Question

Do normal-form games exhibit perfect or imperfect information? Explain.

Short answer

Normal-form games exhibit imperfect information.

Step-by-step solution

Understand Normal-Form Games

Normal-form games, also known as strategic-form games, represent situations where players make their decisions simultaneously. Each player chooses their strategy from a set of possible strategies based on the belief about the strategy choice of other players, without knowing their actual decision at the moment of choice.

Define Perfect Information

A game is said to exhibit perfect information if all players at every decision point know all previous actions chosen by other players. In other words, each player has complete knowledge of the entire history of the game at every stage of play.

Define Imperfect Information

Imperfect information refers to situations where players do not have access to all actions previously taken by other players, making it impossible to be certain about the current state of the game. Usually, decisions must be made with some level of uncertainty.

Analyze Normal-Form Games for Information Type

In normal-form games, players choose their actions simultaneously, meaning no player knows the others' choices at the time of making their decision. As such, players do not have complete information about the actions of their opponents at the time decisions are made.

Conclusion

Based on the simultaneous choice structure of normal-form games, these games do not allow players to have perfect information. Instead, since players make decisions without knowledge of other players' simultaneous choices, normal-form games exhibit imperfect information.

Key concepts

Normal-Form Games

Normal-form games, also known as strategic-form games, are a foundational concept in game theory. These games are designed to capture strategic interactions among players who make their decisions at the same time.
In normal-form games:

• Each player has a set of strategies to choose from.
• Choices are made simultaneously, meaning that no player knows the decision of the others when they choose their strategy.
• The outcome or payoff for each player is determined by the combination of strategies chosen by all players involved.

Normal-form games are useful for analyzing situations where decision-makers must anticipate the actions of others without having the luxury of observing them first. This feature makes normal-form games central to understanding competitive environments and further exploring strategic decision-making in both economic contexts and everyday life.

Perfect Information

Perfect information in a game refers to a situation where every player, at every decision point, is fully aware of all the actions that have taken place before.
This comprehensive knowledge allows players to make more informed decisions since they can consider the full scope of the game so far.
Examples include:

• Chess: Players can observe every move made since the beginning of the game, allowing each player to strategize based on all past developments.
• Checkers: Similar to chess, players have full visibility of the board and past moves.

In these types of games, each player has the ability to predict the results of their actions more accurately because there are no hidden variables. Such information simplifies the strategic decision-making process, transforming complexity into calculable scenarios. However, perfect information is not present in every strategic interaction, such as in normal-form games.

Imperfect Information

In contrast to perfect information, games with imperfect information involve players making decisions without complete knowledge of the actions taken by other players.
This lack of information adds uncertainty and complexity to the decision-making process. Examples in real life include card games like poker:

• Poker: Players do not know the cards held by their opponents, making decisions based on probabilities and guesses about their opponents' hands.
• Choosing a stock portfolio: Investors cannot see the private decisions of other market participants and must make choices considering unknown variables.

In these scenarios, the uncertainty forces players to rely on estimates, probabilities, and sometimes even bluffing to make the best possible decision with the information available. Normal-form games are an example of games that operate under imperfect information, as decisions are made simultaneously, without insight into the choices of other players.

Strategic Decision-Making

Strategic decision-making is the process of selecting the best course of action in situations where the outcome depends not only on one's own actions but also on those of other participants in the game. This element is crucial in both perfect and imperfect information settings.
Key components include:

• Anticipating opponents' moves: Predicting what other players might choose helps in shaping one's strategy.
• Choosing optimal strategies: Analyzing potential outcomes and selecting the strategy that best suits one's goals.
• Adapting to new information: As a game unfolds, players might need to revise strategies based on new evidence or actions observed from others.

Understanding strategic decision-making is vital for success not only in games but also in business and economics, where stakeholders must frequently make decisions amidst uncertainty and competitive pressures. By mastering these skills, one can improve their ability to negotiate, predict competitor behavior, and optimize outcomes in various strategic environments.