Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Add Lanchester attrition handicap function #2

Open
1 of 2 tasks
ajul opened this issue Aug 1, 2017 · 4 comments
Open
1 of 2 tasks

Add Lanchester attrition handicap function #2

ajul opened this issue Aug 1, 2017 · 4 comments
Assignees

Comments

@ajul
Copy link
Owner

ajul commented Aug 1, 2017

The payoff would be the fraction of remaining force after a Lanchester attrition model is applied to completion.

Like the other existing handicap functions it would take an initial matrix encoding the relative effectiveness of the strategies against each other. This matrix should be log-skew-symmetric. Another parameter would be the Lanchester exponent. Handicaps could be interpreted as unit costs.

This is symmetric. Since this depends only on the ratio of the handicaps it is also one-parameter.

One example appeared previously: Hazard, C. J. 2010. What every game designer should know about game theory. Triangle Game Conference. Raleigh, North Carolina.

  • Basic implementation
  • At least one example
@ajul ajul self-assigned this Aug 1, 2017
@ajul
Copy link
Owner Author

ajul commented Aug 2, 2017

Hmm actually as originally stated Hazard's example is not quite the same as the Lanchester model as stated above---the Lanchester model assumes both sides buy up to the same "budget", while Hazard's example has each side having one unit regardless of cost.

Though given that scaling all handicaps (costs) only scales the payoff matrix by the same, I would still expect a unique solution matrix, even if this is not strictly one-parameter as defined in the paper?

@ajul
Copy link
Owner Author

ajul commented Aug 16, 2017

Implemented both Lanchester and Hazard separately. The old convergence issues (#1) reared their head when I used an exponential rectifier, with the same solution.

One thing of note is that in the non-symmetric case Hazard is sensitive to global scaling.

@ajul ajul closed this as completed Aug 16, 2017
@ajul
Copy link
Owner Author

ajul commented Aug 20, 2017

Misremembered the Lanchester attrition model---there is actually a non-trivial effect of exponent on surviving proportion. Will need to fix this.

@ajul ajul reopened this Aug 20, 2017
@ajul
Copy link
Owner Author

ajul commented Aug 22, 2017

Implemented a corrected version. Unfortunately it appears to have a vertical derivative wherever both sides are evenly matched.

Would be good to have an example also.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Projects
None yet
Development

No branches or pull requests

1 participant