Does it Pay to be First? Sequential Locational Choice and Foreclosure
Bibliographic record
Abstract
We analyze the sequential choices of locations in the Hotelling [0, 1] space of\nvariety-differentiated products. n firms locate in sequence, one at a time. In stage n+1, all firms choose prices simultaneously. Firms anticipate correctly the decisions of subsequent entrants, as well as the equilibrium prices, so we analyze subgame-perfect equilibria. We\nanalyze two games. In the first, the number of firms is fixed. In the second, the number of firms is determined by free entry, i.e., entry continues until the last entrant makes nonnegative profits. When the number of firms is fixed, the ordering of profits follows the\norder of action. When the number of firms is determined by free entry, for a range of fixed costs, early entrants choose their positions strategically so as to keep out potential entrants. For a range of fixed costs, early actors reduce the distances among them to foreclose entry even though these actions reduce their profits given the number of active firms. For low enough fixed costs, entry cannot be prevented any more and a new firm enters resulting in a complete disruption of the locational pattern. In the game with a fixed number of firms, we\nfind that the order of the profits of the firms is the same as the order of action, so that it pays to be first. In contrast, in the free entry game it does not always pay to be first. We also note that entry of a new firm significantly reduces the pre-entry profits of incumbents. Thus, if a technology is available that would increase the costs of both incumbents and entrants ( raising both rivals and own costs ), it will be used to deter entry.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.017 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".