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arxiv: 1907.09102 · v1 · pith:46BVR2J4new · submitted 2019-07-22 · 💻 cs.GT · cs.LO

Common Belief in Choquet Rationality and Ambiguity Attitudes -- Extended Abstract

Adam Dominiak (Virginia Tech) , Burkhard Schipper (University of California , Davis) This is my paper

Pith reviewed 2026-05-24 18:10 UTC · model grok-4.3

classification 💻 cs.GT cs.LO
keywords Choquet rationalizabilitycommon beliefambiguity attitudesChoquet expected utilityiterative eliminationstrategic gamesambiguity aversionambiguity love
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The pith

Choquet rationalizability in finite games with ambiguity is characterized by common belief in Choquet rationality and equals iterative elimination of dominated actions in an extended game.

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 finite strategic-form games where players evaluate outcomes with Choquet expected utility, a profile of actions is Choquet rationalizable precisely when it survives iterative elimination of strictly dominated actions in an extended version of the game. This equivalence also holds when players hold common beliefs that others are Choquet rational, modeled inside a universal capacity type space. The approach removes the need to compute Choquet integrals before identifying rationalizable actions. It further establishes that greater ambiguity love shrinks the set of Choquet rationalizable action profiles while greater ambiguity aversion enlarges it.

Core claim

Choquet rationalizability is characterized by Choquet rationality together with common beliefs in Choquet rationality inside the universal capacity type space in a purely measurable setting. It is equivalent to iterative elimination of strictly dominated actions in an extended game rather than the original game. Ambiguity love produces smaller Choquet rationalizable sets of action profiles while ambiguity aversion produces larger ones.

What carries the argument

The universal capacity type space that encodes common belief in Choquet rationality under unambiguous belief, together with the reduction to iterative elimination in an extended game.

If this is right

  • Rationalizable actions can be found by applying ordinary iterative elimination in the extended game without first evaluating any Choquet integrals.
  • Ambiguity-loving players have strictly smaller Choquet rationalizable sets than ambiguity-neutral players.
  • Ambiguity-averse players have strictly larger Choquet rationalizable sets than ambiguity-neutral players.
  • The characterization continues to hold when common belief is imposed inside the universal capacity type space.

Where Pith is reading between the lines

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

  • The size of rationalizable sets could be used as a diagnostic for how much ambiguity different groups perceive in the same strategic setting.
  • Laboratory experiments that control subjects' ambiguity attitudes could directly test whether observed play stays inside the predicted Choquet rationalizable sets.
  • Policy measures that reduce perceived ambiguity might systematically enlarge the range of sustainable outcomes in coordination problems.

Load-bearing premise

The existence of a universal capacity type space that can represent common beliefs in a purely measurable way for finite games.

What would settle it

A finite game in which the action profiles surviving iterative elimination of strictly dominated actions in the extended game differ from those that survive common belief in Choquet rationality inside the universal type space.

read the original abstract

We consider finite games in strategic form with Choquet expected utility. Using the notion of (unambiguously) believed, we define Choquet rationalizability and characterize it by Choquet rationality and common beliefs in Choquet rationality in the universal capacity type space in a purely measurable setting. We also show that Choquet rationalizability is equivalent to iterative elimination of strictly dominated actions (not in the original game but) in an extended game. This allows for computation of Choquet rationalizable actions without the need to first compute Choquet integrals. Choquet expected utility allows us to investigate common belief in ambiguity love/aversion. We show that ambiguity love/aversion leads to smaller/larger Choquet rationalizable sets of action profiles.

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 / 0 minor

Summary. The paper considers finite strategic-form games under Choquet expected utility. It defines Choquet rationalizability using the notion of (unambiguously) believed actions and claims to characterize it via Choquet rationality plus common belief in Choquet rationality inside a universal capacity type space constructed in a purely measurable setting. It further asserts equivalence between Choquet rationalizability and iterative elimination of strictly dominated actions in an extended game (allowing computation without Choquet integrals) and shows that ambiguity-loving (averse) agents have smaller (larger) Choquet-rationalizable action-profile sets.

