A stochastic leader-follower model in competitive facility location
Bibliographic record
Abstract
The competitive facilities location problem is to find the locations of one or more new facilities among existing competing facilities that maximize the captured market share by the new facilities. In the leader-follower models, the leader locates his facility first and anticipates a competing follower to locate his facility optimally, knowing the location selected by the leader. The leader’s objective is to maximize his captured market share following the follower’s action. In this paper we consider the case that the leader is not sure whether there will be a follower or not. We investigate and test the minimax regret and the expected value rules. Algorithms for locating the competing facilities anywhere in the plane, which are more difficult to solve, were designed. The follower’s problem and the leader’s problem when there is no follower are solved to optimality within a given relative accuracy by available algorithms. For solving the leader’s problem when a follower will react knowing the leader’s move, a special heuristic algorithm that can be applied to other location problems is constructed. The leader’s location problem with the objective of minimax regret or expected value decision rules, and 20,000 demand points, were solved in less than 4 min of computer time.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.003 |
| 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".