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First Attack, Final Offensive: The Dark Forest on an Open Roster

Harvey Dam

arXiv:2609.12003v2cs.CRcs.GT

TL;DR

Existing formal models of strike upon detection treat the found civilization as the target and assume the attacker knows the roster is complete. This paper instead models hostility as remaining capacity to retaliate or warn on an open roster, and finds that universal striking is not an equilibrium when strikes are more visible than hiders are findable.

  • Problem

    Prior formal models commonly make the detected civilization the object of a strike and assume a closed roster, although SETI detection is incomplete.

    Source: §2 · p. 2

  • Method

    The paper models hostility as remaining uncontrolled capacity to retaliate or warn and tests whether a strike's timing benefit covers disclosure losses across an open roster.

    Source: §1 · p. 1

  • Results

    With survival as payoff, universal striking is not a Nash equilibrium when strikes are more visible to unfound hunters than hiders are findable, while universal hiding is an equilibrium.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The argument places a capable witness, found or not, inside the attacker's stake before any kill, so its constraint does not depend on successful retaliation.

    Source: §6 · p. 6

    The paper estimates none of the quantities in its conditions, so it does not establish whether those conditions hold for any actor in the sky.

    Source: §5 · p. 6

Abstract

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The Dark Forest argument holds that a civilization that detects another should strike it at once. Existing formal models make the detected civilization the object of the strike and play it on a roster the attacker knows to be complete. This paper changes both choices. The object of hostility is remaining uncontrolled capacity to retaliate or to warn someone who can, and the roster is open: no attacker ever knows it has met everyone. A first strike is then rational only if the timing benefit of what it removes now rather than later is at least the disclosure loss from every survivor that learns of it. A survivor that can bring about the attacker's destruction enters that loss as a lump, not a per-unit rate, and the actors the attacker has never found may be such a survivor, one that no strike removes. Their capacity cannot be estimated, but what they can do is capped at the attacker's destruction, so the test against them asks one answerable question: a first strike is rational only if the attacker accepts that the strike may be its last attack. The Dark Forest premises, read as hypotheses, fix what a general attacker cannot estimate: hidden hunters exist, a hunter that verifies a hostile acts against it with probability at least $q$, and a hider is rarely found, so a believer's first strike is rational only if what it removes is worth a $q$-share of its survival, the whole of it as $q$ approaches one. With survival as the payoff, the profile in which every hunter strikes what it finds is not a Nash equilibrium whenever a strike is more visible to unfound hunters than a hider is findable, while the profile in which every hunter hides is. That visibility comparison is the decisive physical question; an attacker that treats its strike as unseen has assumed the roster closed.

1 Introduction

The paper revises the Dark Forest argument by treating remaining capacity to retaliate or warn as the object of hostility and by leaving the roster open. It argues that a first strike must pay for disclosure to survivors, including hidden witnesses, and that universal striking is unstable under the stated visibility condition.

1 Introduction

  • A detected civilization is treated as an existential threat in the Dark Forest argument, but prior formal models also assume the target is the found civilization and the roster is complete.The paper changes both assumptions rather than taking sides on the existing strike-or-refrain advice.Source: §1 · p. 1
  • Hostility targets remaining uncontrolled capacity to retaliate or warn, while actors the attacker has never found remain on the open roster.Destroying the detected civilization removes its capacity, but does not remove the other leftovers or establish that none remain.Source: §1 · p. 1
  • The framework assumes an open roster, potentially destructive witnesses, greater visibility of strikes than findability of hiders, and rare discovery of hiders.The visibility comparison is the hypothesis on which the paper's conclusions turn, not a premise attributed to Liu.Source: §1 · p. 1
  • A first attack is rational only when its timing benefit covers the disclosure loss to every leftover that learns of it.A witness capable of causing the attacker's destruction contributes a lump loss; an unfound witness cannot be removed, and its possible loss is capped at the attacker's destruction.Source: §1 · pp. 1–2
  • Under the Dark Forest premises, a believer's first strike must be worth a q-share of survival, approaching all survival as q approaches one.With survival as payoff, universal striking is not a Nash equilibrium when strikes are more visible to unfound hunters than hiders are findable; universal hiding is an equilibrium.Source: §1 · p. 2
  • The same accounting applies to a revealing transmission: under observe-and-relay, its sender becomes a witness that hostile receivers must price.The paper presents this as an application of its argument, not as advice about transmission.Source: §1 · pp. 1–2

