Wikipedia provides a list of cognitive biases which may be relevant to the situation. There may be more than one that are relevant. Cognitive biases are confirmed patterns of behavior representing a deviation from a norm.
One should not let the word "bias" suggest that such patterns of behavior represent irrational behavior although they might. As the Wikipedia article notes:
There are also controversies over some of these biases as to whether they count as useless or irrational, or whether they result in useful attitudes or behavior. For example, when getting to know others, people tend to ask leading questions which seem biased towards confirming their assumptions about the person. However, this kind of confirmation bias has also been argued to be an example of social skill: a way to establish a connection with the other person.
Here is the situation:
You do an advertisement, "Lowest price in town", but a vast majority of people now suspect that your prices are not the lowest. They now start hunting around for lower prices than yours and they indeed find them.
The OP also suggests: The reason why people start looking around is after seeing the advertisement.
Just advertising the item may make people aware of it who were not previously aware of it. Although the advertisement claims this particular retailer has the lowest prices, this is something else the comparison shopper will check.
The deviation from the norm would be that the consumer is now looking for something they did not previously realize they wanted and they also have a new distrust in their initial source of information. Trying to find a better priced product may be rational behavior given this new search and distrust of the initial information.
Some possibilities for cognitive bias are:
- Availability heuristic: The tendency to overestimate the likelihood of events with greater "availability" in memory, which can be influenced by how recent the memories are or how unusual or emotionally charged they may be.
- Availability cascade: A self-reinforcing process in which a collective belief gains more and more plausibility through its increasing repetition in public discourse (or "repeat something long enough and it will become true")
- Hostile attribution bias: The "hostile attribution bias" is the tendency to interpret others' behaviors as having hostile intent, even when the behavior is ambiguous or benign.
The first two may be related to the new awareness of the product's available although more context would be useful suggesting that the advertisement were emotionally charged or repeated often.
The third relates to a distrust in the retailer's truthfulness that the retailer's price is lowest.
"List of cognitive biases" Wikipedia https://en.wikipedia.org/wiki/List_of_cognitive_biases