Why to use tiled map in cocos2d game development?

It is never really necessary to use a tiled map. For anything. However, it is helpful for many scenarios.

So, in your case no it is not necessary. There are many other ways you can implement a repeating background or whatever.

No, a tiled map not necessary for your arena + long path concept, but it could work okay for that concept, if you wanted to. Yes, you can add a background image instead.

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