Please refer to Appendix 1 for the complete list.

The customer/consumer utility function is modelled as

$U\left(t_k,t_{k-1}^{*},b,s\right)=-d\left(b,t_k\right)+f\left(t_k,t_{k-1}^{*};\beta ,\lambda ,\gamma \right)+G\left(s,b\right)$

where first term $U\left(t_k,t_{k-1}^{*},b,s\right)$ is total utility of a consumer at time $k$, the second term $-d\left(b,t_k\right)$ is the monetary disutility (Indexed), the third term $f\left(t_k,t_{k-1}^{*};\beta ,\lambda ,\gamma \right)$ is the Psychological utility (Indexed), and the last term $G\left(s,b\right)$ is the exogenous service-enjoyment utility.

In contrast to Azar’s original formulation, which anchors the social norm to an abstract function $n\left(s\right)$, we replace $n\left(s\right)$ with the observed average tip from the previous period $t_{k-1}^{*}$. This is formally presented as $n\left(s\right)\equiv t_k$. Both $d\left(b,t_k\right)$ and $f\left(t_k,t_{k-1}^{*};\beta ,\lambda ,\gamma \right)$ are scaled to the interval [0, 1], allowing for direct comparison of monetary and psychological utilities. To empirically establish the norm, we estimate $t_{k-1}^{*}$ via a constrained OLS regression (through the origin) of this period’s mean tip on the last period’s mean tip using U.S. data (see Appendix 2). This produces a strong positive correlation and justifies treating $t_{k-1}^{*}$ as the collective tipping expectation.

For simplicity, we further assume that all consumers possess perfect information about $t_{k-1}^{*}$, thus ignoring informational lags or learning processes. These simplifications—linking the social norm to realised tipping data, scaling the utility parts consistently, and assuming perfect foresight—result in a clear equilibrium condition that straightforwardly captures the ongoing feedback loop driving tip inflation.

The monetary disutility component in the utility model, modified from Azar (2005) , is given by

$m\left(b,t_k\right)=b\left(1+t_k\right)$

where $b$ denotes bill size and $t_k$ is the tip rate at time $k$. To facilitate comparison of marginal effects and ensure both variables are on a common scale, min-max normalisation is applied to each dimension. For the economically relevant ranges $t_k\in \left[0,1\right)$ and $b\in \left[0,b_{\max }\right]$, the normalised components become:

${\left(\nabla m\right)}_{norm}=\left[\begin{array}{c}{t}_k\\ \frac{b}{b_{\max }}\end{array}\right]$

The composite monetary disutility is rewritten in the form:

$d\left(b,t_k\right)=\frac{1}{\sqrt{2}}\cdot \sqrt{{\left(t_k\right)}^2+{\left(\frac{b}{b_{\max }}\right)}^2}$

$f\left(x;\beta ,\lambda ,\gamma \right)=\{\begin{array}{l}{\text{e}}^{-\beta {\left(x-\lambda \right)}^2},x\ge 0\\ {\text{e}}^{-\gamma \beta {\left(x-\lambda \right)}^2},x<0\end{array}$

where $\beta >0$ controls the steepness of norm-conformity penalties (interpreted as the “painfulness” of undertipping), $\lambda$ (strictly ≥ 0) determines the peak of psychological utility, and $\gamma >1$ imposes asymmetry, penalising under-tipping more significantly than over-tipping.

The graphical interpretation of psychological utility function $f\left(x;\beta ,\lambda ,\gamma \right)$ illustrates a skewed bell curve diagram—the peak of the curve $f=1$ is located at $x=\lambda$. If the tendency to “overshoot” socially acceptable tipping exists, $\lambda >0$, the peak shifts to the right of the prior norm.

The width of the curve is controlled by the parameter $\beta$, which determines how rapidly psychological utility falls off when deviated from $\lambda$. The larger the parameter $\beta$, the narrower and steeper the peak is observed. Economically, in this model, a larger $\beta$ number could imply a more substantial influence of social norms on the individual’s choice of tip rate.

