Thread: UPDATE #3
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Unread 15-01-2009, 09:02
ScottOliveira ScottOliveira is offline
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Re: UPDATE #3

Quote:
Originally Posted by Vikesrock View Post
Here's the thing, if they don't put a trailer out there in some manner for a missing robot 100% of matches will consist of 0 robots and will result in 0-0 ties.

As much as I wouldn't want to waste all our hard work spent on the robot, I also wouldn't want to lose because the other alliance fielded no robots and we put ours out on the field.
Hardly. You have based this assumption on a fundamentally unsound application of game theory.

Using some VERY basic assumptions: If an alliance fields no robots, nobody can win. If an alliance fields more robots than the opposing alliance, the alliance with more robots will win. If both alliances field the same number of robots, nobody wins.

BLUE ALLIANCE
3 2 1 0
RED 3 Robots (0,0) (1,0) (1,0) (0,0)
ALLIANCE 2 Robots (0,1) (0,0) (1,0) (0,0)
1 Robot (0,1) (0,1) (0,0) (0,0)
0 Robots (0,0) (0,0) (0,0) (0,0)


From a pure strategy point, both alliances will go with 3 robots, as that is the dominant strategy - that is for every scenario, 3 robots has a greater or equal outcome to any other strategy.


Now the biggest assumption is that if both alliances play the same number, no body wins. So we'll factor in X as the probability of Blue Alliance winning with equal numbers of bots (allowing for X < 0 if Blue will 'probably' lose, but X<=1,X>=-1). Let's also assume that a loss does more than not harm a team, but negatively affects it.
This gives us:

BLUE ALLIANCE
3 2 1 0
RED 3 Robots (-X,X) (1,-1) (1,-1) (0,0)
ALLIANCE 2 Robots (-1,1) (-X,X) (1,-1) (0,0)
1 Robot (-1,1) (-1,1) (-X,X) (0,0)
0 Robots (0,0) (0,0) (0,0) (0,0)

Thus, at the very least Blue's dominant strategy is 3 if X>=0, and Red's dominant strategy is 3 if X<=0, so one team will play 3 regardless.

Let's go one step further (without working out all of the mixed-strategy equilibriums that is). Let's assume that any team that fields no robot LOSES a match where the other team fields any robots(consider any sporting event, a complete no show results in a forfeit victory for the team that is there). Even if that is not a judged outcome (that is, if the judges declare no show = tie), scouting teams will be disappointed by not being able to see robots in action, and that will likely negatively affect their decisions, hurting the chances of a no show team getting picked for a final alliance.

So we are given:

BLUE ALLIANCE
3 2 1 0
RED 3 Robots (-X,X) (1,-1) (1,-1) (1,-1)
ALLIANCE 2 Robots (-1,1) (-X,X) (1,-1) (1,-1)
1 Robot (-1,1) (-1,1) (-X,X) (1,-1)
0 Robots (-1,1) (-1,1) (-1,1) (-1,-1)

This shows that both alliances will ALWAYS play 3 robots if possible.