How I picture a Hunger Games between all the Doctor's would go

What if all 14 Doctors were gathered together into a Hunger Games type situation. Let's say the time lords caused this so there would be no way to escape and the Doctor's know this. There are no regeneration's and no companions. Each Doctor is equipped with what their Doctor typically has. So 2, 3, 4, War, 9, 10, 11, 12 and 13 all have Sonic screwdrivers while the other Doctor's do not. 7 has an Umbrella etc. It is literally impossible for the Doctors to survive without winning and since the Doctor's are only fighting themselves things like morality and compassion aren't an issue in this case. Each Doctor will fight each other to the best of their abilities. The Arena is a jungle think Hunger Games: Catching Fire but drop all the mutated creatures and clock face thing. Typical Hunger Games rules the Doctor stand on podiums with mines beneath them with a stash of weapons in the middle.

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This is how it would go down. The cannon goes off and 1, 3, 6, War, and 9 all go for the weapons in the middle as they are the most physical and violent doctors. The rest would run off. War and 9 being fresh from the time war would be utterly ruthless. 1 being the weakest physically and also the most naive would die there probably killed by 6. 9 would go for war out of hatred for that incarnation. 9 being younger and physically stronger would kill war right there. 3 could easily take out 6 but would run from 9 who would likely have armed himself at this point. By the end of day 1. 1, 6 and war would be dead.

Day 2 Now we have the violence out the way the doctors would use their heads. Two, Five, Ten and Thirteen would simply be focused on survival as they're the most passive Doctors. They would team up. 3 would likely team up with 9. 7 would be devising some crazy plan while 4 teams up with 11. 8 and 12 go it alone

Day 3. 7 sets up booby traps all over the woods. 2 steps in one and dies there. Hes just a less experienced doctor. 10 gets angry and starts hunting 7 which 7 anticipated. He leads 13, 5 and 10 straight into a trap and takes all three down. 12 comes across one of 7s booby traps he dismantles it and starts tracking 7. 3 and 9 stockpile weapons and build a damn to divert the river and cut off the water supply trying to force the Doctors to come to them. 4 and 11 start a forest fire in the night just because. 8 was hiding in the woods trying to let the Doctor's kill each other and so he burns to death. Now only Doctors 3, 4, 7, 9, 11 and 12 remain.

Day 4. 12 finds 7s base and decides to set a trap to take them all out. He runs into 9 and 3. They negotiate. 12 tells 9 and 3 about the booby traps 7 has laying about. The three go to take on 7 under the pretence of a simple attack. 9 however is less trusting of 12 and diverts the plan by misplacing the explosives and making them go off early. 3 dies through his innocence when faced with a much more ruthless 9 and 12 dies as his ego blinds him to the fact that 9 doesnt trust him. 9 then leaves 7s base thinking it best to face him on his own turf. 4 and 11 notice the river has been diverted and they decide on a plan of action. They dig the mines up from under the podiums and lay them out. 9 discovers their tracks in the river bed and begins to track 11 and 4. He steps on a mine and is left standing there.

Day 5 7 notices the diverted river and decides not to take the bait making water from plant and animal life. 11 and 4 set another forest fire driving 7 out from his hiding place. 9 manages to delay the mines detonation. With the sonic. He runs for it and the blast leaves him injured.

Day 6 We have Doctors 4, 7, 9 and 11 remaining. 4 and 11 move in on 9s weapons pile finding it empty they claim it and booby trap the area. 7 comes across 9 and is able to find out that he set the river trap. He kills 9 too injured to defend himself and heads up to 9s place. He fails to anticipate 4 and 11 being there and is promptly killed by a ruthless 11 who throws him into a booby trap. He also accounted for 4 who was relying on his physical prowess to beat 11. He had snuck a mine into his jacket which he promptly detonates with his sonic killing 4. 11 is the victor.

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Can I just say I had nobody in mind to win this when it started. I just started my version of events and the narrative went in that direction. I was actually rooting for 7 since he's probably the smartest most manipulative and also the most ruthless Doctor. But then 11 beat 7 by pure luck because 7 expected the place to be empty as 9 was working alone. For those if you who think war should've lasted longer. Eccleston's younger body gives him an edge in that fight and he is also fresh out of the time war so would be just as capable in combat as Hurt. Just to recap

Day 1 deaths: 1, 6 and war

Day 2 deaths: none

Day 3 deaths: 2, 5, 8, 10 and 13

Day 4 deaths: 12 and 3

Day 5 deaths: none

Day 6 deaths: 9, 7 and 4 - 11 is victor

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What do you guys think. Got any other ideas.