The asymmetrical factor is designed to create a skew, matching the asymmetric punishment of under-tipping in line with Azar’s work, where not tipping enough causes significant disutility due to social and psychological costs, and tipping more than the norm might generate some positive utility from the “warm glow” effects, for instance.

Differentiating $d\left(b,t_k\right)$ with respect to $t_k$,

$d^{\prime }\left(t_k\right)=\frac{t_k}{\sqrt{2}\sqrt{{\left(t_k\right)}^2+{\left(\frac{b}{b_{\max }}\right)}^2}}$

where $d^{\prime }\left(t_k\right)$ measures the marginal monetary cost of increasing the tip rate by an infinitesimal amount. In the first-order condition for optimal tipping, this term is set equal to the marginal social-conformity benefit $f^{\prime }\left(t_k-t_{k-1}^{*}\right)$, so that the extra dollar spent on the tip just compensates the additional disutility.

Differentiating $f\left(x;\beta ,\lambda ,\gamma \right)$ with respect to $x$ where $x\ge 0$,

$f^{\prime }\left(x\right)=-2\beta \left(x-\lambda \right){\text{e}}^{-\beta {\left(x-\lambda \right)}^2}$

where $f^{\prime }\left(x\right)$ is the marginal social utility of deviating from last period’s norm by an amount $x$. Its sign and magnitude depend on whether $x$ is below, at, or above the peak $\lambda$, and on the steepness $\beta$.

Let $x=t_k-t_{k-1}$ denote the deviation of the tip rate from the prevailing social norm, such that $x^{*}=t_k^{*}-t_{k-1}^{*}$ represents the equilibrium deviation capturing the rate of tip inflation year-over-year. Maximizing total utility $U$ with respect to $t_k$ yields the first-order condition:

$0=\frac{\partial U}{\partial t_k}-d^{\prime }\left(t_k\right)+f^{\prime }\left(x\right)$

Given the normalization of the monetary disutility component, the equilibrium is obtained by equating the marginal monetary and psychological utilities, which for the functional forms specified in this model simplifies to:

$2\beta \left(\lambda -x^{*}\right){\text{e}}^{-\beta {\left(x^{*}-\lambda \right)}^2}=\frac{t_k^{*}}{\sqrt{2}{t}_k^{*}}=\frac{1}{\sqrt{2}}$, for $d^{\prime }\left(t_k\right)=\underset{b_{\max }\to \infty }{\lim }\left[\frac{t_k}{\sqrt{2}\sqrt{{\left(t_k\right)}^2+{\left(\frac{b}{b_{\max }}\right)}^2}}\right]$

This equilibrium condition characterizes the optimal tipping deviation $x^{*}$, allowing for comparative static analysis with respect to the key model parameters $\lambda$ and $\beta$, while holding the other constant. This framework enables explicit examination of how changes in social norm sensitivity ( $\beta$) or horizontal shift ( $\lambda$) influence the trajectory of tipping norms over time.

This section investigates how cross-cultural values influence the evolution of tipping behaviour over time. The key variable of interest ( $x^{*}$), is defined as the year-over-year change in the optimal tip rate. Specifically, the difference between the optimal tip rate at time $k$, ( $t_k^{*}$), and the preceding period’s social norm ( $t_{k-1}^{*}$). This difference is interpreted as a proxy for tip inflation, where higher values of $x^{*}$ indicate a steeper increase in tipping expectations over time. With this interpretation, I have selected four country-level indices to examine the correlation between the $x^{*}$ value and the individual cultural index. First, Embeddedness (EMB), based on Schwartz’s Embeddedness orientation, reflects societies where individuals are seen as integral parts of the collective. In such cultures, meaning in life is mainly derived through social relationships and identification with group goals. High EMB scores will thus indicate a strong focus on maintaining the status quo, preserving in-group solidarity, and restraining actions that might disrupt traditional social order. Second, Affective Autonomy (AUT_AFF) measures the extent to which individuals are encouraged to pursue affectively positive experiences, such as pleasure, excitement, and comfort, regardless of group norms. Higher AUT_AFF values, therefore, denote a cultural allowance for personal gratification. Third, Intellectual Autonomy (AUT_INT) assesses the degree to which societies promote independent thought and the development of one’s own ideas. Cultures with high scores on AUT_INT explicitly support exploring new intellectual directions, even when these conflict with prevailing social expectations. Finally, the Combination Cultural Tightness-Looseness (CTL_C) index, developed by Uz (2015) , combines multiple norms enforcement axioms to gauge a society’s tolerance for deviance. Higher CTL_C values correspond to greater looseness, indicating weaker sanctions against non-conformity. Empirical evidence also suggests that looser cultures tend to show more positive attitudes towards social deviance and stronger individualistic orientations. These indicators are chosen based on their qualitative assessments regarding cultural aspects. A correlation analysis of these aims to create a more comprehensive understanding of how cultural differences relate to tipping phenomena.

