#### Document Type

Article

#### Publication Date

9-23-2020

#### 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*, agent

_{i}**i*will choose action in their self-interest. When

*p*>

*p*, agent

_{i}*

*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*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

_{i}**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. (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

This paper later underwent peer review and was published as:

Campbell, M. J., & Smith, V. L. (2020). An elementary humanomics approach to boundedly rational quadratic models.

Physica A, 562, 125309. https://doi.org/10.1016/j.physa.2020.125309