Buena Muerte Social Club

Fabien Mathieu

► To cite this version:

Fabien Mathieu. Buena Muerte Social Club. 2026. hal-05521314

HAL Id: hal-05521314

https://hal.science/hal-05521314v1

Preprint submitted on 20 Feb 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
# Buena Muerte Social Club

Fabien Mathieu ✉敲ID

Swapcard Lab, Paris, France

Sorbonne Université, CNRS, LIP6, Paris, France

## Abstract

Most people believe that the principal weaknesses of vampires are sunlight, wooden stakes in inconvenient places, and extortionate dentist bills.

Most people are mistaken.

Being creatures of undeniably aristocratic persuasion, vampires fear social humiliation above all. In particular, exhibiting symptoms of haematological indigestion (typically induced by an incompatible blood type) constitutes a social death sentence, occasionally followed by the literal kind.

In a generous attempt to save polite vampiric society from disaster of a gastric nature, Renfield, a devoted but emotionally challenged human, established the *Buena Muerte Social Club*. For a modest and entirely reasonable fee, vampires may join its *Ghoul Exchange Programme*, allowing them to trade prospective victims and avoid potentially explosive dietary mishaps.

What algorithm should operate this fine establishment? Can we preserve both nourishment and decorum within the undead community? These are the pressing questions this paper humbly dares to address.

**2012 ACM Subject Classification** Mathematics of computing → Queueing theory; Mathematics of computing → Markov processes; Mathematics of computing → Matchings and factors

**Keywords and phrases** Vampires, online matchings, gastronomical disturbances, stability

## 1 Introduction

The transformation of a human into a vampire has been exhaustively described in the literature [1, 3, 11, 12, 14]. Yet one rather neglected fact remains: even when completely drained of its original blood, a vampiric body retains some characteristics of its former blood type, a phenomenon sometimes referred to as “memory of blood”, in analogy with the notorious and undisputed “memory of water” [4, 7]. Thus, counter-intuitive as it may seem, it is perfectly meaningful to speak of a vampire’s blood type.

This memory manifests itself through an extremely strong digestive intolerance, called *acute haemolytic feeding reaction*, whenever the blood type consumed is incompatible with the vampire's own type [13]. For instance, a vampire with type $A^-$ can safely feed on $O^-$ and $A^-$ victims, but will react rather dramatically to any victim carrying a *B* antigen or a positive Rhesus factor.

Haemolytic reaction has become a real problem because of the rather precise ritual that is vampiric alimentation: having selected a prospective victim, the vampire hypnotises it into a state of docile subservience. By a slight abuse of notation, such a hypnotised human is termed a *ghoul*. Each ghoul may nourish only one vampire (not necessarily its creator). Like an opened bottle of fine claret, however, a ghoul should be consumed promptly or unceremoniously discarded. Further complications arise from a critical etiquette constraint: a vampire cannot inquire after a human's blood type *prior* to hypnosis, such an inquiry being considered vulgar in the extreme, bordering on a *faute de goût*. Consequently, vampires frequently find themselves burdened with ghouls unsuitable for personal consumption.

In the late XIXth century, Renfield, a connoisseur of bugs, vampires, and questionable life choices, fled the European chill for the sultry embrace of New Orleans. In that city of
jazz dirges, hurricane libations, and whispered vampire coteries, he grasped a simple truth: vampires, for all their aristocratic airs, suffered chronic mismanagement of their supply chain.

Thus was born the Buena Muerte Social Club, a discreet establishment where the undead might trade dietary disappointments over Cuban cigars. Count X ($A^+$) no longer needs to endure the social horror of his $B^-$ ghoul whilst Baroness Y ($AB^-$) bemoans her $O^+$ surplus (cf Figure 1). For a modest inscription fee<fnref n="1" />, members could exchange ghouls civilly, resolving supply-demand imbalances with algorithmic precision.

