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arxiv: 2606.31802 · v1 · pith:PGBZMZNSnew · submitted 2026-06-30 · ⚛️ physics.soc-ph · econ.TH· math.DS

Feedback dynamics in matching networks drive behavioral differentiation despite overlapping objectives

Alexandros Gelastopoulos This is my paper

Pith reviewed 2026-07-01 02:18 UTC · model grok-4.3

classification ⚛️ physics.soc-ph econ.THmath.DS
keywords matching networksfeedback dynamicsselectivitybehavioral differentiationbipartite matchingequilibrium analysistarget matching rate
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The pith

Feedback from repeated matching pushes one group to high selectivity and the other to low, even when their target rates overlap almost completely.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that in a bipartite matching process where each person adjusts selectivity only to hit a personal target matching rate, sufficiently frequent encounters produce a single stable outcome: one side becomes highly selective while the other accepts nearly every opportunity. The mechanism is a direct feedback loop in which greater selectivity on one side lowers matching success on the other, which then lowers its own selectivity in response. This polarization occurs even when the two groups draw their target rates from nearly identical distributions. A reader would care because the result supplies an endogenous explanation for observed asymmetries in dating, hiring, and housing markets that does not require pre-existing differences between the groups.

Core claim

When encounters are frequent enough, the adaptation dynamics converge to a unique equilibrium in which one group is highly selective and the other is non-selective; this qualitative split persists for heterogeneous populations whose target matching rates are drawn from overlapping, nearly indistinguishable distributions.

What carries the argument

The closed feedback loop in which one side's rise in selectivity reduces the other side's matching opportunities, prompting the second side to lower its selectivity threshold, which in turn increases opportunities for the first side.

If this is right

  • Raising the encounter rate sharpens the selectivity split until one side rejects almost all offers and the other accepts almost all.
  • The equilibrium split is insensitive to the precise initial selectivity values once encounters become frequent.
  • Even small differences in the overlap of the two target-rate distributions do not eliminate the polarization.
  • The same qualitative outcome appears in both analytic fixed-point analysis and numerical simulations of the adaptation rule.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The result suggests a simple way to test market interventions: artificially increasing encounter frequency should increase behavioral differentiation on real platforms.
  • The mechanism could be checked in controlled experiments by giving participants explicit target rates and varying the rate at which they see potential matches.
  • If the assumption of a fixed personal target is relaxed to allow targets that themselves adapt, the polarization might weaken or disappear.

Load-bearing premise

People change selectivity only in response to whether they are above or below their fixed personal target matching rate, and the resulting dynamics always reach one stable equilibrium rather than cycling or settling at multiple points.

What would settle it

A simulation or experiment that raises encounter frequency yet ends with both groups retaining similar, intermediate selectivity levels instead of splitting into high and low.

Figures

Figures reproduced from arXiv: 2606.31802 by Alexandros Gelastopoulos.

Figure 1
Figure 1. Figure 1: Simulation of the system of eqs. (1) and (2) with homogeneous within-group target matching rates (A) males: c = 2, females: d = 1, (B) males: c = 1.05, females: d = 1, (C) males: c = 0.95, females: d = 1. In (A) and (B), all males are driven to eventually be non-selective (acceptance rate ai(t) → 1) and males highly selective (bj (t) ≈ 0). In (B), this is the case despite the highly similar target matching… view at source ↗
Figure 2
Figure 2. Figure 2: Simulation of the system of eqs. (1) and (2) for heterogeneous populations. (A) We draw the ci ’s i.i.d. from a uniform distribution on (0, 2.5) and the dj ’s i.i.d. from a uniform distribution on (0, 2), resulting in E[ci ] = 1.25 and E[dj ] = 1. Other parameter values are as in fig. 1. (B) Trajectories of acceptance probabilities ai(t) and bj (t). (C) Histogram of equilibrium values ˆai and ˆbj . Despite… view at source ↗
Figure 3
Figure 3. Figure 3: Simulation of the system of eqs. (1) and (2) with different mean target matching rates for males. (A-F) The ci ’s are drawn i.i.d. from a uniform distribution on (0, 2¯c), with ¯c indicated at the top of each panel. In all cases, ¯d = 1. All other parameters are as in fig. 1. The equilibrium selectivity distributions change very little until ¯c ≈ ¯d = 1, and they reverse when ¯c falls below that value. The… view at source ↗
Figure 4
Figure 4. Figure 4: Mean acceptance probabilities at equilibrium of males and females ( [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Equilibrium distributions from a simulation of the system of eqs. ( [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
read the original abstract

