If the transactions, and blocks are not valid/doesn't follow the consensus rules. Those transactions/blocks won't be relayed by full nodes. The energy spent will be wasted. That's the game theory.
Nope.
The incentive may help encourage nodes to stay honest. If a greedy attacker is able to assemble more CPU power than all the honest nodes, he would have to choose between using it to defraud people by stealing back his payments, or using it to generate new coins. He ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth.
That's the game theory.
That WAS the game theory BEFORE the cartelization of mining. Satoshi did not fully know future. How could the community express themselves if their ability to run a full node was taken away?
Full nodes creates demand for blocks for the miners to supply, and relays them only if valid/follows consensus rules.
Plus if you truly believe that your one node network will be adversarially safe from a collusion by a cartel of miners, because "game-theory", and that users shouldn't run nodes, then what are we in Bitcoin for? Remove POW too, and make it cheaper.
Firstly, I don't say users shouldn't run nodes, on the contrary I'm thinking of and advocating for mobile full nodes: every user one full node!
I'm saying it is not helping bitcoin security to have a zillion full nodes, it is just about every single user to avoid being the one whose name is supposed to go first to the news. Full nodes do not form an institution to keep bitcoin safe! How people have managed to deduct such a stupid argument?
But full nodes do secure the network. Any block/transaction that isn't following the consensus rules, won't be relayed. Bitcoins is actually a network of validation.
Secondly, PoW is essential for the game theory behind bitcoin and it is why PoS is shit.
Not if the network is centralized towards the miners, and can collude to co-opt Bitcoin's development WITHOUT community consensus. Maybe they should remove POW, to remove costs. Haha.