Mobile App (Android, iOS) plus backend as a sort of geocaching game

The idea is that the player can find other players and earns points therewith. Points are earned as a percentage from the person found. The goal of the game is to make people talk to each other and get in contact. Let's make an example. Player 1 switches on the app and his location is transferred to the server and he becomes visible to other players. Player 1 has a score of 1000. Player 2 looks at the map in the app and sees Player 1 he can see that he was at that position 1 minute again and the walking distance is 3 minutes. So he gives it a try and finds Player 1. He sees in the real world a guy with a smartphone in his hand and asks him if he is Player 1. He says yes. Player 2 asks him if they could exchange the code. Player 1 gives him his code e.g. 123456. Player 2 enters the code in his app. That moment the back end realises, that Player 1 is near Player 2 by the coordinates received from both players and verifies that the code is correct. The back-end credits Player 1 and Player 2 with points. The points granted are 0,1% Player 1 to Player 2 and 0,1% of Player 2 to Player 1. That way there are Players with higher value, and so the hunter becomes the hunted. The map shows the points of the player. If the player moves he the coordinates are updated to the back-end. I know there are some restrictions about what can be done in background in iOS (I don't know about Android) but that is no problem. We do what is possible. One thing I am very concerned about is the data security. No hacker should be apple to manipulate points or locations or should be able to fake his location and be able to enrich him with a second account falsely to alot of points. Especially it is not possible to meet more people per minute as for example 2 and a travel speed cannot be higher then a certain sensible amount to be defined. Also with the same player can no code be exchanged for the next hour at the same location and not for the next 15 minutes at different location more than 1 KM away. Still allows some systematic but that is ok. Every player starts with 1000 initial points. Later version maybe we allow him to buy points as in app purchase (but I have still to make up my mind if I want that). Quote should include upload and handling of upload to Google Play Store and Apple App Store. I would prefere the app to be Xamarin but are open for suggestions other cross platform development strategies, even for 2 native apps if you find this to be the better way. I have written apps for both operating systems and are a competent partner to deal with. Regarding the back-end I am quite open and expect a suggestions that has scalability and stability in mind as well as "easy to handle". A admin web client would be nice, but for now a regular line command query tool, and mySQL query would be sufficient. But do not restrict yourself to mySQL. I am totally open for any other good method for data storage in the back-end. But keep one thing in mind: If the app is a success then we might provide a user front-end where he can query his gaming history. This also implies that all user actions need to be logged and a history of everything should please be kept (and again security first). Any questions, then please let me know. The budget is set to a range where I still expect you to give me reasons why the price is higher than specified budget. I am open to this. I want it done with quality, so if you can convince me I am open to give more.