Many bipartite social networks exhibit pronounced asymmetries in selectivity and matching opportunities: members of one side can afford to be highly selective, while members of the opposite side are forced to accept less desirable matches. While it is natural to try to explain this asymmetry in terms of the intrinsic characteristics of the two sides or other exogenous factors, here we show that such asymmetries can also emerge endogenously through a feedback process generated by the matching process itself: as one side becomes more selective, the other side is pushed to be less selective due to reduced matching opportunities, and vice versa. We develop a model in which individuals repeatedly form one-to-one matches across two groups and adapt their selectivity to achieve a target matching rate. Using both analytic and numerical methods, we show that when encounters are sufficiently frequent, the unique equilibrium is for one group to be highly selective and the other non-selective. This qualitative outcome holds even for heterogeneous groups with overlapping, almost indistinguishable distributions of target matching rates. The model makes several testable predictions, and it provides a mechanism for behavioral differentiation in repeated matching environments, with applications ranging from online dating to hiring and housing markets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that in bipartite matching networks, individuals adapt their selectivity to achieve fixed personal target matching rates, generating a feedback process that produces a unique stable equilibrium with strong behavioral asymmetry (one group highly selective, the other non-selective) when encounter frequency exceeds a threshold. This outcome is shown via analytic fixed-point analysis and numerical integration of the dynamics, and it persists even for heterogeneous groups whose target matching rate distributions overlap almost completely.

Significance. If the central result holds, the work supplies a parsimonious endogenous mechanism for observed selectivity asymmetries in repeated matching markets (dating, hiring, housing) that does not require exogenous group differences. The model yields several testable predictions and isolates encounter frequency as the key control parameter driving differentiation.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (model description): the uniqueness and stability of the equilibrium are asserted on the basis of analytic fixed-point analysis and numerical integration, yet the manuscript must supply the explicit derivation, including the fixed-point equation, Jacobian or Lyapunov stability argument, and handling of the heterogeneous case, so that readers can verify absence of post-hoc assumptions or parameter tuning.
  2. [Numerical results section] Numerical results section: convergence criteria, integration step size, and sensitivity to initial conditions or stochastic encounter realizations should be reported with quantitative error bounds; without these, it remains unclear whether the reported asymmetry is robust or an artifact of the simulation protocol.
minor comments (2)
  1. Define the precise functional form of the selectivity-update rule (e.g., continuous or discrete adjustment) and the distribution from which heterogeneous target rates are drawn; a short appendix tabulating parameter values used in all figures would improve reproducibility.
  2. Clarify whether the encounter-frequency threshold is derived endogenously or imposed exogenously; if the latter, state its value explicitly in the main text rather than only in figure captions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which identify opportunities to strengthen the transparency of both the analytic and numerical components of the work. We address each point below and will incorporate the requested details in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (model description): the uniqueness and stability of the equilibrium are asserted on the basis of analytic fixed-point analysis and numerical integration, yet the manuscript must supply the explicit derivation, including the fixed-point equation, Jacobian or Lyapunov stability argument, and handling of the heterogeneous case, so that readers can verify absence of post-hoc assumptions or parameter tuning.

    Authors: We agree that the explicit derivations are necessary for full verification. The revised Section 3 will present the fixed-point equation obtained by setting the time derivatives of selectivity to zero, the Jacobian matrix evaluated at the candidate equilibria for the homogeneous case, and the corresponding eigenvalue analysis establishing local stability. For the heterogeneous case we will derive the analogous fixed-point condition under the overlapping target-rate distributions and discuss why the asymmetric solution remains the unique stable attractor. These additions will be placed immediately after the model equations. revision: yes

  2. Referee: [Numerical results section] Numerical results section: convergence criteria, integration step size, and sensitivity to initial conditions or stochastic encounter realizations should be reported with quantitative error bounds; without these, it remains unclear whether the reported asymmetry is robust or an artifact of the simulation protocol.

    Authors: We will expand the numerical methods subsection to specify the Euler integration step size, the convergence tolerance (maximum change in selectivity vector per 100 steps), results of sweeps over a range of initial conditions, and quantitative error bounds obtained from 50 independent stochastic realizations (mean and standard deviation of the final selectivity values). These diagnostics will be reported both in the text and in a new supplementary table. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper constructs a dynamical model in which agents adjust selectivity parameters solely to meet fixed, exogenous target matching rates; the claimed asymmetry is then shown to be the unique stable fixed point of the resulting feedback equations when encounter frequency exceeds a threshold. Both the analytic fixed-point derivation and the numerical integration follow directly from the stated adaptation rule and the bipartite matching process without any parameter being fitted to the output asymmetry, without self-referential definitions of selectivity in terms of the equilibrium itself, and without load-bearing self-citations. The target distributions remain independent inputs, so the qualitative outcome is a genuine consequence of the model rather than a restatement of its assumptions.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The model rests on individual adaptation rules driven by target matching rates (free parameters) and standard dynamical-systems assumptions about equilibrium existence and stability. No new entities are postulated.

