I have google adsense for content on my web pages, I don't have a google search bar because I want to use this other search bar. Can anyone tell me if it would be against Google’s policies if I put a competitor’s search box on these same pages that show the adsense ads?

I put this search bar on my links page so you could see what I'm talking about
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Thank you
Monica

I think you would be allowed to do that. Googles rule is you aren't allowed to have competing contextual adverts on the same page as adsense, A search box isn't a competing contextual ad.

For a better answer though you should contact google.

I think you'd be fine too. It's just as stOx said. You can't use other contextual advertising on a page that contains AdSense, but the search box should be fine.