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 pi*, i = 1,2, exists for each agent. When p < pi*, agent i will choose action in their self-interest. When p > pi*, 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 pi* 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.
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/