free parameters (2)
  • target matching rate per individual
    Each agent adjusts selectivity to meet a personal target rate; these targets are inputs that differ across agents and groups.
  • encounter frequency threshold
    The condition 'sufficiently frequent' encounters is required for the unique asymmetric equilibrium to hold.
axioms (1)
  • domain assumption The adaptation dynamics converge to a unique stable equilibrium under high encounter frequency
    Invoked to guarantee the reported qualitative outcome for both homogeneous and heterogeneous groups.

pith-pipeline@v0.9.1-grok · 5723 in / 1275 out tokens · 44597 ms · 2026-07-01T02:18:54.269278+00:00 · methodology

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Reference graph

Works this paper leans on

49 extracted references

  1. [1]

    2021 Webinar on the Job Market for New Economics Ph.D.s (Part 1) , year =

    2021

  2. [2]

    JOE Network , year =

  3. [3]

    Job Market Graphs: Job Openings for Economists , year =

  4. [4]

    Journal of Economic Theory , volume=

    A search model of two-sided matching under nontransferable utility , author=. Journal of Economic Theory , volume=. 2003 , publisher=

    2003

  5. [5]

    Journal of Political Economy , volume=

    Unbalanced random matching markets: The stark effect of competition , author=. Journal of Political Economy , volume=. 2017 , publisher=

    2017

  6. [6]

    Sex roles , volume=

    Has dating become more egalitarian? A 35 year review using sex roles , author=. Sex roles , volume=. 2011 , publisher=

    2011

  7. [7]

    Sex Roles , volume=

    Young singles' contemporary dating scripts , author=. Sex Roles , volume=. 1993 , publisher=

    1993

  8. [8]

    and Simon, William , title =

    Gagnon, John H. and Simon, William , title =. 1973 , publisher =

    1973

  9. [9]

    and Simon, William , title =

    Gagnon, John H. and Simon, William , title =. Society , year =

  10. [10]

    Journal of evolutionary biology , volume=

    Parental investment, sexual selection and sex ratios , author=. Journal of evolutionary biology , volume=. 2008 , publisher=

    2008

  11. [11]

    Annual review of psychology , volume=

    Mate preferences and their behavioral manifestations , author=. Annual review of psychology , volume=. 2019 , publisher=

    2019

  12. [12]

    Nature communications , volume=

    Coevolution of parental investment and sexually selected traits drives sex-role divergence , author=. Nature communications , volume=. 2016 , publisher=

    2016

  13. [13]

    Philosophical Transactions of the Royal Society B: Biological Sciences , volume=

    Positive feedback and alternative stable states in inbreeding, cooperation, sex roles and other evolutionary processes , author=. Philosophical Transactions of the Royal Society B: Biological Sciences , volume=

  14. [14]

    The Public and Online Dating in 2025 , year =

    2025

  15. [15]

    Journal of Economic Theory , volume=

    Stable marriages and search frictions , author=. Journal of Economic Theory , volume=. 2014 , publisher=

    2014

  16. [16]

    2000 , publisher=

    Equilibrium unemployment theory , author=. 2000 , publisher=

    2000

  17. [17]

    1996 , publisher=

    Projected dynamical systems and variational inequalities with applications , author=. 1996 , publisher=

    1996

  18. [18]

    2013 , publisher=

    Differential equations with discontinuous righthand sides: control systems , author=. 2013 , publisher=

    2013

  19. [19]

    2022 , publisher=

    Learning in the marriage market: The economics of dating , author=. 2022 , publisher=

    2022

  20. [20]

    Handbook of the Economics of Matching , volume=

    Matching with frictions , author=. Handbook of the Economics of Matching , volume=. 2025 , publisher=

    2025

  21. [21]

    Journal of Economic Literature , volume=

    Sorting through search and matching models in economics , author=. Journal of Economic Literature , volume=. 2017 , publisher=

    2017

  22. [22]

    Frictional matching models , author=. Annu. Rev. Econ. , volume=. 2011 , publisher=

    2011

  23. [23]

    Ecology letters , volume=

    Predicting the direction of sexual selection , author=. Ecology letters , volume=. 2001 , publisher=

    2001

  24. [24]

    Philosophical Transactions of the Royal Society of London

    Why is mutual mate choice not the norm? Operational sex ratios, sex roles and the evolution of sexually dimorphic and monomorphic signalling , author=. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences , volume=. 2002 , publisher=

    2002

  25. [25]