Subsequently, the hypotheses are as follows:

H1 (Embeddedness): Societies with greater embeddedness will show larger year-over-year increases in the average tipping rate. This indicates a positive correlation between embeddedness and tip inflation. H2 (Affective Autonomy): Societies emphasising affective autonomy are expected to have smaller annual increases in the tipping rate, suggesting a negative correlation between affective autonomy and tip inflation. H3 (Intellectual Autonomy): Societies that value intellectual autonomy are predicted to experience more moderate tipping inflation, implying a negative relationship between intellectual autonomy and yearly tipping fluctuations. H4 (Cultural Tightness-Looseness): Societies with looser norms, characterised by weaker enforcement, are expected to have lower tipping deviations than tighter societies, indicating a positive link between cultural tightness and tip inflation.

To analyse the sensitivity of the equilibrium tip deviation $x^{*}$ to changes in the norm-shift parameter $\lambda$, the equilibrium condition is implicitly differentiated with respect to both $x^{*}$ and $\lambda$:

$F_{x^{*}}=2{\beta }_i{\text{e}}^{-{\beta }_i{\left(x^{*}-\lambda \right)}^2}\left[2{\beta }_i{\left(\lambda -x^{*}\right)}^2-1\right]$

$F_{\lambda }=2{\beta }_i{\text{e}}^{-{\beta }_i{\left(x^{*}-\lambda \right)}^2}\left[1-2{\beta }_i{\left(\lambda -x^{*}\right)}^2\right]$, with the symmetry $F_{\lambda }=-F_{x^{*}}$

Consequently, implicit differentiation yields:

$\frac{\text{d}\lambda }{\text{d}{x}^{*}}=-\frac{F_{x^{*}}}{F_{\lambda }}=1$

By application of the chain rule, and $\frac{\text{d}{x}^{*}}{\text{d}{t}_{k-1}^{*}}=-1$,

$\frac{\text{d}\lambda }{\text{d}\left(\text{Cultural Index}\right)}=-\frac{\text{d}{t}_{k-1}^{*}}{\text{d}\left(\text{Cultural Index}\right)}$

This establishes a direct and theoretically grounded relationship between the rate of change in the norm-shift parameter and the evolution of tipping norms as influenced by underlying cultural factors.

Interpretation of the relationship between $\lambda$ and the Cultural Index:

A similar procedure is used to investigate the impact of the conformity parameter $\beta$ on equilibrium tip deviation. Implicit differentiation with respect to $\beta$ and $x^{*}$ yields:

$F_{\beta }\left(\beta ,x^{*}\right)=2\left({\lambda }_i-x^{*}\right){\text{e}}^{-\beta {\left(x^{*}-{\lambda }_i\right)}^2}\left[1-\beta {\left({\lambda }_i-x^{*}\right)}^2\right]=0$

$F_{x*}\left(\beta ,x^{*}\right)=2\beta {\text{e}}^{-\beta {\left(x^{*}-{\lambda }_i\right)}^2}\left[2\beta {\left({\lambda }_i-x^{*}\right)}^2-1\right]=0$

Comparative static expression:

$\frac{\text{d}\beta }{\text{d}{x}^{*}}=-\frac{F_{x*}}{F_{\beta }}=\frac{\beta \left[2\beta {\left({\lambda }_i-x^{*}\right)}^2-1\right]}{\left({\lambda }_i-x^{*}\right)\left[1-\beta {\left({\lambda }_i-x^{*}\right)}^2\right]}$

For small deviations where $\lambda -x^{*}\approx 0$, this simplifies to a negative value, indicating that increases in norm-conformity pressure ( $\beta$) systematically reduce the equilibrium tip deviation. This approximation is valid throughout the empirically relevant range, given the construction of the equilibrium.

