types based on new evidence or actions observed in the game.

Incomplete Information:

A situation where players do not have full knowledge of the other players' characteristics or payoffs, impacting their strategy choices.