    Journal of sex research , volume=

    Sexual double standards: A review and methodological critique of two decades of research , author=. Journal of sex research , volume=. 2003 , publisher=

    2003

  26. [26]

    Behavioral Sciences , volume=

    Sex differences in sexual motivation in humans and other mammals: The role of conscious and unconscious processes , author=. Behavioral Sciences , volume=. 2024 , publisher=

    2024

  27. [27]

    Psychological science , volume=

    Sex differences in mate preferences across 45 countries: A large-scale replication , author=. Psychological science , volume=. 2020 , publisher=

    2020

  28. [28]

    2006 , publisher=

    Adapting minds: Evolutionary psychology and the persistent quest for human nature , author=. 2006 , publisher=

    2006

  29. [29]

    Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences , volume=

    It takes two: sexual strategies and game theory , author=. Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences , volume=. 2010 , publisher=

    2010

  30. [30]

    , author=

    Gender differences in sexuality: a meta-analysis. , author=. Psychological bulletin , volume=. 1993 , publisher=

    1993

  31. [31]

    Behavioral and Brain sciences , volume=

    Sociosexuality from Argentina to Zimbabwe: A 48-nation study of sex, culture, and strategies of human mating , author=. Behavioral and Brain sciences , volume=. 2005 , publisher=

    2005

  32. [32]

    2013 , url =

    Jon Millward , title =. 2013 , url =

    2013

  33. [33]

    , author=

    Perceived proposer personality characteristics and gender differences in acceptance of casual sex offers. , author=. Journal of personality and social psychology , volume=. 2011 , publisher=

    2011

  34. [34]

    Journal of Applied Social Psychology , volume=

    The impact of AIDS on gender differences in willingness to engage in casual sex , author=. Journal of Applied Social Psychology , volume=. 1990 , publisher=

    1990

  35. [35]

    The Journal of Social Psychology , pages=

    Gender differences in receptivity to sexual invitations: two naturalistic replication studies , author=. The Journal of Social Psychology , pages=. 2024 , publisher=

    2024

  36. [36]

    Psychological Inquiry , volume=

    The ape that thought it was a peacock: Does evolutionary psychology exaggerate human sex differences? , author=. Psychological Inquiry , volume=. 2013 , publisher=

    2013

  37. [37]

    Archives of sexual behavior , volume=

    Effects of solicitor sex and attractiveness on receptivity to sexual offers: A field study , author=. Archives of sexual behavior , volume=. 2011 , publisher=

    2011

  38. [38]

    Evolution and Human Behavior , volume=

    Receptivity to sexual invitations from strangers of the opposite gender , author=. Evolution and Human Behavior , volume=. 2010 , publisher=

    2010

  39. [39]

    Archives of sexual behavior , volume=

    Gender differences and similarities in receptivity to sexual invitations: Effects of location and risk perception , author=. Archives of sexual behavior , volume=. 2015 , publisher=

    2015

  40. [40]

    , author=

    A meta-analytic review of research on gender differences in sexuality, 1993--2007. , author=. Psychological bulletin , volume=. 2010 , publisher=

    1993

  41. [41]

    Psychology of Women Quarterly , volume=

    Backlash from the bedroom: Stigma mediates gender differences in acceptance of casual sex offers , author=. Psychology of Women Quarterly , volume=. 2013 , publisher=

    2013

  42. [42]

    Journal of Psychology & Human Sexuality , volume=

    Gender differences in receptivity to sexual offers , author=. Journal of Psychology & Human Sexuality , volume=. 1989 , publisher=

    1989

  43. [43]

    2016 , publisher=

    The evolution of desire: Strategies of human mating , author=. 2016 , publisher=

    2016

  44. [44]

    Journal of personality , volume=

    Evolution, traits, and the stages of human courtship: Qualifying the parental investment model , author=. Journal of personality , volume=. 1990 , publisher=

    1990

  45. [45]

    2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (

    A first look at user activity on tinder , author=. 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (. 2016 , organization=

    2016

  46. [46]

    , author=

    The origins of sex differences in human behavior: Evolved dispositions versus social roles. , author=. American psychologist , volume=. 1999 , publisher=

    1999

  47. [47]

    Sexual selection and the descent of man , pages=

    Parental investment and sexual selection , author=. Sexual selection and the descent of man , pages=. 1972 , publisher=

    1972

  48. [48]

    The American mathematical monthly , volume=

    College admissions and the stability of marriage , author=. The American mathematical monthly , volume=. 1962 , publisher=

    1962

  49. [49]

    Handbook of game theory with economic applications , volume=

    Two-sided matching , author=. Handbook of game theory with economic applications , volume=. 1992 , publisher=

    1992