pith. sign in

arxiv: 2605.23539 · v1 · pith:6CVYSRA6new · submitted 2026-05-22 · 💰 econ.EM

Process Utility in High-Stakes Competition

Arnaud Dupuy This is my paper

Pith reviewed 2026-05-25 02:46 UTC · model grok-4.3

classification 💰 econ.EM
keywords process utilityoutcome utilitytennissecond-service rulenonparametric boundsstructural estimationplayer preferenceshigh-stakes decisions
0
0 comments X

The pith

Tennis players positively value process utility and sacrifice success probabilities to increase it.

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 professional tennis, players trade off outcome utility from winning against process utility from how they perform actions like serving. Using optimality conditions derived from the second-service rule, it derives a sufficient condition for a positive lower bound on the weight players place on process utility. High-frequency data under mild shape restrictions indicate that most players value process utility positively. This has consequences for match outcomes and expected earnings as players choose riskier or less successful serves to gain process benefits.

Core claim

Under mild shape restrictions on preferences, the high-frequency tennis data indicate that most players likely value process utility positively. Players systematically sacrifice success probabilities to increase process utility, with economically meaningful consequences for match outcomes and expected earnings.

What carries the argument

Optimality conditions combined with the second-service rule, which derives a sufficient condition for a nonparametric lower bound on the process utility weight to be positive.

If this is right

  • Most players have a positive weight on process utility.
  • Players choose actions that reduce win probability but increase process utility.
  • This affects match outcomes and expected earnings in economically meaningful ways.
  • A structural model recovers player-specific preferences over outcomes and processes.

Where Pith is reading between the lines

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

  • The same identification strategy could apply to other strategic settings where rules create observable optimality conditions.
  • Accounting for process utility may improve predictions of behavior in labor markets or other high-stakes competitions.
  • If process utility is widespread, standard outcome-only models will understate the value players place on certain choices.

Load-bearing premise

Players satisfy optimality conditions given the second-service rule, together with mild shape restrictions on their preferences.

What would settle it

Observing that players' serving choices do not satisfy the derived sufficient condition for positive process utility weight under the second-service rule would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.23539 by Arnaud Dupuy.

Figure 3
Figure 3. Figure 3: Conditional probabilities of winning one-shot (top) and multi-shot (bottom) rallies [PITH_FULL_IMAGE:figures/full_fig_p030_3.png] view at source ↗
read the original abstract

We study how individuals trade off outcome ("what") and process ("how") utility in high-stakes strategic decisions, namely professional tennis. Using optimality conditions and the second-service rule, we derive a sufficient condition for the nonparametric lower bound on the weight of process utility to be positive. Under mild shape restrictions, the high-frequency data indicate that most players likely value process utility positively. We then develop a structural model that recovers player-specific preferences over outcomes and processes. Estimates show that players systematically sacrifice success probabilities to increase process utility, with economically meaningful consequences for match outcomes and expected earnings.

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 manuscript claims that professional tennis players trade off outcome utility against process utility in high-stakes decisions. Using optimality conditions implied by the second-service rule, the authors derive a sufficient condition under which the nonparametric lower bound on the weight of process utility is positive. High-frequency data indicate that most players place positive weight on process utility and are willing to sacrifice success probability to increase it. A structural model then recovers player-specific preference parameters, showing economically meaningful effects on match outcomes and expected earnings.

Significance. If the identification arguments hold, the paper offers novel nonparametric evidence on process utility in a strategic, high-stakes field setting. The reliance on optimality conditions and mild shape restrictions rather than strong parametric assumptions is a methodological strength, and the use of granular tennis data allows direct quantification of the implied trade-offs. The work could inform models of non-consequentialist preferences in competitive environments.

major comments (2)
  1. [Section deriving the sufficient condition for the nonparametric lower bound] The derivation of the sufficient condition for a positive nonparametric lower bound (the central identification result) rests on players satisfying optimality given the second-service rule plus mild shape restrictions on preferences. The manuscript does not report explicit tests or sensitivity analyses showing how the sign of the bound changes if these conditions are violated for even a subset of observations.
  2. [Structural model and estimation section] The structural model recovers player-specific process-utility weights by maximum likelihood (or analogous) estimation on the same match-level data used to establish the nonparametric bounds. Because the weights are fitted quantities by construction, the reported magnitudes of sacrificed success probabilities and effects on expected earnings are in-sample implications rather than independent, out-of-sample predictions; this weakens the claim that the structural results provide separate corroborating evidence.
minor comments (2)
  1. [Abstract] The abstract states that 'most players likely value process utility positively' but does not report the exact fraction of players or matches for which the lower bound is positive; adding this summary statistic would improve transparency.
  2. [Throughout the model sections] Notation for the process-utility weight parameter should be defined once and used consistently; occasional switches between symbols or subscripts make it harder to follow the mapping from the nonparametric bound to the structural estimates.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and indicate planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Section deriving the sufficient condition for the nonparametric lower bound] The derivation of the sufficient condition for a positive nonparametric lower bound (the central identification result) rests on players satisfying optimality given the second-service rule plus mild shape restrictions on preferences. The manuscript does not report explicit tests or sensitivity analyses showing how the sign of the bound changes if these conditions are violated for even a subset of observations.