By application of the chain rule, $\frac{\text{d}\beta }{\text{d}{t}_{k-1}^{*}}=\frac{\text{d}\beta }{\text{d}{x}^{*}}\cdot \frac{\text{d}{x}^{*}}{\text{d}{t}_{k-1}^{*}}=\text{positive}$,

$\text{sign of}\frac{\text{d}\beta }{\text{d}\left(\text{Cultural Index}\right)}=\text{sign of}\frac{\text{d}{t}_{k-1}^{*}}{\text{d}\left(\text{Cultural Index}\right)}$

Since $\frac{\text{d}\beta }{\text{d}{t}_{k-1}^{*}}$ is signed by the curvature of $f$ under this model, a culture that raises social norms $t_{k-1}^{*}$ can alter the steepness $\beta$. Combined with $\frac{\text{d}{t}_{k-1}^{*}}{\text{d}\left(\text{Cultural Index}\right)}$, the net effect of culture on the psychological sensitivity to norm deviation $\frac{\text{d}\beta }{\text{d}\left(\text{Cultural Index}\right)}$ can thus be obtained.

Interpretation of the relationship between $\beta$ and the Cultural Index:

$\frac{\text{d}{x}^{*}}{\text{d}\left(\text{Cultural Index}\right)}=\frac{\text{d}{x}^{*}}{t_{k-1}^{*}}\cdot \frac{\text{d}{t}_{k-1}^{*}}{\text{d}\left(\text{Cultural Index}\right)}=-\frac{\text{d}{t}_{k-1}^{*}}{\text{d}\left(\text{Cultural Index}\right)}$

Interpretation of the relationship between $x^{*}$ and the Cultural Index:

Table 1 shows that from all the selected cultural indices, the correlation between $t_{k-1}^{*}$ and CTL_C is the greatest, followed by EMB.

Figure 2 shows a negative relationship between the EMB index and the Restaurant Tip. The results estimate that the derivative of $\lambda$ with respect to Embeddedness is positive ( $\frac{\text{d}\lambda }{\text{d}\left(\text{EMB}\right)}>0$) and the derivative of $\beta$ with respect to Embeddedness is negative ( $\frac{\text{d}\beta }{\text{d}\left(\text{EMB}\right)}<0$. Across the dataset, higher values of EMB are associated with higher values of $\lambda$ and lower values of $\beta$ in the tipping utility model. Within the model framework, an increase in $\lambda$ represents a greater horizontal shift of the optimal tipping point from the individual’s intrinsic norm toward the prevailing social norm, while a decrease in $\beta$ reflects a reduced steepness of the psychological utility function near the optimum. The analysis also finds a positive correlation between EMB and the tip deviation ( $x^{*}$), such that higher EMB is associated with larger increases in the norm over time ( $t_k^{*}-t_{k-1}^{*}$), suggesting a greater rate of tip inflation (Hypothesis H1 is largely supported).

Figure 3 shows a positive relationship between the AUT_AFF index and the Restaurant Tip. The estimated derivative of $\lambda$ with respect to AUT_AFF is negative ( $\frac{\text{d}\lambda }{\text{d}\left(\text{AUT\_AFF}\right)}<0$) and the derivative of β with respect to AUT_AFF is positive ( $\frac{\text{d}\beta }{\text{d}\left(\text{AUT\_AFF}\right)}<0$). Higher AUT_AFF values are observed alongside lower $\lambda$ and higher $\beta$ values in the model estimates. The data further show a negative correlation between AUT_AFF and the tip deviation ( $x^{*}$), indicating that greater affective autonomy is associated with smaller increases in tip over time (Hypothesis H2 is mildly supported).

