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arxiv: 2304.05515 · v3 · submitted 2023-04-11 · 💰 econ.TH

A Comparison of Cursed Sequential Equilibrium and Sequential Cursed Equilibrium: Different Concepts of Cursedness in Dynamic Games

Meng-Jhang Fong , Po-Hsuan Lin , Thomas R. Palfrey This is my paper

Pith reviewed 2026-05-24 08:42 UTC · model grok-4.3

classification 💰 econ.TH
keywords cursed equilibriumdynamic gamessequential equilibriumbelief updatingpublic historieswinner's curseBayesian games
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The pith

CSE and SCE extend cursed equilibrium to dynamic games using distinct notions of cursedness and belief updating.

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

This paper compares Cursed Sequential Equilibrium and Sequential Cursed Equilibrium, two extensions of cursed equilibrium designed to handle dynamic games. It establishes that the extensions work through fundamentally different ideas about cursedness, how players update beliefs after observing actions, and how they incorporate public histories. A sympathetic reader would care because the original cursed equilibrium concept has known limitations once games involve sequences of moves and information revealed over time. The comparison clarifies these foundations so that the appropriate concept can be selected for modeling specific sequential interactions.

Core claim

CSE and SCE address the limitations of cursed equilibrium in dynamic games in fundamentally different ways, with distinct notions of cursedness, belief updating, and treatment of public histories.

What carries the argument

The distinct definitions of cursedness together with the associated rules for belief updating and handling of public histories in CSE versus SCE.

If this is right

  • CSE and SCE can yield different equilibrium behavior in the same dynamic game with incomplete information.
  • The models diverge in how observed actions and public histories affect subsequent beliefs and play.
  • Applications to sequential auctions or bargaining games may produce different forecasts depending on which concept is used.
  • The choice between the two concepts changes which forms of cursedness are assumed to persist across periods.

Where Pith is reading between the lines

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

  • Empirical studies of dynamic games could compare observed behavior against the distinct predictions of each concept to see which fits better.
  • The distinction may inform mechanism design choices when the designer wants to account for different types of cursed reasoning.
  • Hybrid models that blend features of both concepts could be developed for games with mixed public and private information.

Load-bearing premise

The conceptual and technical differences between CSE and SCE are sufficiently important to warrant a dedicated systematic comparison that clarifies their foundations.

What would settle it

A demonstration that CSE and SCE produce identical equilibrium outcomes and predictions in every class of dynamic game would undermine the claim that the two concepts rest on meaningfully different foundations.

Figures

Figures reproduced from arXiv: 2304.05515 by Meng-Jhang Fong, Po-Hsuan Lin, Thomas R. Palfrey.

Figure 1
Figure 1. Figure 1: Game Tree for the Illustrative Example Consider the signaling game depicted in [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The solution set of (χS, ψS)-SCE Since the incentives of both types of player 1 are perfectly aligned, the existence of such a separating (χS, ψS)-SCE is unexpected. In summary, a key difference between CSE and SCE is about the way of treating public histories. From the illustrative example, we can find that when the coarsest valid partition is not consistent with the public histories, (χS, ψS)-SCE and χ-C… view at source ↗
Figure 3
Figure 3. Figure 3: A Two-Player Game with Complete Information [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (χS, ψS)-SCE of an unscrambled and scrambled signaling game [PITH_FULL_IMAGE:figures/full_fig_p025_4.png] view at source ↗
read the original abstract

Cursed Equilibrium of Eyster and Rabin (2005) has been a leading theory for explaining winner's-curse-type behavior in static Bayesian games, but it faces conceptual limitations when applied to dynamic games. Two recent extensions, Cursed Sequential Equilibrium (CSE) by Fong, Lin and Palfrey (2025) and Sequential Cursed Equilibrium (SCE) by Cohen and Li (2026), address these limitations in fundamentally different ways. Complementing these two papers, this paper provides a systematic comparison of CSE and SCE, clarifying their conceptual foundations and technical implications, including their notions of cursedness, belief updating, and treatment of public histories.

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

0 major / 1 minor

Summary. The paper claims that Cursed Sequential Equilibrium (CSE) by Fong, Lin and Palfrey and Sequential Cursed Equilibrium (SCE) by Cohen and Li extend cursed equilibrium to dynamic games in fundamentally different ways, with distinct notions of cursedness, belief updating, and treatment of public histories; it provides a systematic comparison to clarify their conceptual foundations and technical implications.

Significance. If the reconstruction of the two concepts is accurate, the comparison could assist applied theorists in selecting between the frameworks when modeling sequential games with winner's-curse-type behavior. The manuscript is expository rather than theorem-driven, so its contribution rests on faithful mapping of the source definitions rather than new derivations or proofs.

minor comments (1)
  1. The abstract cites the source papers with future dates (2025, 2026); the manuscript should clarify whether these refer to working-paper versions and include precise citation details or DOIs if available.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation for minor revision. The report correctly identifies the paper as an expository comparison whose value lies in accurately mapping the conceptual differences between CSE and SCE. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

This manuscript is an expository comparison of two pre-existing solution concepts (CSE from the authors' 2025 working paper and SCE from Cohen-Li 2026) rather than a derivation of new predictions or first-principles results. No equations, fitted parameters, or theorems are presented whose outputs reduce by construction to the paper's own inputs. The central claim—that the two concepts differ in their treatment of cursedness, belief updating, and public histories—rests on reconstruction from the cited source definitions and does not invoke self-citation as load-bearing justification for any novel result. The single self-citation is therefore incidental and does not trigger any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No full manuscript text was available; the abstract does not introduce or rely on new free parameters, axioms, or invented entities beyond referencing the two prior papers.

pith-pipeline@v0.9.0 · 5648 in / 1018 out tokens · 16547 ms · 2026-05-24T08:42:59.532363+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages

  1. [1]

    Sequential Cursed Equilibrium,

    Cohen, S. and S. Li (2023): “Sequential Cursed Equilibrium,” arXiv preprint arXiv:2212.06025v3 First version posted December 13, 2022

    work page arXiv 2023

  2. [2]

    Cursed equilibrium,

    Eyster, E. and M. Rabin (2005): “Cursed equilibrium,” Econometrica, 73, 1623–1672

    work page 2005

  3. [3]

    Cursed Sequential Equilibrium,

    Fong, M.-J., P.-H. Lin, and T. R. Palfrey (2023): “Cursed Sequential Equilibrium,” arXiv preprint arXiv:2301.11971

    work page arXiv 2023

  4. [4]

    Perfect Bayesian equilibrium and sequential equilibrium,

    Fudenberg, D. and J. Tirole (1991): “Perfect Bayesian equilibrium and sequential equilibrium,” Journal of Economic Theory , 53, 236–260

    work page 1991

  5. [5]

    Analogy-based expectation equilibrium,

    Jehiel, P. (2005): “Analogy-based expectation equilibrium,” Journal of Economic Theory, 123, 81–104

    work page 2005

  6. [6]

    Revisiting games of incomplete information with analogy-based expectations,

    Jehiel, P. and F. Koessler (2008): “Revisiting games of incomplete information with analogy-based expectations,” Games and Economic Behavior , 62, 533–557

    work page 2008

  7. [7]

    Sequential Equilibria,

    Kreps, D. M. and R. Wilson (1982): “Sequential Equilibria,” Econometrica, 50, 863– 894. 27

    work page 1982