2 Related work

Prior strike-on-detection models differ in their advice but commonly treat the found civilization as the target and assume a closed roster. The paper reframes the comparison around what a strike removes and what remains capable of harming the attacker.

2 Related work

  • Strike-on-detection models can be compared by who plays, what a strike removes, and why striking now beats waiting.The prior models generally leave whoever remains outside the object of hostility, whereas this paper uses an open roster.Source: §2 · p. 2, Table 1 · p. 3
  • The Dark Forest argument derives an immediate strike against a detected civilization from survival, growth under finite matter, chain of suspicion, and technological explosion [Liu 2008].Those premises address unverifiable intent and sudden capability shifts, while the conclusion concerns the civilization just found, not the rest of the sky.Source: §2 · p. 2
  • Prior models use closed rosters, so an attacker can know who is in the game and when no one remains.In SETI, detection is difficult and incomplete, so an undetected civilization cannot be equated with an absent one.Source: §2 · p. 2
  • The paper says its mechanism is a capable witness, found or not, entering the attacker's stake before any kill.This differs from Korhonen's estimated chance of escaping punishment and Jebari and Asker's belief-based mechanism, which remains conditional on a detected encounter [Korhonen 2013] [Jebari and Asker 2024].Source: §2 · pp. 2–3

3 Remaining-capacity hostility

The paper defines hostility by the uncontrolled capacity others retain to harm an actor, rather than by how many civilizations remain. Its account includes both direct retaliation and warnings, and leaves an uncatalogued part of the roster that an opening cannot remove.

3 Remaining-capacity hostility

  • Remaining-capacity hostility measures what others can still take from an actor, regardless of whether that capacity belongs to a civilization, coalition, copies, or machine cluster.The hostile's utility is capped at its maximum possible loss, so capacity is non-additive across actors.Source: §3 · p. 3
  • Warning and retaliation are two channels of the same capacity: a witness can use its own force or direct another capable actor against the hostile.A leftover need not be able to strike personally if it can warn someone who can.Source: §3 · p. 3
  • The analysis groups actors by whether they treat one another's remaining capacity as external, with hostility between the group and leftover independents.A smaller alliance leaves more capacity external, making coverage hardest for an attacker without allies.Source: §3 · p. 3
  • At a first type-revealing strike, a leftover may be included, remain unaware, survive as a responder, or enter the hostile's group.An unseen strike requires that no witness relay it; striking only the detected civilization leaves other hunters as threats unless extra structure is added.Source: §3 · p. 4
  • The roster is finite but never known to be complete, and an opening can remove only actors the attacker has found.The uncatalogued part has positive probability of being nonempty; its possible capacity remains a credence of the attacker.Source: §3 · p. 4

4 Opening coverage

The analysis weighs the timing benefit of an opening against the disclosure losses it creates, then tests when Dark Forest premises can justify striking and what conditions might restore it.

4.1 What a first strike must pay for

  • A rational opening must cover every witness’s disclosure loss with the timing benefit of removing capacity now rather than later.A capable witness imposes a lump rather than a per-unit rate; an unfound witness remains beyond any opening, putting the attacker’s survival at stake.Source: §4.1 · pp. 4–5

4.2 The believer’s last attack

  • Under the formalized premises, a believer stakes at least a (q-f)-share of survival on a first strike; as q nears one and f stays small, it may be its last.The strike reveals hostility, while the hidden hunters cannot be counted on to be found before they act.Source: §4.2 · p. 5