Figure 4 shows a positive relationship between the AUT_INT index and the Restaurant Tip. The analysis likewise shows that $\frac{\text{d}\lambda }{\text{d}\left(\text{AUT\_INT}\right)}<0$ and $\frac{\text{d}\beta }{\text{d}\left(\text{AUT\_INT}\right)}>0$. Increases in the Intellectual Autonomy, AUT_INT, are associated with lower $\lambda$ and higher $\beta$, and the correlation between AUT_INT and $x^{*}$ is negative. This pattern corresponds to a less pronounced increase in tipping over time in societies with higher intellectual autonomy (Hypothesis H3 is mildly supported).

Figure 5 shows a positive relationship between the CTL_C index and the Restaurant Tip. With respect to the Cultural Tightness-Looseness Combination Index (CTL_C), results show $\frac{\text{d}\lambda }{\text{d}\left(\text{CTL\_C}\right)}<0$ and $\frac{\text{d}\beta }{\text{d}\left(\text{CTL\_C}\right)}>0$. Greater values of CTL_C are associated with lower $\lambda$ and higher $\beta$. The analysis reveals a negative correlation between CTL_C and the tip deviation ( $x^{*}$), such that higher cultural looseness is associated with lower tip inflation across periods (Hypothesis H4 is largely rejected).

Amongst the four indices, Embeddedness (EMB) and Cultural Tightness (CTL_C) hold greater explanatory power (Higher R²) for $\lambda$, $\beta$, and $x^{*}$. While correlations do not necessarily imply causation, this may highlight their greater involvement in shaping the evolution of tipping norms when supported by qualitative research. In societies marked by both high Embeddedness and strong cultural tightness (low CTL_C), empirical evidence indicates both an increased displacement of the optimal tipping point from norm (high $\lambda$) and a higher rate of tip-inflation over time. These findings suggest that such societies foster collective behavioral mechanisms in which repeated acts of exceeding the prevailing norm incrementally raise the societal standard for tipping, generating a self-reinforcing cycle of norm escalation. This is consistent with theoretical predictions that, in conformity-driven environments, individuals accrue additional utility by tipping above the established norm, thereby shifting the reference point for the broader population, a claim primarily raised in the Azar theory and Proto theory ( Azar, 2004b ). The present analysis explicitly conditions this process on the presence of a conformity-driven environment, which was not specified in the previous theories.

Moreover, the observed reduction in sensitivity to norm deviation (lower $\beta$) also reflects a counterintuitive cultural dynamic, interestingly. This contradicts the common perception that a society with low tolerance for deviation is more likely to impose greater psychological cost on anyone who strays from the established tipping norm. Explaining this phenomenon may require further analysis of the factors driving each cultural index. In embedded cultures, individuals often perceive themselves as part of a close-knit collective ( Brewer & Gardner, 1996 ), so a shared sense of belonging cushions minor departures from the norm, such that small under-tips are met with communal understanding rather than harsh judgment. Cultural Looseness is highly positively correlated with the violation of legal rules and laws ( Uz, 2015 ). Thus, likewise, in tight societies, strict enforcement of formal rules (for example, mandatory service charges) may instead paradoxically lead to greater tolerance for minor deviations from informal tipping norms, if the correlation works reversibly and implies that the focus shifts to compliance with codified policy rather than personal discretion ( Jackson, Gelfand, & De Merit, 2019 ). Under these conditions, it would thus be logical for the psychological-utility curve around the norm to be effectively flattened, not because people are more forgiving, but because minor nonconformity no longer registers as a breach of individual responsibility and therefore generates little additional “pain”. Together, these qualitative reviews try to explain the correlation between the most pronounced tip-inflation effects observed in this set of cross-cultural data, substantiating the critical role of EMB and CTL_C as potential structural determinants of tipping behaviour and its temporal evolution.

