Bounded pliability
Should social context change expectimax itself, or rerank a bounded set of alternatives?
01Freeze the reference
02Bound the concession
03Choose with context
The decision at the table
The search prefers a build. A negotiator prefers a slightly lower-scoring trade that may preserve goodwill. Calling the trade “suboptimal” is premature: it is worse under the fixed search estimate, but could be better under a more complete model of future responses.
The mechanism to test
Keep three operations distinct. Update beliefs when a message provides evidence. Change the evaluator when modelling a future social consequence. Rerank candidates when applying an explicit preference or concession budget. Preserve the original search report before all three, so each change can be audited.
A practical proposal admits only actions whose foregone reference value is at most ε, then scores eligible actions with a separately estimated social continuation term. The social weight λ expresses how much to trust that term. An eligibility threshold that merely calls a language model is not the same as a hard bound on its selected move.
How much should a player bend?
Adjust the assumptions to see when a concession becomes worthwhile. These example values are not measured game results.
Score = Q + λ × p × F
Q: fixed search value. F: assumed future benefit if reciprocity happens (A: 0, B: 8, C: 16). Only choices with Q(best) − Q(choice) ≤ ε are eligible. Future benefits use the same toy utility units as Q and exclude benefits already counted in Q.
| Choice | Q | Foregone | Score | Decision |
|---|---|---|---|---|
| A · Build now | 100 | 0 | 100.00 | Eligible |
| B · Modest concession | 98 | 2 | 101.00 | Selected |
| C · Large concession | 92 | 8 | 98.00 | Over budget |
Selected: B · Modest concession. Foregone reference value: 2 units.
Where the preferred choice changes
Illustrative · syntheticScroll the chart horizontally to inspect all values.
Only eligible candidates are drawn. Crossing lines show a change in the toy ranking as social weight increases; they do not establish a causal benefit from reputation.
Source: Teaching model: Q + λ × p × F; p and ε follow the controls above.
View data table
| Series | Social weight λ (current: 0.50) | Toy utility |
|---|---|---|
| A · Build now | 0 | 100 |
| A · Build now | 0.25 | 100 |
| A · Build now | 0.5 | 100 |
| A · Build now | 0.75 | 100 |
| A · Build now | 1 | 100 |
| A · Build now | 1.25 | 100 |
| A · Build now | 1.5 | 100 |
| B · Modest concession | 0 | 98 |
| B · Modest concession | 0.25 | 99.5 |
| B · Modest concession | 0.5 | 101 |
| B · Modest concession | 0.75 | 102.5 |
| B · Modest concession | 1 | 104 |
| B · Modest concession | 1.25 | 105.5 |
| B · Modest concession | 1.5 | 107 |
Proposed experiment
Compare fixed expectimax, updated opponent beliefs with unchanged preferences, a social evaluator, and an external social reranker. Then ablate the reranker’s concession cap. Hold candidates, search time, message policy, and context window fixed. Hypothesis: bounded reranking helps in ambiguous social choices without expensive deviations in clear tactical positions.
Plot the frontier of completed-game wins against cumulative foregone reference value, and latency against intervention frequency. Retain reference and selected IDs, both values, social rationale, cap, eligibility, actual applied action, and fallbacks. State the units: the existing reference is heuristic value, not win probability.
What could disprove it
Do not count the same future trade in both Q and the social correction. Do not convert a heuristic gap into a percentage chance of winning. Choosing among only three surfaced candidates may miss a better social action; candidate generation needs a separate experiment.
Agent notes
Use the shared experiment design to freeze candidate versions, full lineups, budgets, sample size, primary contrast, and stopping rules before collecting evidence. This is a draft study brief, not a preregistration. No run IDs exist for this proposal.
The deployable policy reads only its own observation and recipient-visible events. The diagram is a conceptual schematic. Build new measured exhibits from retained artifacts using the visual publishing guide.
The interactive model below is an illustration, not the current agent implementation or a tuned policy setting.