Game theory problem... I think...

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I need some help with the following:
Let's say I'm running a store of electronic devices (call it Store $A$). and let's say that right next to me, there's another electronic devices store (store $B$) which is an old time competitive.
Suppose that my store - store $A$ - and the competitive - store $B$ - we both buy the same exact products, and that we both pay the same amount of money on our products (the cost prices for the products are the same).

Now, whenever a customer is passing by, he randomly picks one of the two stores, picks some product $X$ and looks at its price tag. At this point, he does not know how much product $X$ cost at the second store, but he can decide whether if he wants to buy it, or he would prefer to go to the second store and buy it from there (he must buy product $X$ either from store $A$ or $B$).
The tricky part is that if he will decide to go to the second store, he must pay some fine.
Of course, from the customer perspective, he would prefer to pay as low as possible for the product $X$, and from my perspective, as the owner of store $A$, I would prefer to tag the product $X$ with a price that will be high enough to make a good profit, but not too much so that I won't scare the customer away, and make the fine for moving to the competitive store $B$ suddenly worth his while.
What strategy should I pick for price tagging the products in my store?