This research builds upon the literature of the socio-economics of tipping by empirically validating and extending the recursive, norm-based theoretical framework first proposed by Azar (2004a, 2005) . By explicitly modelling the dynamic adjustment of tipping norms in response to both individual psychological utility and macro-level cultural indicators, the study has illustrated the critical role of culture in shaping the trajectory of tip inflation. The data supported 3 out of 4 hypotheses, and provided interesting observations, especially the correlation between tipping deviations ( $x^{\ast }$) and Embeddedness (EMB), as well as the Combination Cultural Tightness-Looseness (CTL_C). While conventional intuition might predict that higher embeddedness and cultural tightness would produce greater social pressure to tip at or above the norm, thereby steepening the psychological utility curve (higher $\beta$), the results reveal a more nuanced dynamic. Instead, the empirical evidence and mathematical model jointly suggest that the influence of social tolerance and communal cohesion in highly embedded and tight cultures can, in certain respects, attenuate the psychological disutility associated with under-tipping (lower $\beta$). This implies that, even as conformity-driven environments drive up tipping norms through positive displacement (higher $\lambda$), the communal fabric may mitigate the “pain” of falling short, allowing both tip inflation and a degree of leniency toward norm deviation to coexist. This insight provides a new interpretive lens that bridges microeconomic behaviour, macro-level culture, and the empirical trajectory of social norms, offering a richer understanding than previously afforded by static or one-dimensional models.

The prevailing social norm at time k, denoted n(s) in the original Azar’s Customer Utility function, is proxied by the average tip given in the previous period in this model. This formulation assumes that consumers update their perception of the social norm based on observed tipping behaviour in the immediate past. While supported in U.S. contexts, its applicability across different cultural settings may be limited, given that norm internalisation and feedback mechanisms vary widely. Future work could further enhance the model’s cross-cultural validity by incorporating independent survey-based measures of tipping norms and their evolution in other national environments. This would provide stronger empirical foundations for analysing how tipping expectations evolve within specific national contexts. Overall, these findings offer practical insights for businesses and policymakers in high-embeddedness or tight-norm cultures, where tipping expectations may escalate more sharply. Understanding the social and cultural influences on tipping behaviour can enable governments to more effectively evaluate whether tipping remains an appropriate form of compensation within their societies. In contexts where tipping norms are escalating due to cultural conformity pressures, alternative strategies, such as implementing standardised service charges or mandating greater transparency in compensation structures, may help mitigate wage inequality and reduce reliance on informal tipping practices.

Several promising avenues for interesting future research may arise from this study. First, the impact of political cycles, such as the four-year U.S. presidential election cycle, on national culture and social behaviour presents a fertile ground for exploration. It remains an open question whether such macro-political fluctuations may induce observable changes in tipping behaviour and norm adaptation, potentially through shifts in national mood, uncertainty, or societal values.

Second, the potential for government intervention to modulate tipping inflation through cultural policy or social norm campaigns warrants rigorous empirical examination. Targeted efforts to foster inclusivity, reduce status anxiety, or reshape perceptions of service could have significant downstream effects on both the level and distribution of tipping in society.

Third, the rapid integration of automation and artificial intelligence into hospitality and service industries presents a structural challenge to the traditional cultural drivers of tipping. As human interaction is supplanted by algorithmic service provision, the salience of cultural factors in tipping decisions may diminish, potentially leading to new equilibria where economic rationality and technological design dominate over social norm adherence.

Finally, future work could broaden the analytical framework developed here to examine other settings where economic outcomes are closely entwined with dynamic social norms, including charitable giving, peer-to-peer transactions, and digital economies. Longitudinal studies, experimental interventions, and international panel data analysis would all serve to deepen our understanding of how culture, psychology, and technology co-evolve to shape prosocial economic behaviour over time.

In summary, this research contributes to a robust platform for analysing the complex interplay between individual psychology, cultural context, and economic behaviour. It provides a theoretical explanation for tipping norm inflation, grounded in individual psychology and social conformity, and connects that explanation to measurable cultural traits. These findings are also noteworthy in that they extend beyond tipping itself, revealing that small changes in cultural norms, as captured by different indices, can lead to significantly different behavioural outcomes.

*Represents a general outlier for cultural indicators against the Restaurant Tip; **Represents an outlier for AUT_AFF against the Restaurant Tip (Data is consolidated from various reliable sources).