4.3 Strike or hide

  • When a strike is more visible to unfound hunters than a hider is findable, universal striking is not a Nash equilibrium, while universal hiding is.For a hunter holding the Dark Forest premises about the unfound, striking first is never a best response.Source: §4.3 · p. 6

4.4 What would restore a first strike

  • The proposed routes to restoring a first strike are contrived: urgency, an unverifiable closed-roster duel, and changes among known actors leave the unfound-witness problem intact.An incomplete strike creates urgency for a second strike, not a first, because the hostile type has already been revealed.Source: §4.4 · p. 6

5 Limitations

The paper derives conditions for rational first strikes but does not estimate the real-universe quantities needed to assess whether any actor meets them.

5 Limitations

  • The paper estimates none of the quantities in its displays, including hidden-civilization detection, strike attribution, hidden capacity, and responses to verified hostility.Some quantities, including strike detectability and attribution and the reach of hiding, could be constrained by astrophysics.Source: §5 · p. 6
  • The conditions specify what would have to be true for a first strike to be rational, not whether it is true of any actor in the sky.No number in the paper should be read as a claim that those conditions hold in reality.Source: §5 · p. 6
  • The paper leaves real-world applicability unresolved because it does not attempt estimates of the quantities its conditions depend on.The quantities include how likely hidden civilizations are to be found and how a verified hostile would be treated.Source: §5 · p. 6

6 Conclusion

The strike-upon-detection conclusion does not follow from detection alone: under the paper’s premises, hiding is an equilibrium while universal striking is not. The model also treats observability as a public good and leaves learning, evolution, and capacity growth as open questions.

6 Conclusion

  • Under the paper’s premises, universal striking is not an equilibrium, while universal hiding is; the strike-upon-detection conclusion does not follow from detection alone.The conclusion is about the world described by the premises, not a claim about the actual sky.Source: §6 · p. 6
  • Each additional independent able to see a strike can only increase the disclosure cost an attacker must pay.A signal that reveals its sender adds the sender to every hostile receiver’s witnesses, but whether a beacon’s expected payoff exceeds its transmission cost depends on parameters the paper does not estimate.Source: §6 · p. 7
  • Which no-shoot profile learning or evolution selects remains open, as does when differing capacity-growth rates make Bcost dominate coverage.Source: §6 · p. 7

A Related work (extended)

Prior work commonly treats the detected civilization as the strike’s object and assumes a closed roster, even when it includes other civilizations in the analysis. This paper’s comparison turns on modeling the remaining uncontrolled capacity of survivors and the actors an attacker has not found.

Two players

  • Two-player first-strike models make the struck adversary the whole remainder, so they cannot pose how much of a larger remainder must be covered or when revealing the sender helps [Schelling 1960; Wohlstetter 1959; Jebari and Olsson-Yaouzis 2018].The two-player roster is closed by fiat, and being revealed can only add exposure in that setup.Source: A Related work (extended) · p. 7

Many players, leftovers outside the object

  • Jebari and Asker [2024] use unobserved civilizations as evidence for a peace mechanism, but the game remains a two-player Attack/Don’t Attack choice.Korhonen [2013] instead includes the probability of no capable Nth civilization in escape from punishment, with warning after a kill; remaining-capacity hostility counts warning capacity before the kill.Source: A Related work (extended) · pp. 7–8

Shared conclusions, different arguments

  • Korhonen’s deterrence depends on the sender’s ability to retaliate, while beacon deterrence can instead arise from warning capacity even when the sender cannot strike [Korhonen 2013].The beacon’s effect follows from adding the sender to the hostile receiver’s witness set under the observe-and-relay assumption.Source: A Related work (extended) · p. 8

Many players, leftovers outside the object

  • Models that add civilizations still keep the strike focused on a detected target or named coalition, leaving other actors outside remaining uncontrolled capacity [Kuusela and Roy 2024; Best and Bracken 1995; Powell 1999].Kuusela and Roy call common knowledge of all civilizations’ existence and locations an invalid assumption and list open-agent models as future work.Source: A Related work (extended) · p. 8

