What are well-founded, off-line ranking algorithms for assymmetric games? Consider the following setting:
$n$ players (attackers) play an asymmetric, adversarial, 2-player game against $m$ other players (defenders). Two players may play each other $0$ to $k$ times, but each player will play at least some amount of games. The attackers' goal in each game is to maximize the score. Are there any well-founded methods to estimate the strength of each attacker (perhaps expressed as the expected score in a game against an average defender) under the simplifying assumptions listed below?

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*Outcomes of games are not deterministic, since certain aspects of the games should be considered random.

*Both the attackers and defenders have the same strength of play for all games played. Any variation in their strength of play should be considered a result of noise. (No need to have the strength evolve like in elo-like rating systems.)

*There are no cyclical win patterns, so you can consider strength to be one-dimensional. (There are in practice, but they should be considered artifacts of noise.)

*All numbers involved are extremely small. Total number of games played is well under 1000.

Any ranking methods which can be easily adjusted to fit this setting are of course also welcome.
 A: You can use the formula for an Elo system which describes the win probability as a logistic function of the difference in the strength/Elo score.
The algorithm for the Elo computes this in steps and allows the strength to evolve in between steps.
What you can do is compute the ranking in one single step by fitting a logistic model.
$$p_{\text{attacker wins}} = \frac{1}{1+ \exp(x_\text{defender} - x_\text{attacker})}$$
You can do this for instance using a generalized linear model for which there are many software options to compute the result.
You might, after having performed the fit which gives you m+n-1 values (one will be zero by default because only the differences are important), rescale the values of $x$ to get some desired values. E.g. a particular range, median, or mean. Possibly you can impose such restrictions also directly in the fitting method.
A: If you replace "attackers" with "students", and "defenders" with "exam questions", your problem can be tackled using a whole range of models from Item Response Theory. This is a pretty conventional IRT problem, so I won't go into details on particular models, but the standard one parameter logistic IRT model is equivalent to the logistic model suggested by @SextusEmpricus (with a slightly different parametrisation).
