Even in a situation where your agent is representing only you, they still have a massive incentive to get you to raise your bid so they get 1/4 of the total commission (and their brokerage house gets 1/4 of it). Their incentive is even stronger than that of the listing agent, because when it comes time to choosing a bid, the listing agent and brokerage is getting their commission one way or another and so a 1% difference in final contract price on a $1M house represents a difference of around $150 pre-tax to the listing agent. A difference of 1% that causes that specific buyer to get the house can represent a $15150 pre-tax difference to the buyer's agent.

If you tell "your" agent that you'd like to bid $1M but are able to and would pay up to $1.2M because you really love the house, you're giving away a lot of information that I decided I wasn't willing to give up and so kept all Realtors at arms-length.