guess i will step in before more young developers gets turned off by comments in this thread (not digging up last year's topic (ayy), google directed me here).
pretty much every comment from last year talks about hundreds of thousands or milions of dollars and that is not correct to author's question. We do not speak about AAA/e-sports games here but mobile games rather.
let's start by digging into project (i am not game dev yet but making games is no different than making apps or websites even). So we need:
networking - synchronous battles, users, chat
client based game for iOS and Android, possibly other platforms
authorative server that will scale
1. cross-platform development
since this is our first-ish game, using game engine would be wise idea. LibGDX or Unity should do, depends whether u want 2D or 3D game and installer size matters. If not, let's just stick with unity for good measure. There are thousands of guides and tutorials on how to start with it so don't worry, you will quickly find a way needed to publish games on mobile with simple steps.
Since it might be similar to clash royale, we will probably use 3d assets. download free template kit for tower defense game from unity or see guides/tutorials of how tower defense works behind the scenes. change some assets, try making game single player (lobby screen, start random match). When you are satisfied with sample, continue to networking.
2. authorative server will probably be best way for online game. first start researching good cloud backends for gaming such as playfab. SDK is easy to implement and theres ton of guides how to do it with unity. It will enable matchmaking, room generation, sessions and all kinds of things for your game. Alternatively, try some opensource or free backend engines such as colyseus.io
With that, you will be able to implement multiplayer mechanics to your game.
if you had to pay for assets, just by trying to get it done, we are looking probably at $30-$50 for assets that may or may not be customised at all (be sure to see licensing to assets you bought) - yes all assets, not one file each.
you will need to implement multiplayer into single game that you probably can get through unity assetsstore as well so only your time will be required here. Plenty of examples, just follow them.
Cloud platforms tend to charge for indie licensing but you would probably get away with persnal gamesparks license that is completely free until 100000 MAU (monthly active users). For typical pricing it's around $100 monthly for indie. Otherwise use engine to develop own server (all it needs to do is to authenticate users, process payments and store data). Going this route you will need dedicated machine to host it 24/7 which might be costly.
tl;dr; we are looking at 1-5k us dollars for whole package that uses pre-made assets or require minor asset editing (changing colors or remodelling) and publishing to desired platforms + i dont know how much to get your company going, get trademarks and all that law bs that you will find on different parts of this forum.
i would recommend watching some tutorials on unityTD overall, here is very good example:
remember @horuz - u do not need to spend hundreds of thousands of dollars to make games. not anymore, it's 2019 already. Most code is already open sourced and there is many cloud based backends that will implement complex networking for your game for low price. If you are not making multimilion user game, you probably don't need to develop/create everything from scratch.