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Record W4414593628 · doi:10.11647/obp.0490.14

14. Bargaining

2025· book-chapter· en· W4414593628 on OpenAlexaff
Martin J. Osborne

Bibliographic record

VenueOpen Book Publishers · 2025
Typebook-chapter
Languageen
FieldEconomics, Econometrics and Finance
TopicGame Theory and Voting Systems
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsSubgame perfect equilibriumOutcome (game theory)Status quoSubgameRepeated gameVotingSequential equilibriumInterval (graph theory)Distribution (mathematics)

Abstract

fetched live from OpenAlex

Suppose that an individual is selected randomly to propose an alternative, all individuals vote for or against this alternative, and the proposal is implemented and the game ends if a majority is in favor, while otherwise the procedure is repeated until a proposal is accepted by a majority. Every alternative is the outcome of a subgame perfect equilibrium of the resulting extensive game, and, if the individuals' votes are observable, most alternatives are outcomes of subgame perfect equilibria in which every individual's vote is undominated. If only the outcomes, not the individuals' votes, are observable, and the individuals are sufficiently patient, then if the alternatives are distributions of a fixed amount of a good, every alternative is the outcome of a subgame perfect equilibrium with undominated voting, while if the set of alternatives is an interval of numbers and the individuals' preferences are single-peaked, the outcome of a subgame perfect equilibrium with undominated voting is close to the median of the individuals' favorite alternatives. Now suppose that bargaining is on-going. An individual is selected randomly to propose a distribution of a fixed amount of a good, and all individuals vote for or against this proposal. If a majority votes in favor, the proposal is implemented in the current period, and otherwise the status quo is implemented. In both cases, the procedure is repeated in the next period, with the status quo in each period equal to the previous period's outcome. There are examples in which almost any distribution is the outcome of a stationary subgame perfect equilibrium of this model, including distributions in which some of the good is wasted.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Scholarly communication, Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.426
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.000
Meta-epidemiology (narrow)0.0000.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0030.002
Open science0.0020.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0130.004

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.

Opus teacher head0.048
GPT teacher head0.234
Teacher spread0.186 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; both teacher heads agree on what is shown here.

Study designNot applicable
Domainnot available
GenreOther

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".

Quick stats

Citations0
Published2025
Admission routes1
Has abstractyes

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