Transmission

  • Prior METI accounts leave transmission’s sign dependent on an unknown watcher motive, whereas remaining-capacity hostility asks whether the sender becomes a witness the receiver must pay for [Gertz 2016; Baum et al. 2011; Haqq-Misra et al. 2013; Haqq-Misra 2019].Under the observe-and-relay hypothesis, a beacon can make the sender a witness; whether its expected payoff exceeds transmission cost depends on parameters the paper does not estimate.Source: A Related work (extended) · pp. 8–9

The location problem

  • A beacon establishes the sender’s existence and ability to transmit to the receiver’s region, but only gives a loose posterior about the sender’s position and capacity.The paper distinguishes a transmitter’s apparent position at emission from the location of forces a hostile must find and remove.Source: A Related work (extended) · pp. 8–9

Occupancy

  • Colonization and grabby-alien models treat occupancy of volume as the relevant object, unlike this paper’s focus on leftover uncontrolled capacity after a revealing strike [Brin 1983; Armstrong and Sandberg 2013; Hanson et al. 2021; Sandberg and Armstrong 2013].Source: A Related work (extended) · p. 9

B Formal statements

The formal model defines hostility in terms of the remaining inflictable loss from uncontrolled actors, including witnesses who can warn others. With an open roster, an attacker cannot remove unfound actors, and the resulting disclosure risk shapes both first-strike rationality and the strike-or-hide game.

Definitions

  • The model separates timing benefit B(K), disclosure loss D(W), campaign cost C(K), and maximum loss H_i, with remaining inflictable utility loss abbreviated R.Source: B Formal statements · p. 9

Leftover cases

  • At a hostile act, an actor outside [i] is either removed, unseen and unable to respond, a surviving responder whose continuation loss enters the account, or incorporated into [i].An act is unseen by an actor only if no witness can relay it.Source: B Formal statements · p. 9

Open roster

  • The open-roster assumption gives the attacker a catalogued set and an uncatalogued set U_i, which has positive probability of being nonempty; every opening leaves U_i intact.Assessed disclosure loss is the conditional expectation of the loss from actors outside the opening.Source: B Formal statements · p. 9

Capable witness

  • A capable witness’s disclosure loss is at least π_w q_w H_i, so a rational opening that excludes that witness must meet a whole-loss threshold rather than merely price a per-unit rate.The witness may destroy the attacker directly or warn an actor that can.Source: B Formal statements · p. 9

The uncatalogued witness

  • An uncatalogued actor that can bring about the attacker’s destruction creates a necessary bound even for an opening that removes every actor the attacker has found.The bound includes the assessed destruction risk and a campaign-cost condition; no opening removes the uncatalogued witness.Source: B Formal statements · pp. 9–10

Strike or hide

  • With survival as payoff, universal striking is not a Nash equilibrium when strikes are more visible to unfound hunters than hiders are findable, while universal hiding is an equilibrium.Under the Dark Forest premises, each hunter prefers to hide; the result uses the visibility comparison rather than the hunters’ strike probabilities or their number.Source: B Formal statements · p. 10

Observe and relay

  • Under observe and relay, a sender that can reach a receiver’s region can observe an unconcealed hostile opening and warn actors within its transmission reach.A hostile receiver assigns probability π_s that the sender or its warning brings about the receiver’s destruction.Source: B Formal statements · p. 10

Beacon and witness

  • When the sender cannot be removed with the required probability and a hostile fears someone within the sender’s reach, a beacon’s negative strategic increment requires a hostile opening despite the witness lump.Otherwise the beacon’s strategic increment is nonnegative, and is positive if it delays an opening or draws an exchange; witnessing does not require the sender to retaliate.Source: B Formal statements · pp. 10–11

C Constant-rate coverage

The constant-rate coverage result compares timing benefit and disclosure loss per unit of an additive measure of remaining capacity. Its required coverage share approaches one when timing benefit is small relative to disclosure loss, while saturation limits the usefulness of the rate bound.