<figure><img src="image_2.png" /><figcaption>■ **Figure 1** The Ghoul Exchange Programme in action: Count X ($A^+$) can safely feed on Baroness Y's $O^+$ ghoul, while she claims his discarded $B^-$ ghoul. Red dashed lines indicate initial incompatibilities; green solid lines show successful feedings post-exchange.</figcaption></figure>

The club swiftly became the preeminent venue for nocturnal commerce: clarinets wailed as blood types swapped hands, etiquette preserved, gastric decorum triumphantly restored. Today, the club remains one highlight of New Orleans' undead social "life". Yet its new owner<fnref n="2" /> senses that the club and its famous *Ghoul Exchange Programme* could benefit from recent advances in matching theory.

Towards that noble goal, this article presents the following contributions. First, we model the Ghoul Exchange Programme as an online stochastic matching problem, categorising vampire-ghoul pairs into three types: *autarkic*, *swinger*, and *helpless*. We show that, while the compatibility graph exhibits appealing structural properties, no stable matching algorithm exists under the assumptions that there is some symmetry between vampires' and ghouls' blood-type distributions and that all ghouls must eventually be consumed. This remains true even when *food orgies* are tolerated.

One solution is the introduction of additional human “volunteers”. Any positive proportion suffices, and we discuss the trade-off between hunger discomfort and the inconvenience of procuring “volunteers”. Another option is to accept that a small fraction of ghouls should be discarded. In that case, the trade-off lies, paradoxically, between hunger and food waste.

All our results are grounded in theory and supported by extensive simulations<fnref n="3" />.

<footnote n="1">¹ Less than student-rate IEEE conference fees (adjusted for 2026 inflation), yet covering premium cigar humidors and jazz trio retainers. Quite a deal, indeed!</footnote>

<footnote n="2">² One Guillermo de la Cruz, who apparently prefers to do things in the shadows [1].</footnote>

<footnote n="3">³ Approval for large-scale clinical trials has been refused. The ethics committee declared that the well-being of vampiric society did not constitute a sufficient justification for sacrificing humans, except perhaps if the outcome of the study could include a miracle cure for baldness.</footnote>
## Disclaimers

- Apparently, the author wanted to pay homage to Sir Terry Pratchett and Gail Carriger with this article<fnref n="4" />. Sadly, his literary talent more closely resembles that of an anvil<fnref n="6" />. This is why, as a Large Language Model (LLM), I was employed to render the result both readable and faithful to whatever the author's original intent may have been (assuming such a thing exists). As an LLM, I can only hope that the scientific content —in which I took no part— is not entirely as nonsensical as his lame attempt to be FUN.

- All cited references genuinely exist. The interpretation of medical literature may however exhibit certain creative liberties, particularly regarding recent advances in vampire haematology.

- Any resemblance to other real-world applications of online matching, such as *Kidney Exchange Programs* [14], must naturally be regarded as purely coincidental. In particular, real-life transplantation compatibility goes well beyond *ABO* types [16]: vampiric culinary algorithms should not be directly applied to human surgeries.

- No vampires were harmed during the writing of this article. Similarly, no humans remain able to testify to any misconduct toward them, and all human remains were disposed of in an ecologically responsible manner.

The remainder of the paper is organised as follows: we introduce online stochastic matching in Section 2. Section 3 presents the adaptation of the model to the Ghoul Exchange Programme. Section 4 shows a general impossibility result, which is circumvented in Section 5. Section 6 concludes.

# 2 Online Stochastic Matching

Our journey towards vampiric gastric well-being begins with a brief review of online stochastic matching. All results presented in this section are drawn from [3] and references therein.

## 2.1 Model

An online stochastic matching model consists of items arriving at random instants to be matched with other items. Matching may occur immediately upon arrival or following a period of queueing.

Formally, a matching model is defined by a triple $(G, \lambda, \phi)$.

