Keeping up with the Joneses in a World of Misinformation: Probit Excess Payoff Dynamic
By Ceili Kirkaldie
Abstract:
This paper introduces the Probit–Excess-Payoff Dynamic, a novel evolutionary dynamic that integrates excess-payoff revision protocols with probit-style stochastic choice. Agents update their strategies based on noisy perceptions of others’ payoffs, allowing the model to capture the influence of misinformation on strategic behavior. The resulting framework preserves analytical tractability, yielding closed-form switching probabilities while maintaining behavioral realism. By linking probabilistic choice with payoff-based adaptation, this dynamic provides a foundation for studying how imperfect information and social noise shape equilibrium selection and convergence in strategic environments.
Immigration, Fertility, and Cultural Replacement: An r/K Approach to Cultural Persistence
By Ceili Kirkaldie and Jiabin Wu
Abstract:
This paper develops a cultural transmission model inspired by the r/K selection theory in biology. In the model, culturally aware parents strategically adopt different reproductive strategies depending on their relative group sizes. When they are in the minority, they increase fertility to amplify their representation (r-strategy). When they are in the majority, they instead focus on ensuring that their fewer children inherit the culture with higher probability in a supportive environment (K-strategy). The resulting dynamics converge to asymmetric, culturally heterogeneous stable states: the majority emphasizes socialization, while the minority emphasizes fertility expansion. Although the minority has higher fertility, it need not become culturally dominant because assimilation offsets its demographic advantage. The model therefore shows why fertility differentials alone do not mechanically imply cultural replacement.
A Model of Cultural Transmission with Rebellious Children
By Ceili Kirkaldie
Abstract:
This paper explores the interplay between cultural transmission, fertility decisions, and rebellion. Parents seek to pass on their cultural traits, but children may resist these efforts, leading to uncertain transmission outcomes. The model distinguishes between conservative and liberal cultures based on their propensity for rebellion: conservative cultures, characterized by stricter norms, face higher rebellion rates, while liberal cultures, which emphasize individuality, experience lower rates. Two models are presented. The first focuses on socialization effort, showing that conservative parents invest less in cultural transmission due to anticipated rebellion, whereas liberal parents invest more. The second model endogenizes fertility, demonstrating that conservative parents respond to higher rebellion rates by having more children, while liberal parents rely on socialization. The analysis reveals how rebellion influences cultural persistence and population dynamics, helping to explain why conservative cultures, despite facing more resistance from their children, may sustain and even dominate over time.