How does asymmetric information and bid-ask spread are connected? For instance, economic theory tells us that, the more the problem of information asymmetry, the higher the spread is. What is the intuition behind it? Can this change? Furthermore, what is the difference between asymmetric information, incomplete infortation and imperfect information?
You want to look at a previous post: Imperfect vs incomplete information .
Basically complete information relates to the assumption that players have common knowledge about the game and the utility function of all players. However, they may not know the cards that a player was dealt with, or there might be an action taken by some player that they do not observe.
Perfect information relates to observing all moves and strategies available to a player, but perhaps not knowing the utility or being uncertain about the game. Examples of perfect but incomplete information are a bit harder to imagine, but the examples I like to think of are board games where players have secret goals or missions.
Asymmetric information intersects with both of these classifications. A game has asymmetric information if one player has more information than another player. That is, perhaps one player has complete information and the other one has incomplete information, or perhaps one player has perfect information and the other one has imperfect information. There are many examples here, perhaps one of the most famous ones is the market for used cars, where the seller usually knows better the condition of the car than the buyer. I.e. the information is asymmetric.
Your question about the bid-ask spread is a bit too general. I think that people have used economic theory to rationalize the existence and size of the bid-ask spread. To my knowledge, there are many reasons why this spread exists, and some of these mechanisms have nothing to do with the information.
For example, consider the market for currencies. If in a small town there is a single bank that exchanges currency X for currency Y and vice versa. The bank has market power and can get away with a large bid-ask spread. Even if there is complete, perfect and symmetric information, people might prefer to exchange currencies at a relatively large ask and a relatively low bid, instead of traveling to the next town to find a different bank.
Pertaining information, I can think of traders in the financial market exchanging currencies. If there is a dealer with better information as to where to find more favorable exchange rates, it will have more leeway to increase their own bid-ask spread. Since the their clients might not know there are better options out there in the market.