Significance. If the central claims hold, the work would extend rationalizability theory to non-additive beliefs, supply a dominance-based computational shortcut, and link ambiguity attitudes directly to the size of rationalizable sets. The measurable universal-type-space construction for capacities would be a technical contribution, but its absence from the provided text leaves the significance conditional on verification.

major comments (2)
  1. [Abstract] Abstract: the claimed characterization of Choquet rationalizability by common belief in Choquet rationality rests on the existence of a universal capacity type space in a purely measurable setting. No construction, inductive argument, or reference to an existence result for non-additive capacities is supplied; standard Kolmogorov-style constructions rely on countable additivity that capacities lack, so the common-belief operator may not be well-defined on the claimed space.
  2. [Abstract] Abstract: the manuscript states characterizations and equivalences (Choquet rationalizability = common belief in Choquet rationality; equivalence to iterated strict dominance in an extended game) but supplies neither proofs nor detailed derivations. Soundness of these load-bearing claims cannot be assessed from the given text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed comments on our extended abstract. We address each major comment below and indicate how we plan to revise the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claimed characterization of Choquet rationalizability by common belief in Choquet rationality rests on the existence of a universal capacity type space in a purely measurable setting. No construction, inductive argument, or reference to an existence result for non-additive capacities is supplied; standard Kolmogorov-style constructions rely on countable additivity that capacities lack, so the common-belief operator may not be well-defined on the claimed space.

    Authors: We agree that the extended abstract does not include the construction or a reference for the universal capacity type space. This is a valid point. In the full paper, we will provide either a reference to an appropriate existence result for type spaces with capacities or include a construction adapted to the measurable setting without relying on countable additivity. We believe such constructions are possible using the theory of capacities and belief hierarchies in non-additive settings, but we will make this explicit in the revision. revision: yes

  2. Referee: [Abstract] Abstract: the manuscript states characterizations and equivalences (Choquet rationalizability = common belief in Choquet rationality; equivalence to iterated strict dominance in an extended game) but supplies neither proofs nor detailed derivations. Soundness of these load-bearing claims cannot be assessed from the given text.

    Authors: Since the submission is an extended abstract, the detailed proofs are not included in this version. We will incorporate outlines or full proofs of the characterizations and the equivalence to iterative elimination of strictly dominated actions in the extended game in the complete manuscript. This will allow readers to verify the claims. We can also add a short explanation of the key steps in the abstract if the editor allows. revision: yes

Circularity Check

0 steps flagged

No significant circularity; characterization rests on external definitions

full rationale

The paper's central result equates Choquet rationalizability with common belief in Choquet rationality inside a universal capacity type space and shows equivalence to iterative elimination of dominated strategies in an extended game. These steps invoke standard Choquet expected utility and the existence of a measurable universal type space for capacities as background notions rather than deriving them from fitted parameters or self-referential definitions internal to the paper. No quoted equations reduce a prediction to a prior fit by construction, and no self-citation chain is shown to be load-bearing for the main claims. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard domain assumptions from decision theory and game theory under ambiguity; no free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Finite games in strategic form admit Choquet expected utility
    Stated as the modeling framework.
  • domain assumption Existence of universal capacity type space in purely measurable setting
    Invoked for the common-belief characterization.

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Works this paper leans on

43 extracted references · 43 canonical work pages

  1. [1]

    Ahn, D. S. (2007). Hierarchies of ambiguous beliefs, Jou rnal of Economic Theory 136, 286–301, https://doi.org/10.1016/j.jet.2006.08.004

    work page doi:10.1016/j.jet.2006.08.004 2007

  2. [2]

    Aryal, G. and R. Stauber (2014). Trembles in extensive ga mes with ambiguity averse players, Economic Theory 57, 1–40, https://doi.org/10.1007/s00199-014-0828-9

    work page doi:10.1007/s00199-014-0828-9 2014

  3. [3]

    Marinacci (2016)

    Battigalli, P ., Cerreia-Vioglio, S., Maccheroni, F., and M. Marinacci (2016). A note of comparative ambiguity aversion and justifiability, Econometrica 84, 1903–1916, https://doi.org/10.3982/ECTA14429

    work page doi:10.3982/ecta14429 2016

  4. [5]

    complet e

    Brandenburger, A. (2003). On the existence of a “complet e” possibility structure, in: Dimitry, N., Basili, M., and I. Gilboa (Eds.), Cognitive processes and economic beha vior, Routledge: London, 30–34

    work page 2003

  5. [6]

    Keisler (200 8)

    Brandenburger, A., Friedenberg, A., and J. Keisler (200 8). Admissibility in games, Econometrica 76, 307– 352, https://doi.org/10.1111/j.1468-0262.2008.00835.x

    work page doi:10.1111/j.1468-0262.2008.00835.x 2008

  6. [7]

    Chateauneuf, A. (1994). Modeling attitudes towards unc ertainty and risk through the use of Choquet integral, Annals of Operations Research 52, 3–20, https://doi.org/10.1007/BF02032158

    work page doi:10.1007/bf02032158 1994

  7. [8]

    Grant (2003)