Constant-rate coverage

  • As b/d approaches zero, a rational opening must cover a share of remaining capacity that approaches one.The constant-rate assumptions bound timing benefit above by b per unit and disclosure loss below by d per unit.Source: C Constant-rate coverage · p. 11

Limits of the rate bound

  • The per-unit share bound becomes loose when witness losses saturate at the attacker’s destruction cap, and overlapping warnings can make the additive measure overcount disclosure loss.The rate share is exact only below saturation, where no witness set’s disclosure loss approaches the cap.Source: C Constant-rate coverage · p. 11

Believer’s share

D Detection decomposition

Detection updates the expected safety margin through selection and any target-specific benefit of attacking now. When more remaining capacity makes detection more likely and waiting safer, detection raises the margin for waiting; an attack can become rational only through negative selection or a sufficiently large target-specific extra.

D Detection decomposition

  • The decomposition separates a selection term from the direct reduction in the safety margin caused by identifying the newly detected capacity.The direct reduction is denoted u and includes a closing window or another target-specific extra.Source: D Detection decomposition · p. 11
  • A detection raises the expected margin for waiting when detectability and the pre-detection safety margin are both nondecreasing in remaining capacity.The result follows from nonnegative covariance between detectability and the pre-detection margin.Source: D Detection decomposition · p. 11
  • If newly detected capacity can be included in the opening, the wait margin need not rise; otherwise the selection argument extends to detections of previously unknown capacity.The nearby-find result transports Jebari and Asker [2024] from civilization counts to remaining capacity.Source: D Detection decomposition · pp. 11–12
  • After a detection, a first attack can become rational only through negative selection or a sufficiently large target-specific benefit from attacking now.Negative selection means detection is disproportionately likely in worlds with a small safety margin; the extra can include a closing window.Source: D Detection decomposition · p. 12

E Application: a transmission that reveals the sender

A beacon reveals the sender and, under an additional observation-and-relay assumption, demonstrates warning capacity that enters a receiver’s accounting of remaining capacity. Exposure alone does not determine the sender’s payoff: harm beyond transmission cost requires an in-horizon hostile opening that removes the sender, while exchange or delay can benefit the sender.

E Application: a transmission that reveals the sender

  • Under Assumption B.10, a beacon demonstrates a communication channel that can serve as warning capacity, and receivers account for the sender through remaining-capacity coverage.The channel bounds the receiver’s assessed loss from the sender away from zero; without B.10, the beacon proves transmission but nothing more.Source: E Application: a transmission that… · p. 12
  • A beacon that cannot be included weakly lowers a receiver’s attack margin, while inclusion tips the receiver only when added timing benefit covers the shortfall and the risk of a surviving sender.A sender’s apparent position loosely identifies where its forces were when the signal left, not necessarily where they are now.Source: E Application: a transmission that… · pp. 12–13
  • Harm beyond transmission cost requires an in-horizon hostile opening that removes the sender, through a sure kill, urgency, disbelief, or concealment.The opening must also pay the receiver’s witness loss from actors it has not found, whether or not the sender is among its targets.Source: E Application: a transmission that… · p. 13
  • Off those harm routes, a beacon can have positive strategic increment through an acceptable exchange or by delaying a hostile beyond the sender’s horizon.Whether sending is worthwhile depends on the sender’s expected strategic increment relative to its transmission cost; the paper estimates neither quantity for any sender.Source: E Application: a transmission that… · p. 13

F Beacon accounting

Beacon accounting tracks how revealing the sender changes a receiver’s attack margin and how that response changes the sender’s payoff. Inclusion can tip an attack only when its timing benefit pays for the pre-existing shortfall and the risk of a surviving sender; uncovered witnesses remain part of the cost.