The graph $G = (V, E)$, with $|V| = n$ and $|E| = m$, is the *compatibility graph*. Nodes of $V$ represent item types, while edges of $E$ indicate which types may be matched together. If $G$ is a *simple graph*, each edge matches exactly two distinct types. More generally, $G$ may be a hypergraph, where edges represent arbitrary non-empty multisets of $V$ (including self-loops). We assume that every node belongs to at least one edge. Unless otherwise stated, only simple edges and self-loops are considered.

The vector $\lambda \in \mathbb{R}_{>0}^n$ represents *arrival rates* per type, with each type typically following an independent Poisson process.

<footnote n="4">⁴ With a slight preference for Pratchett, a footnote lover⁵ who enjoys one highly-valued artistic virtue that Carriger does not possess: he is dead.</footnote>

<footnote n="5">⁵ I.e. a fetishist that delights in inappropriate footnote insertions.</footnote>

<footnote n="6">⁶ This is not entirely accurate. Some anvils bear correctly spelled English inscriptions.</footnote>
The matching policy $\phi$ determines which matches are executed. It is invoked upon each arrival and performs at most one match per call$^7$, with unmatched items remaining in queue.

One central property of matching models is stability, which states that the number of items waiting in the system will not explode with time. Formally, a model $(G, \lambda, \phi)$ is stable if its evolution forms a positive recurrent Markov chain. A matching problem $(G, \lambda)$ is stabilisable if some policy $\phi$ stabilises it.

Other metrics of interest include delay (related to queue length by Little's law) and matching quality (via edge utilities). In simulations, we will use the measured average queue size as a proxy for both stability and delay.

## 2.2 Main Results

Let $A = (a_{i,j}) \in \mathbb{N}^{n \times m}$ be the incidence matrix of $G$, where $a_{i,j}$ indicates whether node $i$ is an endpoint of edge $j$ (possibly with multiplicity if $j$ is a hyperedge). Under stability, the matches per edge and unit of time define a matching rate $\mu \in \mathbb{R}_{\ge 0}^m$. The arrival rates $\lambda$, matching rates $\mu$, and incidence matrix $A$ are then linked by a conservation equation:

$$ \lambda = A\mu. \qquad (1) $$

Note that $A$ defines a linear map from $\mathbb{R}^m$ (edge space) to $\mathbb{R}^n$ (node space). This map may be surjective, injective, bijective, or none of these. For simple graphs, the surjectivity of $A$ is equivalent to the absence of bipartite connected components in $G$.

Remarkably, stability is entirely characterised by Equation (1) and the surjectivity of a submatrix of $A$.

**▶ Theorem 1** (Adapted from [3], Propositions 7, 8, and proof of Proposition 17). A matching problem $(G, \lambda)$ is stabilisable if and only if Equation (1) admits a non-negative solution $\mu \in \mathbb{R}_{\ge 0}^m$ such that the restriction of $A$ to the support of $\mu$ is surjective.

When stabilisability is established, an effective policy must be identified. Fortunately, certain policies, such as longest queue first (for simple graphs) or virtual queue (a primal-dual algorithm designed for hypergraphs), stabilise any stabilisable problem. These universal policies, while not necessarily optimal for specific instances, offer remarkable robustness.

# 3 The Ghoul Exchange Programme

We now specialise the online stochastic matching model to the Ghoul Exchange Programme by introducing vampire-ghoul pairs (VGs). Each VG is characterised by an ordered pair of blood types, using the notation $T_1/T_2$: the vampire's type $T_1$ (left) and the ghoul's type $T_2$ (right). For instance, $A^+/B^-$ represents an $A^+$ vampire and their $B^-$ ghoul.

For notational convenience, we refer to the antigens $A, B$, and the Rh factor $+$ as markers$^8$. Thus each blood type is a combination of the presence (or absence) of the markers $A, B$, and $+$.