    Chateauneuf, A., Eichberger, J., and S. Grant (2003). A s imple axiomatization and con- structive representation proof for Choquet expected utili ty, Economic Theory 22, 907 – 915, https://doi.org/10.1007/s00199-002-0345-0

    work page doi:10.1007/s00199-002-0345-0 2003

  8. [9]

    and Luo X

    Chen Y .C. and Luo X. (2012). An indistinguishability res ult on rationalizability under general preferences, Economic Theory 51, 1–12, https://doi.org/10.1007/s00199-010-0596-0

    work page doi:10.1007/s00199-010-0596-0 2012

  9. [10]

    Karni (1994)

    Chew, S.H., and E. Karni (1994). Choquet expected utili ty with a finite state space: Commutativity and act- independence, Journal of Economic Theory 62, 469–479, https://doi.org/10.1006/jeth.1994.1026

    work page doi:10.1006/jeth.1994.1026 1994

  10. [11]

    Choquet, G. (1954). Theory of capacities, Annales Inst itut Fourier 5, 131–295, https://doi.org/10.5802/aif.53

    work page doi:10.5802/aif.53 1954

  11. [12]

    and J.-P

    Dominiak, A. and J.-P . Lefort (2011). Unambiguous even ts and dynamic choquet preferences, Economic Theory 46, 401–425, https://doi.org/10.1007/s00199-009-0512-7

    work page doi:10.1007/s00199-009-0512-7 2011

  12. [13]

    Di Tillo, A. (2008). Subjective expected utility in gam es, Theoretical Economics 3, 287–323, https://econtheory.org/ojs/index.php/te/article/view/20080287/0

    work page arXiv 2008

  13. [14]

    Dominiak, A. and J. Eichberger (2019). Games in Context : Equilibrium Under Ambiguity for Belief Func- tions, Virginia Tech

    work page 2019

  14. [15]

    Dow, J. and S. R. Costa Werlang (1994). Nash equilibrium under Knightian uncer- tainty: Breaking down backward induction, Journal of Econo mic Theory 64, 305–324, https://doi.org/10.1006/jeth.1994.1071

    work page doi:10.1006/jeth.1994.1071 1994

  15. [16]

    Eichberger J. and D. Kelsey (2000), Non-Additive Belie fs and Strategic Equilibria, Games and Economic Behavior 30, 183–215, https://doi.org/10.1006/game.1998.0724

    work page doi:10.1006/game.1998.0724 2000

  16. [17]

    Eichberger J. and D. Kelsey (2014), Optimism and pessim ism in games, International Economic Review 55, 483–505, https://doi.org/10.1111/iere.12058

    work page doi:10.1111/iere.12058 2014

  17. [18]

    Eichberger, J., Kelsey D. and B.C. Schipper (2009). Amb iguity and social interaction, Oxford Economic Papers 61, 355–379, https://doi.org/10.1093/oep/gpn030

    work page doi:10.1093/oep/gpn030 2009

  18. [19]

    Epstein, L. (1997). Preference, rationalizability an d equilibrium, Journal of Economic Theory 73, 1–29, https://doi.org/10.1006/jeth.1996.2229

    work page doi:10.1006/jeth.1996.2229 1997

  19. [20]

    Epstein, L. and T. Wang (1996). ‘Beliefs about beliefs’ without probabilities, Econometrica 64, 1343–1373, https://www.jstor.org/stable/2171834

    work page arXiv 1996

  20. [21]

    Lee (2016)

    Ganguli, J., Heifetz, A., and B.S. Lee (2016). Universa l interactive preferences, Journal of Economic Theory 162, 237–260, https://doi.org/10.1016/j.jet.2015.12.012. 154 Common Belief in Choquet Rationality and Ambiguity Attitud es

    work page doi:10.1016/j.jet.2015.12.012 2016

  21. [22]

    Ghirardato, P . and M. Le Breton (1999). Choquet rationa lizability, Caltech

    work page 1999

  22. [23]

    Siniscalchi (2003)

    Ghirardato, P ., Macheroni, F., Marinacci, M., and M. Siniscalchi (2003). A subjective spin on roulette wheels, Econometrica 71, 1897–1908, https://www.jstor.org/stable/1555541

    work page arXiv 2003

  23. [24]

    Gilboa, I. (1987). Expected utility with purely subjec tive non-additive probabilities, Journal of Mathematical Economics 16, 65–88, https://doi.org/10.1016/0304-4068(87)90022-X

    work page doi:10.1016/0304-4068(87)90022-x 1987

  24. [25]

    Haller, H. (2000). Non-Additive Beliefs in Solvable Ga mes, Theory and Decision 49, 313–338, https://doi.org/10.1023/A:1026549117322

    work page doi:10.1023/a:1026549117322 2000

  25. [26]

    Mukerji (2019)

    Hanany, E., Klibanoff P ., and S. Mukerji (2019). Incomp lete Information Games with Ambiguity Averse Players, Mimeo

    work page 2019

  26. [27]

