Interdependent security games in a unidirectional network
Bibliographic record
Abstract
We consider directed tree networks with a single source, where there exists a positive probability of a disruptive event at any node. Such networks model security considerations in pipelines as well as in unidirectional digital networks. If a disruptive event occurs at a certain node, that node and its downstream nodes incur economic losses. Users thus have an incentive to invest in upstream locations as well as their own sites to reduce the probability of a disruptive event. The initial model we develop to reduce the expected investment plus disruption costs is a multiplicative model for which closed-form solutions cannot be obtained in general. We overcome this problem with an additive model that we show closely approximates the initial formulation. This model reduces the security problem to a public goods setting where we minimize the total expected cost at each node. The users then need to share these costs in an equitable fashion, which gives rise to a set of cooperative games. For the case where disutilities to all users are identical, the Shapley value can be computed efficiently, along the lines of an Airport Game. We also treat the case where risk reduction and disutility vary across the network. Finally, we prove that the cooperative game is concave in this general case, which guarantees that the core of the game is nonempty and that the Shapley value is an element of the core.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.006 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".