I was overwhelmed with work and could not do my share.
Genuine hardship
MORALITY · COOPERATION · GAME THEORY
When excuses cannot be verified, rules harden
A flexible rule protects someone who is ill, exhausted or caught in a crisis. The same room for judgment lets an opportunist present convenience as need. A model published in PNAS shows why societies may accept inefficient rules to preserve cooperation when people's motives remain hidden.
The study is theoretical. It identifies a possible logic and testable predictions; it does not measure how much real-world morality this logic explains.
2cooperative equilibria
4outcome regions
1central trade-off
The same lapse can conceal two causes
I could not contribute. I had an impossible day.
genuine hardship
opportunistic excuse
the rule must judge before it knows
THE CENTRAL GESTURE
Two identical excuses. Two different truths.
The observer hears the same explanation in both cases. In one, cooperation would have cost more than it produced. In the other, the excuse protects a selfish gain. Choose the rule before you see what happened.
Apply a rule without seeing the motive
The scenario uses the model's information problem: behaviour is public, while circumstances remain private.
WHAT THE MODEL FINDS
Two ways to preserve cooperation
The model separates reputation from motive. People can see who contributed, but they cannot always verify the illness, crisis or obligation that made contribution too costly.
Flexible norm
An apparently legitimate exception preserves trust
People can opt out under genuine hardship without destroying their reputation. The rule maximises welfare when partners are reliable and false excuses are difficult to sustain.
Risk: opportunists can imitate hardship and preserve access to trust.
The trade-off
Efficiency versus resistance to exploitation
Flexibility avoids needless costs. Rigidity removes an excuse that free-riders can exploit. The model identifies the conditions under which each advantage becomes decisive.
Rigid norm
Every lapse produces the same loss of trust
A bright line can sustain cooperation where exceptions make reputations too ambiguous. The rule pushes some opportunists to contribute even when they would exploit flexibility.
Cost: cooperation is demanded even when genuine hardship makes it inefficient.
FIGURE 2, REBUILT
Where can each rule survive?
The map numerically reproduces the paper's domains with the same parameters. Move the point. The horizontal axis increases average impatience; the vertical axis increases the chance that opportunism looks like genuine hardship.
- Flexible norm only
- Both norms
- Rigid norm only
- Cooperation fails
The calculation uses the truncated normal distribution and the parameters in Figure 2: σ = 0.3; c = 1; b = 2; γ = 0.5; β = 0.75; γH = 2; p = 0.2. Classification applies conditions F2, R3 and R4 directly.
TESTABLE PREDICTIONS
The model expects stricter rules when trust becomes risky
The authors derive predictions about settings in which flexibility should be easier or harder to sustain. These are consequences of the model, not new empirical findings.
more flexibilitymore rigidity
Visible, easily verified hardship
Stress, fatigue or obligations that are hard to verify
Observable cases permit accommodation; opaque motives increase the risk of strategic excuses.
Family, friends and stable teams
Strangers, short relationships and formal institutions
A shared future makes reputation more valuable and reduces the gain from opportunistic defection.
Partners seen as patient and reliable
Partners seen as impulsive or unreliable
Categorical rules become more attractive when discretion is granted to people considered easy to tempt.
Security and a long time horizon
Threat, scarcity and an uncertain future
The authors connect shorter horizons with tighter cultures and lower tolerance for deviance.
A DERIVED IMPLICATION
Better information can make exceptions safer
The model suggests a route to less rigidity without losing cooperation: reduce the ambiguity between observable behaviour and the real motive behind it.
01
Verify hardship
Credible evidence, independent assessment or visible circumstances reduce the chance that opportunism passes as need.
02
Lengthen the relationship
Repeated interaction makes future reputation more valuable and raises the cost of using an excuse strategically.
03
Improve reliability signals
Institutions can grant discretion where history and accountability make future cooperation more predictable.
THE LIMIT OF THE EVIDENCE
What the model establishes and where it stops
Inside the model
- A flexible equilibrium and a rigid equilibrium can sustain cooperation under different conditions.
- Rigidity extends cooperation in some environments where flexibility collapses.
- The gain in resistance to exploitation comes with a loss of efficiency.
In the real world
- The paper introduces no new empirical data and does not estimate how often the mechanism operates.
- The model isolates one ambiguous decision, separates roles and simplifies the formation of cultural norms.
- The result does not morally justify strict rules or explain every form of rigidity.
In the model, rigidity arises from the inability to verify context even when people can understand it perfectly well. Credible excuses and a shared future make flexibility sustainable.
SOURCES AND METHOD
A theoretical demonstration published with open model materials and code
Primary paper
Why human societies adopt rigid moral rules: The efficiency–robustness trade-off
Julien Lie-Panis, Léo Fitouchi, Nicolas Baumard and Jean-Baptiste André. PNAS 123(28), e2535467123. Published 8 July 2026. Open access, CC BY 4.0.
Pages 1-3 describe the information problem and the game; pages 4-6 define the equilibria and map; pages 6-8 set out predictions and limitations.
Open the paperCode and materials
Rigid moral rules · OSF
The public repository named by the authors contains the code used for Figures 2 and 3 and the analytical derivations in the supplement.
Open the repositoryFigure 2 is reproduced numerically. The social examples are predictions and illustrations from the authors. The idea that better verification can permit more flexible rules is an implication derived from the model's structure.