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Why should other nations praise G-d because of His mercy towards us?

The shortest chapter in the book of Psalms is one we recite as part of our prayers on holidays and the New Moon:

Psalms 117:1-2 (translation from Sefaria):

הַֽלְל֣וּ אֶת־יְ֭הוָה כָּל־גּוֹיִ֑ם שַׁ֝בְּח֗וּהוּ כָּל־הָאֻמִּֽים׃ כִּ֥י גָ֘בַ֤ר עָלֵ֨ינוּ ׀ חַסְדּ֗וֹ וֶֽאֱמֶת־יְהוָ֥ה לְעוֹלָ֗ם הַֽלְלוּ־יָֽהּ׃

O praise the LORD, all ye nations; Laud Him, all ye peoples. For His mercy is great toward us; And the truth of the LORD endureth for ever. Hallelujah.

Why should the nations praise G-d for showing mercy to Jews? How does this benefit them or what incentive is there for them to do so? And, how does the author of this Psalm suggest that they do this? Is it by reciting these verses or via some other means?