## 3.1 Vampire-Ghoul Compatibility Graph

There are $2^3 = 8$ possible blood types, yielding $8^2 = 64$ distinct VG types. Among the VG types, 8 are symmetric, i.e. vampire and ghoul share identical blood types. Two VG types

<footnote>$^7$ For most reasonable policies, multiple matches per call offer no advantage.</footnote>

<footnote>$^8$ Medical terminology distinguishes antigens and factors, but this distinction is gastronomically irrelevant.</footnote>
are compatible if each vampire can feed on the opposing ghoul, as illustrated by Figure 1. Notably, type $T_1/T_2$ is always compatible with its mirror type $T_2/T_1$.

This definition extends to hyperedges: a compatible hyperedge admits a compatible perfect matching between involved vampires and ghouls.

VG types can be classified into three categories:

**Autarkic** The vampire can feed directly on their ghoul. Example: $AB^-/A^-$. Autarkics lack natural incentive for the Ghoul Exchange Programme.

**Property:** The vampire possesses all markers present in their ghoul.

**Helpless** Compatible only with autarkic VGs. Example: $A^+/AB^+$. Helpless VGs starve without autarkic participation.

**Properties:**

- Mirror of a non-symmetric autarkic type;

- The ghoul has all the markers of their vampire plus at least one additional marker.

**Swingers** Neither autarkic nor helpless. Example: $AB^-/O^+$. Each swinger type is compatible with at least one other swinger type. For obvious reasons, switchers are the main supporters of the Ghoul Exchange Programme.

**Property:** The vampire (resp. the ghoul) possesses a marker absent from their ghoul (resp. their vampire).

Among the 64 VG types, 27 are autarkic, 19 are helpless, and 18 are switchers.

<figure><img src="image_3.png" /><figcaption>Figure 2 Restriction of the VG compatibility graph to its swinger component.</figcaption></figure>

Figure 2 illustrates the swinger subgraph of the compatibility graph<fnref n="9" />.

<footnote n="9">⁹ Larger views of the compatibility graph are available in the *companion notebook*, cf. Section 3.3.</footnote>
## 3.2 Blood type distribution

For numerical experiments, realistic data are desirable. Lacking detailed statistics for New Orleans, we adopt the US blood type distribution proposed in [17]<fnref n="10" />, shown in Table 1.

<table><caption>Table 1 US Blood Type Distribution, from [17]</caption><thead><tr><th>O<sup>+</sup></th><th>A<sup>+</sup></th><th>B<sup>+</sup></th><th>AB<sup>+</sup></th><th>O<sup>-</sup></th><th>A<sup>-</sup></th><th>B<sup>-</sup></th><th>AB<sup>-</sup></th></tr></thead><tbody><tr><td>37.4%</td><td>35.7%</td><td>8.5%</td><td>3.4%</td><td>6.6%</td><td>6.3%</td><td>1.5%</td><td>0.6%</td></tr></tbody></table>

For VG pairs, unless otherwise stated, we assume vampires and ghouls follow identical independent distributions: VG pairs are sampled i.i.d. across both components. For instance, the probability of an $AB^+/O^-$ VG is $3.4\% \times 6.6\% \approx 2.2\%$.

Table 2 reports the resulting market shares across VG categories.

<table><caption>Table 2 VG Category Distribution</caption><thead><tr><th>Autarkic</th><th>Helpless</th><th>Swinger</th></tr></thead><tbody><tr><td>56.6%</td><td>28.2%</td><td>15.2%</td></tr></tbody></table>

## 3.3 Companion Code

In lieu of clinical trials, all numerical analyses and simulations of the Ghoul Exchange Programme were performed using the Python package `stochastic-matching` [8].

All results, code, and interactive visualisations are available at:

https://balouf.github.io/stochastic_matchring/companion/muerte.html

Each simulation processed $10^9$ arrivals<fnref n="11" />.

# 4 Instability of the Programme

We begin with a broad instability result, then we quantify its practical impact.

