The Inbox as a Coordination Primitive for LLM Agent Societies

1 Introduction

• An inbox holds messages outside the agent’s context until its privately set rules decide what to read and respond to, giving those rules public coordination consequences.The paper calls it a coordination primitive because every form of coordination runs through it.Source: §1 · p. 1

1.1 Scope

• The study tests inboxes in simulated societies of up to 16,000 agents across coordination goals, while using deliberately simple rules and not claiming any tested rule is optimal.It examines four design choices rather than every possible inbox decision.Source: §1 · p. 1, §1.1 · p. 2

1 Introduction

• At 20 negotiations, push makes an agent with full memory propose already-rejected options 97% of the time.The agent drops the oldest replies.Source: §1 · pp. 1–2
• Under heavy traffic where first-come, first-read misses every request, refundable-deposit-first reading finds about 60% of the agents a request needs at sizes from 1,000 to 16,000.Source: §1 · p. 2
• The best rule for each of an inbox’s four decisions depends on traffic and the agent’s role, so no single design suits every society.The decisions are what to read, what to keep, what a sender pays for attention, and what a reply may say.Source: §1 · p. 2

2 Related Work

• Coordination research covers task allocation, coalition formation, protocols, communication costs, search and routing, and forwarding incentives,,,,,, while this paper studies recipients’ capacity to read and remember.Source: §2 · p. 2
• The rules build on established queueing, caching, and email-management ideas,,, while the study examines coordination effects of independently chosen inbox rules under limited attention and memory.Source: §2 · p. 2
• Unlike work on LLM-agent systems, this paper examines competing requests, limited reading budgets, bounded memory, and how recipient inbox rules shape coordination across multiple recipients.Source: §2 · p. 2

Inbox model

• Inbox design separates which messages to read from what information to keep, since a message read now may be forgotten before a later decision needs it.These choices build on queueing and caching problems.Source: §3 · p. 2
• An inbox holds messages outside the model context; validation and fixed sender or category rules run before remaining messages wait for selection.The model judges selected messages using retained context and private information, then decides whether and how to respond.Source: §3 · p. 2
• A recipient-set refundable sender stake can prioritize reading, while reply vocabulary limits disclosure from simple decisions to private information.The stake affects reading order but does not guarantee acceptance or a useful reply.Source: §3 · p. 2

Push: the sender decides what the model sees

• With 20 meetings and full memory, push repeats previously rejected times 97% of the time; keeping every reply lowers this to 11% at 10.5× the tokens.Under heavy spam, push finds 0% of the group.Source: §3 · p. 3

Pull: the recipient’s inbox decides what the model sees

• Under heavy spam, paid mail first finds 60–63% of the group at 1,000 to 16,000 agents, while push finds 0%.At 16 of 32 messages, paid mail first is right 98% of the time at half the tokens of push.Source: §3 · p. 3

Push and pull

• Pull makes reading and retention recipient-controlled, whereas push delivers messages in arrival order and drops the oldest when context fills.The compared rules are representative, not exhaustive, and are not claimed to be optimal.Source: Figure 1 · p. 3, §3 · p. 3

Experimental questions

• The experiments ask how push scales with concurrent coordination, whether inboxes matter across roles, team sizes, societies, and networks, and which rules suit different limits and traffic.Additional experiments test discovery, adoption, competing requests, and adversarial senders.Source: §4 · p. 3

Coordination tasks

• Meeting scheduling tests negotiations over shared times across several rounds, while group formation tests whether a requester finds enough agents with matching private interests before expiry.Group formation includes direct and forwarded communication.Source: §4 · p. 3

Agent decisions and comparisons

• The simulation provides messages, private information, network structure, and correct outcomes; an LLM decides from only the information available to its agent.The study uses gpt-5.6-terra unless stated otherwise, with additional tests using gpt-5.4-mini and gpt-5.6-sol.Source: §4 · p. 4
• Where possible, rules face the same decisions under equal reading and memory limits, with all-information and exact-retrieval controls and both manageable and heavy traffic.Scheduling measures repeated proposals and conflicting commitments; group formation measures relevant agents found and groups formed, alongside message reading, response correctness, and token cost.Source: §4 · p. 4

4.1 Concurrent Coordination with Limited Memory

• At 20 meetings, forgetting the oldest causes 97% of proposals to repeat rejected times; at the same memory limit, keeping whole conversations yields 80% and model-selected retention 58%.The entire history yields about 11%; both inbox rules read substantially fewer tokens than keeping everything.Source: §4.1 · p. 4
• At 20 concurrent meetings, keeping the full history requires 10.5 times the tokens of perfect retrieval while performing almost as well at every tested load.At two meetings, all memory rules perform similarly.Source: §4.1 · p. 4
• Forgetting by age can leave part of a conversation while dropping earlier rejections, whereas retaining whole conversations may discard the conversation needed next.When the required conversation remains intact, performance matches perfect retrieval.Source: §4.1 · p. 4
• The same ordering holds across five societies, but results depend on model instructions, and correcting them erased an earlier full-history versus perfect-retrieval difference.The authors frame the main finding as history-retention cost and consequences of losing replies, not a fixed ranking of memory rules.Source: §4.1 · p. 4

Takeaway 1: Scaling coordination requires pull

• As coordination grows, pull separates message receipt from deciding what to read and retain, allowing agents to manage attention and memory.Push instead requires reading an increasingly large history or forgetting information needed for later decisions.Source: §4.1 · p. 4

4.2.1 Team size.

• Across team sizes, retaining all replies stays within 0.05 of perfect retrieval but costs three to eight times as many tokens.The main limitation of push comes from concurrent interactions rather than group size alone; larger groups can also change which memory rule works best.Source: §4.2.1 · pp. 4–5

