How do you compare and contrast dynamic games with perfect information and imperfect information?

1 Perfect information

Perfect information means that each player knows everything that has happened and will happen in the game, including the actions, payoffs, and preferences of all players. Perfect information games are often represented by extensive form trees, where each node corresponds to a decision point and each branch corresponds to an action. A classic example of a perfect information game is chess, where both players can see the entire board and the possible moves at each stage. The main solution concept for perfect information games is backward induction, which involves starting from the end of the game and working backwards to determine the best action at each node.

2 Imperfect information

Imperfect information means that some aspect of the game is unknown or hidden to some or all players. This could include the actions, payoffs, preferences, or types of other players, or the state of nature or the rules of the game. Imperfect information games are often represented by extensive form trees with information sets, which are groups of nodes that a player cannot distinguish between. A common example of an imperfect information game is poker, where each player has private cards and does not know the cards of other players or the cards that will be revealed later. The main solution concept for imperfect information games is the subgame perfect Nash equilibrium, which involves finding the Nash equilibrium for each subgame of the game and eliminating strategies that are not credible or consistent.

3 Comparing and contrasting

One way to compare and contrast perfect and imperfect information games is to look at their properties and implications. For instance, perfect information games are always deterministic, meaning that there is no randomness or uncertainty involved in the outcome. Imperfect information games, on the other hand, are often stochastic, meaning that there is some probability or chance involved in the outcome. Another way to compare and contrast them is to look at their applications and examples. For example, perfect information games are often used to model strategic interactions in warfare, politics, or bargaining, where the players have full knowledge of the situation and the consequences of their actions. Imperfect information games are often used to model situations involving incomplete or asymmetric information, such as auctions, signaling, or screening, where the players have to infer or reveal information from their actions or beliefs.

4 Solving dynamic games

Solving dynamic games with perfect or imperfect information requires applying the appropriate solution concepts and tools. For perfect information games, the main tool is backward induction, which involves reasoning from the end of the game to the beginning and finding the optimal action at each node. For imperfect information games, the main tool is the subgame perfect Nash equilibrium, which involves finding the Nash equilibrium for each subgame of the game and eliminating strategies that are not credible or consistent. However, there are also other solution concepts and tools that can be used for different types of dynamic games, such as forward induction, Bayesian Nash equilibrium, perfect Bayesian equilibrium, sequential equilibrium, or trembling hand perfection.

5 Challenges and limitations

While dynamic games with perfect or imperfect information can provide useful insights and predictions for many strategic situations, they also face some challenges and limitations. For instance, some dynamic games can be very complex and difficult to solve or analyze, especially if they involve many players, actions, stages, or information sets. Some dynamic games can also be sensitive to the assumptions or specifications of the game, such as the order of moves, the timing of information, or the discount factor. Furthermore, some dynamic games can be unrealistic or incomplete, as they may not capture all the relevant factors or features of the real-world situation, such as bounded rationality, learning, communication, or emotions.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?