Stable Farsighted Coalitions in Competitive Markets
Why this work is in the frame
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Bibliographic record
Abstract
In this paper, we study dynamic alliance formation among agents in competitive markets. We look at n agents selling substitutable products competing in a market. In this setting, we examine models with deterministic and stochastic demand, and we use a two-stage approach. In Stage 1, agents form alliances (coalitions), and in Stage 2, coalitions make decisions (price and inventory) and compete against one another. To analyze the stability of coalition structures in Stage 1, we use two notions from cooperative games—the largest consistent set (LCS) and the equilibrium process of coalition formation (EPCF)—which allow players to be farsighted. Thus, in forming alliances, players consider two key phenomena: First, players trade off the size of the total profit of the system versus their allocation of this total pie, and second, they weigh the possibility that an immediate beneficial defection can trigger further counter defections that in the end may prove to be worse than the status quo. In particular, one such example is that of the grand coalition—which we show to be stable in the farsighted sense—even though players benefit myopically by defecting from it. We also provide conditions under which a situation of a few lone players competing against a large coalition is stable. We examine the impact of the size of the market (n), the degree of competition, the effect of cost parameters, and the variability of the demand process on the prices, inventory levels, and structure of the market. We discuss the possible strategic implications of our results to firms in a competitive market and for new entrants.
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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 | 0.011 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.005 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it