    Authors: We agree that the manuscript does not present explicit sensitivity analyses for potential violations of the optimality conditions or shape restrictions on a subset of observations. In the revision we will add a dedicated robustness subsection that (i) re-estimates the nonparametric lower bound after dropping matches with possible second-service-rule deviations and (ii) varies the maintained shape restrictions (e.g., monotonicity thresholds) to document how the sign and magnitude of the bound respond. These checks will be reported both in the main text and in an appendix table. revision: yes

  2. Referee: [Structural model and estimation section] The structural model recovers player-specific process-utility weights by maximum likelihood (or analogous) estimation on the same match-level data used to establish the nonparametric bounds. Because the weights are fitted quantities by construction, the reported magnitudes of sacrificed success probabilities and effects on expected earnings are in-sample implications rather than independent, out-of-sample predictions; this weakens the claim that the structural results provide separate corroborating evidence.

    Authors: We acknowledge that the structural estimates are obtained from the identical sample used for the nonparametric bounds and therefore constitute in-sample implications rather than out-of-sample validation. The structural exercise is intended to translate the nonparametric lower bounds into player-specific preference parameters and to compute the implied quantitative trade-offs and earnings consequences that are not directly recoverable from the bounds alone. We will revise the text to clarify that the structural results are best viewed as a quantification exercise that is internally consistent with the nonparametric evidence, rather than as independent corroboration. No new out-of-sample tests are feasible with the current data, but we will emphasize this limitation explicitly. revision: partial

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The derivation begins with optimality conditions under the second-service rule to obtain a sufficient condition for a positive nonparametric lower bound on process utility weight; this step is presented as following from the stated theoretical restrictions and does not reduce to fitted quantities. High-frequency data are then applied to evaluate the condition under mild shape restrictions, yielding the conclusion that most players value process utility positively. The subsequent structural model recovers player-specific parameters via estimation on the same data, but the paper does not rename these fitted values as independent predictions or first-principles results. No equation or claim is shown to equal its inputs by construction, and the central nonparametric bound remains independent of the estimation step.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis rests on domain assumptions about player optimization and shape restrictions whose validity is not independently verified; the structural component introduces fitted preference parameters.

free parameters (1)
  • player-specific process utility weight
    Recovered via structural estimation on match data.
axioms (1)
  • domain assumption Players choose serves to satisfy optimality conditions given the second-service rule.
    Invoked to derive the sufficient condition for positive process utility bound.

pith-pipeline@v0.9.0 · 5605 in / 1090 out tokens · 23820 ms · 2026-05-25T02:46:07.169447+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

298 extracted references · 298 canonical work pages · 2 internal anchors

  1. [1]

    Journal of Economic Perspectives , year =

    Ethical Consumption and Fair Trade: A Review of Evidence from Experimental and Field Studies , author =. Journal of Economic Perspectives , year =

    work page

  2. [2]

    World Development , year =

    The Willingness to Pay for Fair Trade Products: A Meta-Analysis , author =. World Development , year =

    work page

  3. [3]

    American Economic Review , year =

    Mas, Alexandre and Pallais, Amanda , title =. American Economic Review , year =

    work page

  4. [4]

    Economics of Innovation and New Technology , year =

    Dupuy, Arnaud and Smit, Jasper , title =. Economics of Innovation and New Technology , year =

    work page

  5. [5]

    Management Science , year =

    Stern, Scott , title =. Management Science , year =

    work page

  6. [6]

    and Deci, Edward L

    Ryan, Richard M. and Deci, Edward L. , title =. Encyclopedia of Quality of Life and Well-Being Research , year =

    work page

  7. [7]

