Miners conceding forks When bitcoin forks, does anyone know how many blocks ahead one chain gets before the miners on the shorter chain concede?

I am doing a research project on modeling Bitcoin, and I am wondering how realistic it is for miners to abandon their chain as soon as they receive a chain that is one longer than the one they have. 

I imagine that as chains get longer (and more money/computational work is at stake) miners are more likely to try to catch up from a 'deficit' of one block. 

There is also the fact that a miner with sufficient hashing power (40+ percent) has a reasonable chance of catching up from being behind.

Any thoughts on this stuff?
Miners are incentivized to always mine at the longest valid chain tip. If there were incentives to not mine on the longest known chain, then we would expect the network to be unable to maintain consensus on the blockchain's state. And without that, it would be impossible to build a reliable financial system. 

So it isn't about 'miners conceding a shorter chain', its just that miners will always all be mining at the chain tip. Currently, the majority of the block reward is constant (the newly minted coins), so a miner should not really care if they mine block X or block X+1: their reward will be ~the same in either case. As such, a miner is incentivized to just mine at the chain tip, because the chance of finding a valid block at either height is equivalent, but the potential reward for finding one at the chain tip (thus extending the longest chain) is much larger. Finding a block at a height that has already been found will likely mean the miner gets no reward, since that block will be rejected by the network as not being a part of the longest chain.

All of the above concerns situations in which there is not a fork due to a change in consensus code, just the regular competition between miners. If you mean to ask about forks caused by changes in consensus code, you'll need to be a little more specific, as the nature of the code change will affect the game theory. But in general: Bitcoin works because miners are incentivized to mine at the chain tip. Without this incentive, the system would likely not achieve the stability required to give any sort of reliability guarantee.