## 4.1 Theoretical result

**► Theorem 2.** Consider a VG matching problem ($G = (V, E), \lambda$) where $(V, \lambda)$ is mirror-invariant: if $v_i = T_1/T_2 \in V$, then $v_j = T_2/T_1 \in V$ and $\lambda_i = \lambda_j$. Assume that $V$ contains at least one non-symmetric VG type and that every edge $e \in E$ is compatible.

Then $(G, \lambda)$ is not stabilisable.

Note that a simple way to achieve mirror-invariance is to assume that VGs arrive according to i.i.d. draws from a blood-type distribution, i.e. for each new arrival, one draws the type of the vampire and their ghoul independently.

<footnote n="10">¹⁰Yes, [17] is a Wikipedia page. Its alleged source is a website advocating for blood donation, which itself refers to [6], which, despite having more than 800 pages, does not contain the desired data, as it focuses on prevalence per ethnicity but entirely ignores possible correlations between Rhesus and antigens. This disappointment illustrates why one should never check the validity of results from Wikipedia.</footnote>

<footnote n="11">¹¹Approximately the combined human population of North and South America. The owner of the *Buena Muerte Social Club* has many flaws; lack of ambition is not among them.</footnote>
**Proof.** Define the compatibility score of $v = T_V/T_G \in V$ by

$$s(v) = |T_V| - |T_G| \in \{-3, \dots, 3\},$$

where $|\cdot|$ counts the markers (between 0 and 3). If vampire $T_V$ can feed on ghoul $T_G$, then $s(T_V/T_G) \ge 0$. The converse is false: $A^+/B^-$ scores +1 but is not autarkic.

First, consider the case where all nodes of $V$ have a compatibility score of 0. One can check then that the incidence matrix of $G$ is not surjective (there is a connected component ofswingers that is bipartite) so the problem is not stabilisable by Theorem 1.

Now, we assume that some nodes of $V$ have a non-zero compatibility score and extend the score definition to edges: the compatibility score of $e \in E$ is the sum of its endpoints' scores. It follows immediately that any compatible edge has a non-negative score.

After $t$ arrivals, let $V_t$ denote the set of VGs that arrived at the club and $E_t$ the set of “matchings” performed. We define the system score as

$$S(t) = \sum_{v \in V_t} s(v) - \sum_{e \in E_t} s(e).$$

The function $t \mapsto \sum_{v \in V_t} s(v)$ behaves as a symmetric random walk over $\mathbb{Z}$, since each type and its mirror appear with identical probability. Since matchings satisfy $s(e) \ge 0$, the compensatory term $t \mapsto \sum_{e \in E_t} s(e)$ is non-decreasing. Thus, $S(t)$ itself performs what might be described as a drunkard's walk with non-positive expectations.

Consequently, one obtains $E[|S(t)|] = \Omega(\sqrt{t})$. Because a system score $S$ requires at least $[|S|/3]$ pending VGs, the queue length diverges, proving instability. ◀

## 4.2 Numerical evaluation

It is not because something is inedible that one cannot sell it<fnref n="12" />. Likewise, theoretical impossibility should not prevent us from trying anyway. In the present case, Theorem 2 establishes instability, but in the best scenario this is just a symmetric random walk: a gentle square-root growth punctuated by frequent returns to zero. Moreover, not all VG types are created equal, so perhaps some categories get a good quality of service anyway. We thus perform numerical benchmarks of Theorem 2.

Our findings, gathered by VG categories, are summarized in Table 3.

