To dominate a radio spectrum usualy ends up with who has the strongest transmitter.

BUT in todays digital age and more refined tunning of radio's into more decimal places. Then I believe the following approach would be the best approach for less power.

Pick your target spectrum range, Then using a highpower transmitter higher powered than the other as above to do a very granular spectrum hopping around the spectrum but at least transmitting on every channel within that spectrum at a period of frequency that would be greater than normal error corrected interferance by that your signal would then cover the spectrum range alocated but instead of having to do a wide band of the entire spectrum you are picking channels (by channels I mean frequency range that is not interfeared with by either side as you can have a transmission on wifi say that is on channel 3 and can be picked up faintly if your on channel 1, bad example but you should follow what I'm meaning by channel in this case of a spectrum block) at a time interval that would exceed error correction and as such rendering others use of the channel extreemly hard and with that all channels in the defined frequency range, aka spectrum.

Now by doing that you would need the least amount of power to block others use of that spectrum and at the same time have a very wide albeit spectrum hopping chunk of bandwith to use and abuse and the faster you make the spectrum hopping to break error handerling of others trying to use that range.

Of course with that approach you would have details to work on like frequency channels and how granular you defined those and also the level of error correction you wish to defeat. Remember if you want to compete with others digital transmissions then this is great BUT with analogue it may very well be a case that somebody talking would still be understandable with the level of interfearance. A look at signal type and how it would be analoguely(sic) interpreted is one aspect that may effect how you encode your data as you may end up disrupting the receaving speaker enough to impeede the other signals sound transmision. There is also the aspect of how long you stay on a channel at certain frequencies with some needing longer than others to transmit something usable and the fun of recieving the signal out of step as different frequencies propergate(travel) at different rates(speed) so that would cause out of step reception, though easily countered if your aware of that design aspect.

NOW there is a far far easier way and sadly I don't think it is what I would calla hacker approach and is more the script-kiddie solution. That would be to send a silly large pulse on the frequency so strong that it blows all the transmitters. Now you would need to inform your chaps ahead so they could switch of and fold there areils in half type of thing ahead of your radio nuke or more a radio DOS attack. Then they could setup ready afterwards and you would of blown all other recievers and with that the only people who can listern are those you want to listern. Not elegant, but certainly a partial solution that would be cheap to implement as it is that crude, hence not what I call a pure hacker solution. I also suspect the amount of power to do this would exceed the prize money being offered, so you would be pushed and indeed insane to build and test such an approach.