4.2.2 Agent role and memory.

• At 20 invitations, a promise list reduces conflicting replies to 28%, though the model offers committed times in 60% to 69% of cases even with all replies available.Keeping whole conversations, which helped an organizer, performs poorly when commitments are spread across conversations.Source: §4.2.2 · p. 5

4.2.3 Society size.

• At 1,000 to 16,000 agents under heavy unwanted traffic, paid mail first finds about 60% of relevant agents, while push finds none.Widening search performs worse as society size grows because it contacts at most 1,000 agents.Source: §4.2.3 · p. 5

4.2.4 Forwarding across a contact network.

• With half of agents using paid mail first, forwarded search retains only 26%, 10%, and 5% of full-adoption results as networks grow, versus 42% to 53% for direct search.Under heavy unwanted traffic, losses increase with the number of inboxes a request must pass through.Source: §4.2.4 · p. 6, Table 3 · p. 6

Choosing rules

• Model selection reads unaffordable offers as often as affordable ones, applying the recipient’s private budget only when responding.A message can appear relevant without being useful to the recipient.Source: §4.3 · p. 7

Reading rules

• With only four reads, model selection finds the relevant message in 77% of cases, versus fewer than half for every other rule, but costs nearly five times as many tokens as perfect retrieval.Figure 6 compares target reading and answering across rules and read budgets.Source: §4.3 · p. 6, Figure 6 · p. 7
• With sixteen reads, paid mail first finds every target and matches perfect-retrieval accuracy at about a quarter of its token cost relative to the assistant’s selection.The figure reports gaps under 0.05 as noise.Source: Figure 6 · p. 7

Choosing rules

• Inbox rules should account for reading limits, selection costs, and competing traffic; sender stakes can offer inexpensive priority when they distinguish useful requests.Model selection can help under tighter limits but costs more tokens and may overlook private constraints.Source: §4.3 · p. 7

Adoption and discovery

• With heavy unwanted traffic, a folder sorter with 89% classification accuracy reaches about half of relevant agents, while arrival-order reading reaches none; even a perfect matcher forms no groups under arrival-order reading.Under the same condition, about a third of groups form with paid mail first.Source: §4.4 · p. 8

Competing traffic and stakes

• When senders compete, paid priority depends on their behavior: matching the stake reduces the rule to arrival order, while doubling it prevents genuine requests from being read.An attacker posting half the required stake gains no priority.Source: §4.4 · p. 8

Additional context

• With 32 additional messages, response accuracy for gpt-5.4-mini falls from 93% to 77%, while larger models show no comparable loss.Selecting eight messages recovers much of the loss at less than half the token cost; nearly a third of relevant agents are consequently missed in group formation.Source: §4.4 · p. 8

Additional checks

• Better discovery cannot ensure requests are read: reading priority depends on competing traffic and sender behavior, and additional-context effects depend on the model.Source: §4.4 · p. 8

5.2 The Inbox is a Coordination Primitive

• Even a matcher that identifies the correct recipients cannot form groups under heavy traffic if those recipients do not read requests; the problem depends on each agent’s load, not society size alone.Source: §5.1 · p. 8, §5.2 · p. 8

5.1 Delivery, Discovery, and Reading

• Delivery and discovery are distinct from incoming attention: an inbox determines which delivered messages receive attention and which remain unread.Source: §5.1 · p. 8

5.2 The Inbox is a Coordination Primitive

• On a 1,005-agent network, direct search retained 42% under full adoption, while forwarded search retained only 5%.The result is reported when half the agents use paid-mail-first inboxes.Source: §5.2 · p. 8

5.3 Implications for Inbox Design

• Reading rules should reflect attention limits, while memory should reflect an agent’s decisions: organizers benefit from full conversations, whereas commitment managers benefit from compact promise lists.Model selection finds more relevant messages with small reading budgets but costs more tokens; simple priority rules can match it at larger budgets for lower cost.Source: §5.3 · p. 8
• A refundable stake can prioritize requests without inspecting every message, but it signals willingness to pay rather than usefulness and can be defeated by senders matching the required stake.Source: §5.3 · p. 8
• Reply choices control what others learn and have privacy implications, while the tested reply set does not establish which disclosure level best supports coordination.Inbox rules should be evaluated by both recipient resources saved and society-level coordination enabled.Source: §5.3 · p. 8

5.4 Limitations and Open Questions

• Evidence covers two simulated tasks, one provider, shared judgments, and fixed rules under deliberately difficult traffic; adaptive rules, manipulation, and broader heterogeneous settings remain open questions.Source: §5.4 · p. 8

• As agents handle more concurrent interactions, reading every message becomes expensive and forgetting information can make later decisions inconsistent.Source: §6 · p. 9
• The inbox lets recipients decide what to read and retain, how senders obtain priority, and what replies may disclose.Source: §6 · p. 9
• Inbox decisions affect coordination, and their effectiveness depends on agent roles, attention limits, and incoming traffic.The conclusion calls for explicit incoming-message management alongside communication and discovery.Source: §6 · p. 9

• The paper’s numbers regenerate from committed data with one command, and its harnesses, analysis scripts, and table and figure data are released.Source: A Reproduction and Detail · p. 10
• In group-formation runs, shared judgments reduce a 16,000-agent run to 6–23 model calls, while the reported meeting-scheduling reply matches range from 95.4% to 99.9%.The match rates differ by reply type: coarse, full, or yes/no.Source: A Reproduction and Detail · p. 10
• Experiment 3’s table reports target-reading and answer accuracy, tokens per decision, and— for priced replies—whether wanted and too-expensive targets were read and stated limits were right.The setup has 32 arrivals, reads 4, 8, or 16, and 100 decisions per cell.Source: Table 4 · p. 11