<table><caption>■ Table 3 Measured average queue size per category for different compatibility graphs</caption><thead><tr><th></th><th>Autarkic</th><th>Helpless</th><th>Swinger</th></tr></thead><tbody><tr><td>Swinger-only</td><td>N/A</td><td>N/A</td><td>43048.16</td></tr><tr><td>All categories</td><td>&lt; 0.01</td><td>49526.05</td><td>10186.27</td></tr><tr><td>All categories, threesomes allowed</td><td>265.47</td><td>21061.44</td><td>7806.32</td></tr><tr><td>Autarkic &amp; Swingler</td><td>4.16</td><td>N/A</td><td>10.75</td></tr></tbody></table>

We first examine theектers' compatibility graph in Figure 2, a natural restriction since autarkics have little incentive to participate (dooming the helpless by their absence). Instability follows from Theorem 2 but also directly from Theorem 1: the conservation law (1) admits a unique non-negative solution, where each swinger type matches only with its mirror, partitioning the 18 swinger types into 9 bipartite components. Numerically,ектers alone exhibit the predicted $\Omega(\sqrt{t})$ explosion: 43048.16, confirming the theorem's grim prognosis.

<footnote n="12">¹² As any good meat-pie seller, or more accurately any good “seller of meat pies”, knows all too well.</footnote>
A workaround might lure autarkics with external incentives (e.g. free cigars) into the full compatibility graph, allowing the matching policy to utilise their self-loops as needed. Instability persists, driven primarily by the mandatory bipartite component linking $AB^+/O^-$ and $O^-/AB^+$.

The full graph dramatically reduces swingers' waiting times. Autarkic queue is near zero, with occasional brief holds due to virtual queue reservations. Helpless vampires fare worse than swingers alone.

Vampires being licentious by nature, we next permit ghoul exchanges among more than two VGs. For instance, {$O^-/AB^+, AB^+/A^+, A^+/O^-$} forms a perfectly compatible hyperedge. Food orgies do not evade Theorem 2 ($AB^+/O^- \text{ vs } O^-/AB^+$, once more, although it is a bit more tricky to observe), but at least feeding may happen in more numerous (if not necessarily better) company.

For computational tractability, we limit ourselves to threesomes. Table 3 shows that this is enough to yield substantial gains for the helpless and modest improvements for swingers, at the cost of increased autarkic queues (aggressive reservations for hyperedges).

For curiosity's sake, Table 3 includes the autarkic-swinger subgraph. Here Theorem 2 does not apply because there is no mirror invariance (e.g. $AB^+/O^-$ has no counterpart) and stability is easily verified via a positive solution of Equation (1) matching $AB^+/O^-$ uniformly across the other nodes. Because of stability, queues remain quite low.

Excluding the entire helpless population (28.2%) seems, however, rather harsh. Our next step proposes subtler alternatives for achieving low-queue performance.

# 5 Stabilising the Programme

To evade Theorem 2, one must violate at least one of its hypotheses. This section explores two avenues: Section 5.1 breaks the mirror invariance; Section 5.2 relaxes compatibility.

## 5.1 To Serve Man

A first path to stability skews the type distributions to induce positive drift in the compatibility score. Excluding the helpless works, but targeted decimation suffices: remove a positive proportion of $O^-$ vampires, or $AB^+$ ghouls, or merely of $O^-/AB^+$ VGs, and the system is stable.

In vampire society, no Thanos-style finger-snap is required for decimation: just aim for the carotid of reputation. Spread rumours that $AB^+$ vampires hypnotising $O^-$ humans have suspiciously werewolf-adjacent family trees, or that they secretly colour-dress<fnref n="13" />, and decimation follows overnight.

The club baulks at this, deeming it borderline genocidal<fnref n="14" />. As an alternative, they propose admitting pre-ghouls, i.e. regular humans, to the exchange programme. Formally, a human is a vampire-ghoul pair where the vampire component is a universal placeholder compatible with any blood type. Humans possess self-loops: if undesired, they exit unharmed.

