Which IR or other sensor to use in a bright/noisy environment.

Hi, I was hoping somebody could help with a project I'm planning.

I am making a robot games table for my living room. It will be based around a 42" LCD TV facing upwards, which acts as the game board for my robots. The robots will be in 2 "teams", each of 5/6 "pawns" and 1 "queen". The game board and game rules will be reconfigurable to allow for different type games (i.e. not only robosumo/robogames type but also resource management/settler type game)

The robots will interact with the game board by way of colour sensors below them and each other by 433Mhz radio.

I would also like them to be able to detect each other. The pawns must be very small, think 3cm cube, meaning the greatest distance from the TV screen to the proximity sensors will be about 3-5cm.
Will the bright environment cause interference with IR proximity sensors?
Can anybody advise on the smallest easily useable proximity sensors available? Space is at a significant premium.

Currently at the top of my list for accuracy is the sharp GP2Y0A02YK, but it's too big to fit 1 on each side of my pawns. I've seen small (single LED sized) IR sensors used in swarm robotics applications for proximity sensing but it seems most of the parts that look like this that I can find are only for v short ranges ~25mm it seems.
Any comments?

leaving out the main Arduino detail: I intend using the Nano v3 boards or possibly the pro minis, currently doing development on a Mega2560

Will the bright environment cause interference with IR proximity sensors?

Do as remotes do, as a frequency (blinking) to overcome background light.
Those reflective-based IR-sensors see 'nothing' (except mirrors) at distnace.
Short range 5mm to 20 mm is 'perfect' distance

Good idea, thanks.

Could the standard reflective IR sensors be used to detect the walls at short distance but other robots at longer distances?
For detecting the other robots, Robot1 wouldn't need to bounce IR off Robot2, it could just detect the IR that Robot2 is putting out.

Maybe by modulating the blink differently on each face it would know which way the robot(s) it was detecting were facing.

This is already giving me a headache figuring out how Robot1 would be able to differentiate between reflected or received IR.

The overall project is going to cost me quite a bit so keeping the costs of the pawns down will be key as there will be 8-12 of them.