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Anyone who has bought a new computer, television or stereo has no doubt encountered the pitch: pay up to $100 more for an extended warranty that lasts up to five years.

The offer is a good deal for retailers, who typically make more on the extended warranty than they do on the sale of the product. It’s not so good for the consumer, who may pay more for the extended warranty than to have the product repaired. Studies have shown that most products break down in the first year – when they are covered by the manufacturer’s warranty – or near the end of their life, after the extended warranty has expired.

Ming Hu, a professor in the Rotman School of Management, and Guillermo Gallego, of Columbia University in New York, together with colleagues at Hewlett-Packard Labs in Palo Alto, California, are using game theory to analyze warranties. They have devised two variations of extended warranties that they say offer a better outcome for consumers, with little downside for the warranty provider (either the retailer or the manufacturer).

In one variation, warranties would be offered at different prices, depending on how many times a consumer expects the product to break down. Consumers who anticipate taking good care of the product or using it infrequently might choose to pay the lowest price for an extended warranty – but would receive protection against only a single breakdown.

Those who anticipate using the product extensively might choose to pay the most and would be covered for unlimited breakdowns. Although the warranty providers would earn less, on average, for each extended warranty they sell, the new lower-priced options could lead to higher sales overall.

In another variation, consumers would get a free product upgrade instead of free repairs, should the model they purchased break down. In other words, if a fourth-generation iPod Nano stops working after a couple of years, the buyer could trade it in for a fifth-generation model, with all the new bells and whistles. Now, that’s an extended warranty one just might take a chance on.