<footnote n="13">¹³ Colour-dressing denotes wearing vibrant garments, deemed indecent in most vampiric circles. Cross-dressing (in black), however, remains acceptable, provided it is not in a literal sense that involves disguising into a religious symbol [1].</footnote>

<footnote n="14">¹⁴ Vampires harbour no principled objection to genocide, as humans have practised it since time immemorial without fatigue. Vampires, however, understand genetics: populations regrow. Why the bother of slaughtering an entire population if one must repeat the effort every millennium?</footnote>
<figure><img src="image_4.png" /><figcaption>Figure 3 Trade-off between delay and proportion of regular humans in the exchange programme.</figcaption></figure>

For any $0 < \alpha < 1$, blending the VG compatibility graph with a proportion $\alpha$ of humans yields a stabilisable problem (you can for example match uniformly $O^{-}$ humans with all VG nodes).

That said, modern technology complicates un-hypnotised human procurement. In the Dark Ages, a swift horse and sturdy net sufficed. Today, the safest method persuades humans (without hypnosis) that mingling with vampires appeals. This requires gothic romance novels wherein the human protagonist discovers that vampires are misunderstood, not bloodthirsty monsters, and falls desperately for a brooding, eternally youthful vampire [9].

In short: with great $\alpha$ comes great romantic absurdity. Vampires, having refined literary tastes, loathe such productions and wish to limit them to a strict minimum.

We thus evaluate the $\alpha$-queue tradeoff numerically; results appear in Figure 3.

Helpless and swinger queues drop sharply with $\alpha$, while human and autarkic queues rise modestly (virtual reservations again). Autarkics barely exceed 1 even in the worst case.

For $\alpha = 0.1\%$ (a haiku on the sensuality of moonlight over ruined castles), the helpless queue falls to $\sim 10000$ (vs 50000 without humans). At $\alpha = 1\%$ (fan-fiction of *Gone with the Wind*, vampire edition), it reaches 1000. With $\alpha = 10\%$ (a 5+ tomes trilogy, adaptation rights bought by Netflix), it drops below 100. Using these results, vampiric society can surely balance haematic famine against literary torment.

## 5.2 Hunger games

The second escape from Theorem 2 permits, sparingly, incompatible edges. It is a standard approach in online matching: approximate an unstable problem via a parameterised family of stabilisable instances [3, Sections 6 and 7].

Here, we render the problem stabilisable by adding self-loops to all non-autarkic types, then deploy a stable policy family minimising their use.

Numerous policy families achieve this; we advocate *k*-filtering for its simplicity and strong
<figure><img src="image_5.png" /><figcaption>Figure 4 Trade-off between delay and ghoul wastage for various cleansing thresholds varying from $k = 1$ (right) to $k = 1024$ (left).</figcaption></figure>

empirical performance<fnref n="15" />. The *k*-filtering mechanism is straightforward: choose a universal matching algorithm, e.g. *virtual queue*; fix parameter *k*; as long as the largest type-specific queue remains below *k*, the system is fluid enough and incompatible edges are forbidden; above *k*, the policy is allowed to select incompatible edges to avert catastrophe.

In practice, selecting an incompatible edge forces the vampire to discard the ghoul and exit hungry, or consume it gambling on negligible gastric repercussions. Most vampires opt for the former.

We evaluate the queue-regret tradeoff numerically (Figure 4), where regret is assessed as follows: assigns reward -1 to forbidden edges, +1 to autarkic self-loops, and +2 to proper exchanges: compute the observed rate-reward gap against the optimal (unstable) policy avoiding forbidden edges entirely [8].

The profile is very similar to Figure 3, without the human part: a clear tradeoff sharply reduces queues for challenged categories (helpless,swingers), at the cost of wasted ghouls<fnref n="16" /> and modestly longer autarkic waits.

## 6 Conclusion

We have examined the delicate balance between vampiric etiquette and haematic compatibility. In particular, we have shown that while food orgies are neither necessary nor sufficient for an efficient ghoul exchange programme, proper stability is attainable provided one accepts a tolerable dent in literary quality or food preservation.

These results open avenues to numerous future works. For instance, the discovery of a miracle cure for baldness<fnref n="17" />.