    , title =

    Sen, Amartya K. , title =. Econometrica , year =

    work page

  8. [8]

    and Mochon, Daniel and Ariely, Dan , title =

    Norton, Michael I. and Mochon, Daniel and Ariely, Dan , title =. Journal of Consumer Psychology , year =

    work page

  9. [9]

    and Kranton, Rachel E

    Akerlof, George A. and Kranton, Rachel E. , title =

    work page

  10. [10]

    and Oberholzer-Gee, Felix , title =

    Frey, Bruno S. and Oberholzer-Gee, Felix , title =. American Economic Review , year =

    work page

  11. [11]

    and Koestner, Richard and Ryan, Richard M

    Deci, Edward L. and Koestner, Richard and Ryan, Richard M. , title =. Psychological Bulletin , year =

    work page

  12. [12]

    American Economic Review , year =

    Falk, Armin and Kosfeld, Michael , title =. American Economic Review , year =

    work page

  13. [13]

    The Effect of Rewards on Performance: Evidence from a Real Effort Task , journal =

    Corgnet, Brice and Esp. The Effect of Rewards on Performance: Evidence from a Real Effort Task , journal =. 2016 , volume =

    work page 2016

  14. [14]

    and Said, Amir , title =

    Bryan, Gordon and Hwang, Sung J. and Said, Amir , title =. Journal of Public Economics , year =

    work page

  15. [15]

    Sticking to Your Job: Non‑Monetary Incentives and the Employment Relationship , journal =

    Kube, Sebastian and Mar. Sticking to Your Job: Non‑Monetary Incentives and the Employment Relationship , journal =. 2013 , volume =

    work page 2013

  16. [16]

    Strategic Management Journal , year =

    Larkin, Ian and Pierce, Lin and Gino, Francesca , title =. Strategic Management Journal , year =

    work page

  17. [17]

    American Economic Journal: Microeconomics , year =

    Falk, Armin and Fehr, Ernst and Zehnder, Christian , title =. American Economic Journal: Microeconomics , year =

    work page

  18. [18]

    Quarterly Journal of Economics , year =

    Bandiera, Oriana and Barankay, Iwan and Rasul, Imran , title =. Quarterly Journal of Economics , year =

    work page

  19. [19]

    and Kranton, Rachel E

    Akerlof, George A. and Kranton, Rachel E. , title =. Quarterly Journal of Economics , year =

    work page

  20. [20]

    Research Quarterly for Exercise and Sport , volume=

    Toward a conceptual understanding of the flow experience in elite athletes , author=. Research Quarterly for Exercise and Sport , volume=

    work page

  21. [21]

    Journal of Applied Sport Psychology , volume=

    Relationships between flow, self-concept, psychological skills, and performance , author=. Journal of Applied Sport Psychology , volume=

    work page

  22. [22]

    Theory and Decision , volume =

    Marc Le Menestrel , title =. Theory and Decision , volume =. 2001 , doi =

    work page 2001

  23. [23]

    Psychology of Sport and Exercise , volume=

    A systematic review of the experience, occurrence, and controllability of flow states in elite sport , author=. Psychology of Sport and Exercise , volume=

    work page

  24. [24]

    Journal of Applied Sport Psychology , volume=

    Psychological states underlying excellent performance in sport: Toward an integrated model of flow and clutch states , author=. Journal of Applied Sport Psychology , volume=

    work page

  25. [25]

    1985 , publisher=

    Intrinsic Motivation and Self-Determination in Human Behavior , author=. 1985 , publisher=

    work page 1985

  26. [26]

    Journal of Personality and Social Psychology , volume=

    Effects of externally mediated rewards on intrinsic motivation , author=. Journal of Personality and Social Psychology , volume=

    work page

  27. [27]

    Quarterly Journal of Economics , volume=

    Pay enough or don't pay at all , author=. Quarterly Journal of Economics , volume=

    work page

  28. [28]

    Journal of Legal Studies , volume =

    A Fine is a Price , author =. Journal of Legal Studies , volume =. 2000 , publisher =

    work page 2000

  29. [29]

    Handbook of Labor Economics , year =

    Rosen, Sherwin , title =. Handbook of Labor Economics , year =

    work page

  30. [30]

    and Stutzer, Alois , title =

    Frey, Bruno S. and Stutzer, Alois , title =. 2002 , address =

    work page 2002

  31. [31]

    Journal of Institutional and Theoretical Economics , volume=

    Introducing procedural utility: Not only what, but also how matters , author=. Journal of Institutional and Theoretical Economics , volume=

    work page

  32. [32]

    for utility theory , author=

    Because it is there: The challenge of mountaineering... for utility theory , author=. Kyklos , volume=

    work page

  33. [33]

