Takata Corp. and some of the world's biggest carmakers face an extensive, expensive to-do list as they try to resolve the worst safety crisis in the auto industry's history.

Executives for the Tokyo-based maker of air bags are scheduled to meet in Japan with Honda Motor Co. and officials from some of more than a dozen other customers this week, according to people with knowledge of the situation. The talks are prompted by five bids made for the beleaguered Takata after months of concern about its solvency.

The central issue for Takata's customers — which include General Motors Co. and Volkswagen AG — is how those takeover bids divvy up responsibility for paying billions of dollars in recall costs and potential legal liabilities stemming from faulty air bags. Takata is at the heart of the largest auto-safety recall in U.S. history after some of its air bags ruptured and killed at least 15 people, prompting repairs that could exceed 100 million devices worldwide.