<footnote n="15">¹⁵The policy's designer is also the present paper's author, but this is, naturally, coincidental.</footnote>

<footnote n="16">¹⁶The attentive reader will have noticed that ghouls are wasted in the human-enhanced case too. *Shhhhhhhh...*</footnote>

<footnote n="17">¹⁷See Footnote 3.</footnote>
References

1 Emilie Buckley. "I mean, who isn't gay?": An Exploration of Queer Performativity in the TV Series, What We Do in the Shadows. *REDEN. Revista Española de Estudios Norteamericanos*, 6(1):38-53, Nov. 2024. URL: https://erevistas/publicaciones.uah.es/ojs/index.php/reden/article/view/2678, doi:10.37536/reden.2024.6.2678.

2 Gail Carriger. *Soulless*. The Parasol Protectorate. Orbit, USA, 2009.

3 Céline Comte, Fabien Mathieu, Sushil Mahavir Varma, and Ana Bušić. Online Stochastic Matching: A Polytope Perspective, November 2025. preprint. URL: https://hal.science/hal-03502084.

4 Elisabeth Davenas, Francis Beauvais, J. Amara, Menachem Oberbaum, Boaz Robinzon, A. Miadonnai, Alberto Tedeschi, Bruce H. Pomeranz, P. Fortner, Philippe Belon, J. L. Sainte-Laudy, Bernard Poitevin, and Jacques E. Benveniste. Human basophil degranulation triggered by very dilute antiserum against IgE. *Nature*, 333:816-818, 1988. URL: https://api.semanticscholar.org/CorpusID:12992106.

5 Joseph Sheridan Le Fanu. *Carmilla*. British & Colonial Publishing, London, 1872.

6 Mark K. Fung, Brenda J. Grossman, Christopher D. Hillyer, and Connie M. Westhoff, editors. *Technical Manual*. AABB, Bethesda, MD, 18th edition, 2014.

7 J Maddox, J Randi, and WW Stewart. "high-dilution" experiments: a delusion. *Nature*, 334(6180):287-291, July 1988. doi:10.1038/334287a0.

8 Fabien Mathieu. Stochastic Matching, 2022. URL: https://balouf.github.io/stochasticMatching/index.html.

9 Stephenie Meyer. *Twilight*. The Twilight Series. Little, Brown and Company, USA, 2005.

10 John William Polidori. The Vampyre. *The New Monthly Magazine and Universal Register*, 1(63):195-206, 1819.

11 Terry Pratchett. *Carpe Jugulum*. Discworld. Doubleday, London, 1998.

12 Anne Rice. *Interview with the Vampire*. The Vampire Chronicles. Knopf, USA, 1976.

13 Preeti Rout, Janine Harewood, Adam Ramsey, and Samip R. Master. Hemolytic transfusion reaction. *StatPearls [Internet]*, Sep 2023. URL: https://www.ncbi.nlm.nih.gov/books/NBK448158/.

14 Shayan Sharifi. Enhancing kidney transplantation through multi-agent kidney exchange programs: A comprehensive review and optimization models. *International Journal of Industrial Engineering Computations*, 16:483-498, 01 2025. doi:10.5267/j.ijiec.2024.12.002.

15 Bram Stocker. *Dracula*. Archibald Constable and Company, 1897.

16 Merel Wemelsfelder, Ronald Weem, Jessie Luken, Masja Haas, René Niessen, C Ellen Van der Schoot, Han Hoogeveen, Folarin Oyebolu, Dick den Hertog, and Mart Janssen. Extensive red blood cell matching considering patient alloimmunization risk. *Vox Sanguinis*, 119, 01 2024. doi:10.1111/vox.13594.

17 Wikipedia contributors. Blood type distribution by country. https://en.wikipedia.org/wiki/Blood_type_distribution_by_country, 2025. Wikipedia page, accessed 2026-01-11.