    Review of Economic Studies , volume=

    Intrinsic and extrinsic motivation , author=. Review of Economic Studies , volume=

    work page

  34. [34]

    American Economic Review , volume=

    Incentives and prosocial behavior , author=. American Economic Review , volume=

    work page

  35. [35]

    European Economic Review , volume=

    Psychological foundations of incentives , author=. European Economic Review , volume=

    work page

  36. [36]

    American Economic Journal: Microeconomics , volume=

    Getting more work for nothing? Symbolic awards and worker performance , author=. American Economic Journal: Microeconomics , volume=

    work page

  37. [37]

    Journal of Economic Behavior and Organization , volume=

    Man's search for meaning: The case of legos , author=. Journal of Economic Behavior and Organization , volume=

    work page

  38. [38]

    Journal of Finance , volume=

    Motivating innovation , author=. Journal of Finance , volume=

    work page

  39. [39]

    American Psychologist , volume=

    Building a practically useful theory of goal setting and task motivation , author=. American Psychologist , volume=

    work page

  40. [40]

    New York: Freeman , year=

    Self-efficacy: The exercise of control , author=. New York: Freeman , year=

    work page

  41. [41]

    Sports Medicine , volume=

    Psychological characteristics of developing excellence in sport , author=. Sports Medicine , volume=

    work page

  42. [42]

    Journal of Sport and Exercise Psychology , volume=

    Development and validation of a scale to measure optimal experience: The Flow State Scale , author=. Journal of Sport and Exercise Psychology , volume=

    work page

  43. [43]

    Handbook of Positive Psychology , pages=

    The concept of flow , author=. Handbook of Positive Psychology , pages=

    work page

  44. [44]

    Springer , year=

    Advances in flow research , author=. Springer , year=

    work page

  45. [45]

    Journal of the American Statistical Association , volume =

    Are Points in Tennis Independent and Identically Distributed? Evidence From a Dynamic Binary Panel Data Model , author =. Journal of the American Statistical Association , volume =. 2001 , doi =

    work page 2001

  46. [46]

    , title =

    Card, David E. , title =. American Economic Review , year =

    work page

  47. [47]

    2005 , address =

    Manning, Alan , title =. 2005 , address =

    work page 2005

  48. [48]

    Quantitative Economics , year =

    Dupuy, Arnaud and Galichon, Alfred , title =. Quantitative Economics , year =

    work page

  49. [49]

    Corblet, Pauline and Dupuy, Arnaud , title =

    work page

  50. [50]

    Dupuy, Arnaud and Raux, Morgan and Signorelli, Sara , title =

    work page

  51. [51]

    Journal of Economic Perspectives , Volume =

    Lavetti, Kurt , Title =. Journal of Economic Perspectives , Volume =. 2023 , Month =. doi:10.1257/jep.37.3.189 , URL =

    work page doi:10.1257/jep.37.3.189 2023

  52. [52]

    Non-wage amenities

    Alexandre Mas , keywords =. Non-wage amenities. , editor =. 2025 , booktitle =. doi:https://doi.org/10.1016/bs.heslab.2025.07.002 , url =

    work page doi:10.1016/bs.heslab.2025.07.002 2025

  53. [53]

    ITF Coaching & Sport Science Review , volume =

    Fitzpatrick, Anna , title =. ITF Coaching & Sport Science Review , volume =. 2024 , doi =

    work page 2024

  54. [54]

    2019 , howpublished =

    O'Shannessy, Craig , title =. 2019 , howpublished =

    work page 2019

  55. [55]

    2014 , publisher =

    Palacios-Huerta, Ignacio , title =. 2014 , publisher =. doi:10.23943/princeton/9780691144023.001.0001 , url =

    work page doi:10.23943/princeton/9780691144023.001.0001 2014

  56. [56]

    The Review of Economic Studies , year =

    Palacios-Huerta, Ignacio , title =. The Review of Economic Studies , year =. doi:10.1111/1467-937X.00249 , url =

    work page doi:10.1111/1467-937x.00249

  57. [57]

    Economisch-Statistische Berichten , year =

    Borghans, Lex , title =. Economisch-Statistische Berichten , year =

    work page

  58. [58]

    Testing mixed-strategy equilibria when players are heterogeneous: The case of penalty kicks in soccer , journal =

    Chiappori, Pierre-Andr. Testing mixed-strategy equilibria when players are heterogeneous: The case of penalty kicks in soccer , journal =. 2002 , volume =. doi:10.1257/00028280260344678 , url =

    work page doi:10.1257/00028280260344678 2002

  59. [59]

