Google Inc. is reaching for its Wallet to keep pace with Apple Pay, but differences in the two companies’ mobile businesses mean it won’t be easy.

The Internet-search giant is trying to marshal an unruly coalition of device makers, wireless carriers, banks and payment networks to shape a new version of its Google Wallet payment service, in some cases by offering them more revenue. Google hopes to unveil the new service at its developer conference in late May, said people familiar with the matter.

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