Price matching done well is a good plan.
To start doing price matching well first decide exactly what products you are going to price match on. The smart way to do it is to only price match on commonly available specific products. You need to do this because these are the benchmarks that shoppers use, whatever you sell.

Price match on products

The next step is to introduce more specific products that are only available from your store. Get the brands to help. They don’t exactly want Amazon to have a monopoly either. Next introduce a wider range of own brand products and own brand brands. They have to be good quality for the price but also fit into several price categories.  You don’t need to price match to these products but retailers do need to invest in promoting their new brands as well as the exclusive products from the brands. Get the budget to do this by stopping spending on promoting products that are price matched. Of course you also need to remember that contrary to popular myth it’s nearly always cheaper to buy a product from somewhere other than. Amazon.
Price matching is not new and many furniture retailers have been offering it for years. They had messages like “If you can buy this bed anywhere cheaper we’ll give you the difference plus xx%.” Needless to say everything they sold was made in their own factory and never supplied to any other retailer.

Read also about pricing scandals.