    American Economic Review , year =

    Walker, Mark and Wooders, John , title =. American Economic Review , year =. doi:10.1257/aer.91.5.1521 , url =

    work page doi:10.1257/aer.91.5.1521

  60. [60]

    and Magnus, Jan R

    Klaassen, Franc J.G.M. and Magnus, Jan R. , title =. Journal of Econometrics , year =. doi:10.1016/j.jeconom.2008.09.013 , url =

    work page doi:10.1016/j.jeconom.2008.09.013 2008

  61. [61]

    and Jeong, S

    Kim, W. and Jeong, S. and Kim, J. , title =. Journal of Human Sport and Exercise , year =

    work page

  62. [62]

    and Morris, T

    Koehn, S. and Morris, T. , title =. Journal of Sports Medicine and Physical Fitness , year =

    work page

  63. [63]

    1990 , publisher =

    Csikszentmihalyi, Mihaly , title =. 1990 , publisher =

    work page 1990

  64. [64]

    1975 , publisher =

    Csikszentmihalyi, Mihaly , title =. 1975 , publisher =

    work page 1975

  65. [65]

    and Ryan, Richard M

    Deci, Edward L. and Ryan, Richard M. , title =. Psychological Inquiry , year =. doi:10.1207/S15327965PLI1104_01 , url =

    work page doi:10.1207/s15327965pli1104_01

  66. [66]

    Harris and Kate L

    David J. Harris and Kate L. Allen and Samuel J. Vine and Mark R. Wilson , title =. International Review of Sport and Exercise Psychology , year =. doi:10.1080/1750984X.2021.1929402 , url =

    work page doi:10.1080/1750984x.2021.1929402 2021

  67. [67]

    Allison , title =

    Paul D. Allison , title =. Sociological Methodology , volume =

    work page

  68. [68]

    International Journal of Sports Science & Coaching , volume =

    Anna Fitzpatrick and Joseph A Stone and Simon Choppin and John Kelley , title =. International Journal of Sports Science & Coaching , volume =. 2021 , doi =

    work page 2021

  69. [69]

    Stone and Simon Choppin and John Kelley , title =

    Anna Fitzpatrick and Joseph A. Stone and Simon Choppin and John Kelley , title =. International Journal of Performance Analysis in Sport , volume =

    work page

  70. [70]

    , title =

    Francesco Lisi and Matteo Grigoletto and and Mirko Gabriel Briglia. , title =. Journal of Sports Analytics , volume =

    work page

  71. [71]

    2020 , publisher =

    The Compound Effect (10th Anniversary Edition): Jumpstart Your Income, Your Life, Your Success , author =. 2020 , publisher =

    work page 2020

  72. [72]

    Franc J. G. M. Klaassen and Jan R. Magnus , journal =. Are Points in Tennis Independent and Identically Distributed? Evidence from a Dynamic Binary Panel Data Model , urldate =

    work page

  73. [73]

    Gill and Swartz, Tim B

    Nirodha, Epasinghege Dona and Paramjit, S. Gill and Swartz, Tim B. , title =. Journal of the Royal Statistical Society Series A: Statistics in Society , volume =

    work page

  74. [74]

    , title =

    Cox, DR. , title =. Journal of the Royal Statistical Society Series B: Methodology , volume =

    work page

  75. [75]

    and Kovalchik, S

    Mlakar, M. and Kovalchik, S. A. , title =. Journal of Sports Analytics , volume =

    work page

  76. [76]

    2007 , publisher =

    Winning Ugly , author =. 2007 , publisher =

    work page 2007

  77. [77]

    Abadie, Alberto and Athey, Susan and Imbens, Guido and Wooldridge, Jeffrey , year =. When. arXiv:1710.02926 [econ, math, stat] , eprint =

    work page arXiv

  78. [78]

    Political

    Abdelgadir, Aala and Fouka, Vasiliki , year =. Political. American Political Science Review , volume =. doi:10.1017/S0003055420000106 , urldate =

    work page doi:10.1017/s0003055420000106

  79. [79]

    and McKinney, Kevin L

    Abowd, John M. and McKinney, Kevin L. and Zhao, Nellie L. , year =. Earnings. Journal of Labor Economics , volume =. doi:10.1086/694104 , urldate =

    work page doi:10.1086/694104

  80. [80]

    and Kramarz, Francis and Margolis, David N

    Abowd, John M. and Kramarz, Francis and Margolis, David N. , year =. High. Econometrica , volume =

    work page

Showing first 80 references.