Money is just an abstraction.
Exactly ! I think we now reached the same conceptual framework (the lack of which was the reason for a bit of misunderstanding in some postings). My issue is the following:
Let's assume we model Bitcoin swarm behavior with game theory. In this case 1 BTC is the payoff and if I increase it to 2 BTC this is a more attractive payoff. If I program a Bitcoin miner to maximize his BTC profits, he will opt for the 2 BTC chain.
No it wouldn't. Once again money is an abstraction. It is possible the chain which pays out less BTC has more buying power. If BTC 1.0 pays 50 BTC per block and BTC pays 2000 BTC that alone provides no measure of value (buying power). If the original chain allows me to buy 1 Whooper combo meal w/ 1 BTC and the second chain take 200,000 BTC to buy the same combo meal it would be flawed thinking to switch chains simply because the "number is bigger".
They know about dilusion and inflation and therefore will not readily switch to the 2 BTC or the 11 quadrillion BTC chain. Thus, we cannot model Bitcoin swarm behavior with game theory alone. We must look at human consensus and at economic aspects. So let us do so...
No need your "game theory" answer is already invalid. The goal of any venture is to maximize wealth not money. Money is merely an accounting system for wealth. If you want lots of money I can get you some Zimbabwe dollars. You can be a trillionaire. They don't buy anything but they have lots of zeros. Likewise an alt-chain which simply increases the nominal number of BTC isn't going to increase the purchasing power of miners or users.
You can't create value or wealth via accounting games. Money is merely arbitrary. Satoshi could have chosen a block reward of 1 BTC or 1000 BTC. All it would do is change the nominal amount of the block reward. The value would remain the same. With a block reward of 1 there would be 1/50th as many BTC in circulation and the exchange rate would be ~$250 per BTC.