Obviously, there must a reason why participants in this particular situation do not seek to exploit this difference by arbitrage or competition. Usually the reason is a particular preference people have. Buyers may perceive one station as having a superior product or buying experience. This kind of thing is common and often related to the personality of the seller or the personalities of the other customers. So trendy restaurants can sell meals at higher prices than the competition. Some Americans are loyal toward American car companies and so, their prices are higher than otherwise and, perhaps, even above technically superior foreign cars that are sold in the same market.
To apply this reasoning to big differences in gas prices in the same town, but not at stations across the street from each other, some buyers may view the location of some station as dangerous and therefore, not compete away a large price difference while the customers at the high price station don’t drive to the lower price stations out of loyalty to their neighborhood. Suppliers of gasoline don’t try to supply more at the dangerous stations because they really are dangerous and therefore, their costs are higher.