F Beacon accounting

  • A beacon tips an attack only when the sender’s added expected timing benefit, net of survival risk, exceeds the receiver’s pre-beacon shortfall.When the receiver cannot include the sender, the post-beacon attack margin weakly falls; when it can, the added target and remaining-capacity accounting otherwise cancel in the margin.Source: F Beacon accounting · pp. 13–14
  • An uncovered leftover that can destroy the receiver or warn someone who can adds a lump disclosure loss, so a believer is tipped only if its opening already pays for unfound hunters.For a believer, the uncatalogued witness contributes q times the receiver’s survival stake regardless of what the opening removes.Source: F Beacon accounting · p. 14
  • Inclusion cost rises when the sender’s capacity is hard to locate and remove, because a failed attempt can leave a capable, informed sender alive.The apparent transmission position only loosely fixes the sender’s capacity location, and the failure loss is assessed as a witness lump.Source: F Beacon accounting · p. 14
  • The sender’s strategic increment depends on hostile reach: in-reach openings that remove it can harm, while out-of-reach delay can benefit it.The accounting distinguishes receivers that can include the sender, can strike it later, or cannot strike it within the sender’s horizon.Source: F Beacon accounting · p. 15
  • With no tipping, harm beyond transmission cost occurs only when an in-reach hostile opens within the sender’s horizon; off that event, the beacon costs at most the transmission cost.Positive strategic increment can also arise from acceptable exchange or delay, and the sender still must compare expected increment with transmission cost.Source: F Beacon accounting · p. 15
  • The sign-probability comparison bounds positive-increment probability against the harm-event probability, using a template rather than a model of the universe’s population.The template’s bounds depend on its stipulated receiver parameters; the expected increment still requires the sender’s own event valuations.Source: F Beacon accounting · p. 15

G Illustrative values

The two tables instantiate displayed inequalities at chosen values; they are illustrative rather than empirical estimates or a census of the sky.

G Illustrative values

  • The two tables instantiate the displayed inequalities at chosen numbers.Their values are illustrations, not parameter estimates.Source: G Illustrative values · p. 16
  • The tables are not estimates of unknown hostiles’ parameters.The paper distinguishes illustrative values from estimates.Source: G Illustrative values · p. 16
  • The tables are not a census of the sky.They do not report a measured population of civilizations.Source: G Illustrative values · p. 16

H Proofs

The proofs derive bounds on when an opening is rational, compare striking with hiding, and establish selection and beacon-related results. They also show how constant-rate assumptions translate disclosure constraints into a minimum coverage share.

H Proofs

  • Rationality requires the opening’s timing benefit B(K) to cover disclosure loss from the remaining roster, so B(K) ≥ D(N\K).With nonnegative opening cost, the proof also gives B(K) ≥ D(N\K) + C(K).Source: H Proofs · p. 16
  • A witness with probability π_u of existing and probability at least q_u of bringing about destruction imposes an expected disclosure-loss bound of at least π_u q_u H_i.The proof combines this witness bound with the rational-opening inequality and a split of the timing benefit into hazard and cost components.Source: H Proofs · p. 16
  • The two rate bounds imply b m ≥ B(K) ≥ D(N\K) ≥ d(R−m), hence (d+b)m ≥ dR and, for d+b>0 and R>0, m/R ≥ d/(d+b).For d>0, d/(d+b) = 1/(1+b/d) approaches 1 as b/d approaches 0.Source: H Proofs · p. 16
  • When strikes are more visible to unfound hunters than hiders are findable, all-strike is not a Nash equilibrium; all-hide is an equilibrium, with equality only in the degenerate case.The proofs identify the strict visibility comparison as the condition favoring hiding.Source: H Proofs · p. 16
  • The posterior wait margin rises by a nonnegative selection term when the selection weight and baseline wait margin are nondecreasing in capacity.The proof derives the sign from the nonnegative covariance of those two nondecreasing quantities.Source: H Proofs · p. 16
  • A sender’s inclusion attempt must make expected removal benefit exceed extra inclusion cost and the failure term; otherwise the attempt does not pay for itself.The proof also derives a constant-rate condition and notes that insufficient timing benefit makes the inclusion condition fail.Source: H Proofs · p. 17
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