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Unread 21-03-2006, 10:02
sw293 sw293 is offline
Former Coach (2005)
AKA: Scott Weingart
FRC #0293 (SPIKE)
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Join Date: Mar 2005
Rookie Year: 2004
Location: Pennington, NJ
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Re: Ideal Alliance Structure

Earlier I wrote:
Quote:
Originally Posted by sw293
The more interesting question is how strong alliances might be formed in alliance selection.
And here is what I mean by that:

Suppose at Championships in Newton Division we get the following rankings for alliance selection (assume all of these are center goal shooters):

1. FRC2001 (#3 Human Loaded Robot)
2. FRC2002 (#1 Ground Loaded Robot)
3. FRC2003 (Ground Loaded Robot)
4. FRC2004 (#2 Human Loaded Robot)
5. FRC2005 (Ground Loaded Robot)
6. FRC2006 (Ground Loded Robot)
7. FRC2007 (#1 Human Loaded Robot)
8. FRC2008 (Ground Loaded Robot)

I submit that each alliance has room for only one human-loaded robot.

FRC2001 wants to pick FRC2002 (best ground-loaded robot). FRC2002 would rather be allied with FRC2007 or FRC2004, who have better human-loaded robots. FRC2002 knows that FRC2001 is probably not going to pick FRC2007 because their robots are incompatible (both human-loaded robots), and even if that selection is made, FRC2004 will still be available (still a better human-loaded robot than FRC2001). Therefore, when FRC2001 picks FRC2002, FRC2002 should decline, right?

But what happens if FRC2001 then picks FRC2007? FRC2007 ought to decline, because an FRC2001/FRC2007 alliance would have two human-loaded robots (=inefficient). So then FRC2001 picks FRC2004, who declines for the same reason. In this scenario, FRC2002 is worse off for having declined FRC2001's offer of alliance. So by declining FRC2001's offer of alliance, FRC2002 is taking a gamble.

However, if FRC2001 were smart, they would have picked pick FRC2007 and FRC2004 first, and after they had declined (as expected), FRC2002 would have accepted FRC2001's subsequent offer of alliance because their two top teams would no longer be available.

The flaw in my argument is the assumption that all teams will make rational decisions in accepting or declining alliance offers.

I hope that was intelligible. Please tell me if it's not and I'll try to clarify it.
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Team 293
Uncrowned Champions, 2005 Philadelphia Regional
Champions, 2007 Chesapeake Regional