    Heifetz, A. and D. Samet (1998). Topology-free typolog y of beliefs, Journal of Economic Theory 82, 324– 341, https://doi.org/10.1006/jeth.1998.2435

    work page doi:10.1006/jeth.1998.2435 1998

  27. [28]

    Klibanoff, P . (1996). Uncertainty, decision, and norm al-form games, Northwestern University

    work page 1996

  28. [29]

    K¨ obberling, V . and P . Wakker (2003). Preference Found ations for Nonexpected Utility: A Generalized and Simplified Technique, Mathematics of Opera tions Research 28, 395-423, https://doi.org/10.1287/moor.28.3.395.16390

    work page doi:10.1287/moor.28.3.395.16390 2003

  29. [30]

    Lo, K.C. (1996). Equilibrium in Beliefs under Uncertai nty, Journal of Economic Theory 71, 443 - 484, https://doi.org/10.1006/jeth.1996.0129

    work page doi:10.1006/jeth.1996.0129 1996

  30. [31]

    Lo, K.C. (1999). Extensive Form Games with Uncertainty Averse Players, Games and Economic Behavior 28, 256–270, https://doi.org/10.1006/game.1998.0696

    work page doi:10.1006/game.1998.0696 1999

  31. [32]

    Marinacci, M. (2000). Ambiguous games, Games and Econo mic Behavior 31, 2000, 191–219, https://doi.org/10.1006/game.1999.0739

    work page doi:10.1006/game.1999.0739 2000

  32. [33]

    Morris, S. (1997). Alternative definitions of knowledg e. In: Bacharach, M.O.L., Gerard-V aret, L.A., Mongin, P ., Shin, H.S. (Eds.), Epistemic Logic and the Theory of Game s and Decisions. Kluwer, 217–233

    work page 1997

  33. [34]

    (1999), Capacities and probabilistic beli efs: a precarious coexistence, Mathematical Social Sci- ences 38, 197–213, https://doi.org/10.1016/S0165-4896(97)00017-6

    Nehring, K. (1999), Capacities and probabilistic beli efs: a precarious coexistence, Mathematical Social Sci- ences 38, 197–213, https://doi.org/10.1016/S0165-4896(97)00017-6

    work page doi:10.1016/s0165-4896(97)00017-6 1999

  34. [35]

    Nakamura, Y . (1990). Subjective expected utility with non-additive probabilities on finite state spaces, Journal of Economic Theory 51, 346–366, https://doi.org/10.1016/0022-0531(90)90022-C

    work page doi:10.1016/0022-0531(90)90022-c 1990

  35. [36]

    Pearce, D.G. (1984). Rationalizable strategic behavi or and the problem of perfection, Econometrica 52, 1029–1050, https://www.jstor.org/stable/1911197

    work page arXiv 1984

  36. [37]

    Pinter, M. (2012). Type spaces with non-additive belie fs, Corvinus University

    work page 2012

  37. [38]

    Riedel, F. and L. Sass (2014). Ellsberg games, Theory an d Decision 76, 469–509, https://doi.org/10.1007/s11238-013-9381-4

    work page doi:10.1007/s11238-013-9381-4 2014

  38. [39]

    Sarin, R. and P . Wakker (1992). A simple axiomatization of nonadditive expected utility, Econometrica 60, 1255–1272, https://www.jstor.org/stable/2951521

    work page arXiv 1992

  39. [40]

    Schmeidler, D. (1986). Integral Representation Witho ut Additivity, Proceedings of the American Mathemat- ical Society 97, 255–261, https://doi.org/10.1090/S0002-9939-1986-0835875-8

    work page doi:10.1090/s0002-9939-1986-0835875-8 1986

  40. [41]

    Schmeidler, D. (1989). Subjective probability and exp ected utility without additivity, Econometrica 57, 571– 587, https://www.jstor.org/stable/1911053

    work page arXiv 1989

  41. [42]

    Spohn, W . (1982). How to make sense of game theory, in: St egm¨ uller, W ., Balzer, W ., and W . Spohn (eds.), Philosophy of economics, Springer- V erlag, 239–270, https://doi.org/10.1007/978-3-642-68820-1_14

    work page doi:10.1007/978-3-642-68820-1_14 1982

  42. [43]

    Wakker, P . (1990). Characterizing optimism and pessim ism directly through comonotonicity, Journal of Eco- nomic Theory 52, 453–463, https://doi.org/10.1016/0022-0531(90)90043-J

    work page doi:10.1016/0022-0531(90)90043-j 1990

  43. [44]

    Wakker, P . (1989). Continuous subjective expected uti lity with non-additive probabilities, Journal of Mathe- matical Economics 18, 1–27, https://doi.org/10.1016/0304-4068(89)90002-5

    work page doi:10.1016/0304-4068(89)90002-5 1989