bobuhito
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Registered User
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May 13 |
comment |
Non-Constant-Sum Blotto Game for Only 2 Players and 2 Battlefields Yep, sorry, first time I've seen that notation. I'll mark your $m/\lfloor B/(B-E)\rfloor $ as the answer in a moment. By the way, is there a generalization of this formula to more than 2 players and/or more than 2 battlefields? I’m just looking for the value/utility formula, not a full strategy like you graciously gave here. |
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May 13 |
comment |
Non-Constant-Sum Blotto Game for Only 2 Players and 2 Battlefields Thanks. I'm trying to follow this, but you have some mistakes throwing me off. Please take a look at your definition of r and your example's calculation of m (I get m=8/3). |
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May 12 |
comment |
Non-Constant-Sum Blotto Game for Only 2 Players and 2 Battlefields Maybe I shouldn't have used the words "non-constant-sum". All I mean is that the two players start with a non-equal number of total soldiers and use them all ("use it or lose it") on the two battlefields. So, utility is the number of battlefields won (you can say ties are split half-half, so technically the possible utility outcomes are 0, 0.5, 1.0, 1.5, or 2.0, but tie treatment is not statistically important if there are many soldiers). |
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May 12 |
asked | Non-Constant-Sum Blotto Game for Only 2 Players and 2 Battlefields |
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Apr 27 |
asked | Fastest Digit Extraction for Any Irrational Number |
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Apr 21 |
comment |
Calculate the inverse of a matrix If A is a simple scalar matrix (1x1) of 1, this equation will not have a stable equilibrium, so I would say no |
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Apr 21 |
comment |
special primes with p'=4p+1 Just knowing that, it becomes easier to search the web. I found that this sequence is documented at oeis.org/A023212 and, from the graphs, guess that about 1 in 14 prime numbers might meet this requirement in the infinite limit. But, if primes were truly random, the prime number theorem makes me think that this ratio should go to zero. I'm leaning towards it going to zero. |
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Apr 21 |
asked | special primes with p'=4p+1 |
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Apr 13 |
comment |
“Box Nodes” in Directed Graphs with Paired IO Symmetry Yes, but marking 2*n independent vertices is probably required (as in the left example above) since I really wanted to mark the lines from the vertices. There are really n labels for permutation because of my pairing. The automorphism then needs to induce the same pairs. If you're curious, this is a practical application for building a network with many inter-communicating IOs from small primitive routers. |
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Apr 12 |
comment |
“Box Nodes” in Directed Graphs with Paired IO Symmetry Each node has two lines with arrows indicating inward flow and two lines with arrows indicating outward flow; these are the two inputs and two outputs (this should be natural to people familiar with directed graphs). To draw this fast, I didn't show arrows on some lines, but please consider all lines to have a flow arrow. Both of my examples have 3 inputs and 3 outputs which are unconnected which can be itemized in pairs by writing in1, out1, in2, out2, in3, out3. Box is more like "black box" where this whole construction is like a node with many inputs and outputs. |
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Apr 12 |
revised |
“Box Nodes” in Directed Graphs with Paired IO Symmetry added 179 characters in body; deleted 29 characters in body |
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Apr 11 |
asked | “Box Nodes” in Directed Graphs with Paired IO Symmetry |
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Jan 20 |
awarded | ● Yearling |
