Invasion of Optimal Social Contracts

Abstract

The stag-hunt game is a prototype for social contracts. Adopting a new and better social contract is usually challenging because the current one is already well established and stable due to sanctions imposed on non-conforming members. Thus, how does a population shift from the current social contract to a better one? In other words, how can a social system leave a locally optimum configuration to achieve a globally optimum state? Here, we investigate the effect of promoting diversity on the evolution of social contracts. We consider group-structured populations where individuals play the stag-hunt game in all groups. We model the diversity incentive as a snowdrift game played in a single focus group where the individual is more prone to adopting a deviant norm. We show that a moderate diversity incentive is sufficient to change the system dynamics, driving the population over the stag-hunt invasion barrier that prevents the global optimum being reached. Thus, an initial fraction of adopters of the new, better norm can drive the system toward the optimum social contract. If the diversity incentive is not too large, the better social contract is the new equilibrium and remains stable even if the incentive is turned off. However, if the incentive is large, the population is trapped in a mixed equilibrium and the better social norm can only be reached if the incentive is turned off after the equilibrium is reached. The results are obtained using Monte Carlo simulations and analytical approximation methods.

A Local Analysis of a Mathematical Pattern for Interactions between the Human Immune System and a Pathogenic Agent

“…Furthermore, a mathematical model for optimal social contracts based on a first-order differential equation was studied in [43], and an approach to the spatial scale effects in epidemic spread models was undertaken in [44]. Moreover, an improved Lotka-Volterra pattern using quantum game theory was investigated in [45], and the classical Lotka-Volterra model was used in order to obtain a global output tracking control by an input-tostate stability analysis of the closed-loop systems [46].…”