#### Document Type

Article

#### Publication Date

9-12-2020

#### Abstract

We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book *Humanomics* by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward /punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude /resentment changes much more slowly than economic equilibrium (“quenched model”). Another model, in which economic equilibrium occurs over a much slower time than gratitude /resentment evolution (“annealed” model) is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A two-agent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1 - *p*) that represents the empirical frequency of opportunity for agent* i* to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p*_{i} ,* i* = 1; 2, exists for each agent. When p < p*_{i}, agent *i* will choose action in their self-interest. When p > p*_{i}, agent* i* will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p*_{i} are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in *Humanomics* about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of *Humanomics* properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.

#### Recommended Citation

Campbell, M. J., Smith, V. L., & Inoua, S. (2020). An elementary humanomics approach to boundedly rational quadratic models. *ESI Working Paper 20-35*. https://digitalcommons.chapman.edu/esi_working_papers/330/

## Comments

ESI Working Paper 20-35