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the claim

The argmax is increasing in multipliers of the objective function under supermodularity conditions.

the verdict
SUPPORTED
the evidence backs this
Recorded sources
4 sources for · 0 against

Counts group repeated records of the same source within each side. They do not measure evidence strength or source independence.

Is it true that the argmax is increasing in multipliers of the objective function under supermodularity conditions?

Yes. Under supermodularity conditions, the set of maximizers (argmax) of an objective function is known to be monotonically increasing with respect to multipliers or parameters of the function, as established in monotone comparative statics.

Verdict: SUPPORTED · 4 sources for, 0 against · Last checked

The analysis

The retrieved papers include foundational and recent work in monotone comparative statics showing that supermodularity (and log-supermodularity) ensures that optimal solutions (such as argmax or equilibrium points) increase with parameters or multipliers. The evidence consistently supports the claim.

Evidence for · 4
Comparative Statics under Uncertainty : Single Crossing Properties and Log-Supermodularity
1996
This paper establishes comparative statics results utilizing log-supermodularity to predict monotonic changes in optimal solutions.
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Athey, S. (1996). Comparative Statics under Uncertainty : Single Crossing Properties and Log-Supermodularity. openalex.org. https://openalex.org/W1495410826

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More for · 3
CHARACTERIZING PROPERTIES OF STOCHASTIC OBJECTIVE FUNCTIONS
1995
The research provides necessary and sufficient conditions for objective functions to maintain supermodular properties in parameters.
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Athey, S. (1995). CHARACTERIZING PROPERTIES OF STOCHASTIC OBJECTIVE FUNCTIONS. openalex.org. https://openalex.org/W1543670376

A qualitative theory of large games with strategic complementarities
2017
The study demonstrates monotone comparative statics with respect to parameters in games using ordered structures.
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Balbus, Ł., Dziewulski, P., Reffett, K., & Woźny, Ł. (2017). A qualitative theory of large games with strategic complementarities. doi.org. https://doi.org/10.1007/s00199-017-1075-7

Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information
2012
The paper derives monotone comparative statics for ordered perturbations in spaces with strategic complementarities.
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Balbus, Ł., Reffett, K., & Woźny, Ł. (2012). Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information. doi.org. https://doi.org/10.1007/s13235-012-0065-4

What does the evidence say?

The retrieved papers include foundational and recent work in monotone comparative statics showing that supermodularity (and log-supermodularity) ensures that optimal solutions (such as argmax or equilibrium points) increase with parameters or multipliers. The evidence consistently supports the claim.

Receipt History
first checked31 Jul 2026
judged → SUPPORTED · 8531 Jul 2026
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