It sounds like you have a credibility problem with your son. Bluffing with a punishment (child abandonment) that you had no intention of following through with was probably not advisable. So what you have now is a 2.5 year old boy who is, from the sound of things, disobeying you without any fear of negative reprecussions.The alternatives you have presented are:(1) Relenting to your son's disobedience by carrying him either in your arms or in a stroller.(2) Promising positive rewards for obedience.(3) "Waiting it out", which you somewhat discount as impractical.I think that option #1 is clearly the worst option here. You are just teaching him that there's no reason to listen to you, at least in this specific circumstance.Option #3 probably is impractical, and still doesn't really give him a reason to listen to you if he doesn't mind sitting around. When he gets bored you will eventually get cooperation, but that won't make him obey you next time.Option #2 is on the right track I think. Nothing wrong with rewarding a child for "being good". But I would tweak your approach a little bit, in two ways:(1) I would pair it with negative consequences for disobedience. And I don't mean an empty threat to abandon your child in a hallway. I mean something you will actually do whenever you tell him to walk with you and he disobeys.(2) I would not promise the rewards ahead of time -- he should not build the expectation that he only needs to obey you if he happens to want the reward you're handing out that day. I would promise the punishment for disobedience ahead of time, because consequences of bad behavior need to be predictable. I would reward him after the fact, which doesn't help you at all the first day you take this approach, but will teach him that its worth obeying you down the road.Of course, this is just my opinion and approach based on my own very limited experience. As always, your milage may vary.