ICTS

Equilibrium multiplicity throws up the question of which equilibria are plausible. How can we distinguish between them? We look to understanding equilibria as emergent properties of dynamic processes of behavioral change and consider some classic behavioral rules and applications, such as the best response rule and coordination problems.

The hawk–dove game admits two types of equilibria: an asymmetric pure equilibrium, in which players in one population play “hawk” and players in the other population play “dove,” and a symmetric mixed equilibrium, in which hawks are frequently matched against each other. The existing literature shows that when two populations of agents are randomly matched to play the hawk–dove game, then there is convergence to one of the pure equilibria from almost any initial state. By contrast, we show that plausible dynamics, in which agents occasionally revise their actions based on the payoffs obtained in a few trials, often give rise to the opposite result: convergence to one of the interior stationary states.

In the ultimatum minigame, proposers can offer either half the total prize or just $1$. Responders can accept or reject. At the subgame perfect equilibrium, proposers offer $1$ and responders accept. We apply the best experienced payoff (BEP) dynamic to the large population version of this game. The BEP dynamic is generated when players try their strategies a certain number of times and choose the strategy that generates the highest average payoff. We establish conditions under which the subgame perfect equilibrium is stable or unstable. If it is unstable, another stable state can arise where a significant fraction of proposers make high offers.

The behavior of social insects, like ants and termites, is fascinating not only to children but also from the perspective of researchers in several disciplines. In recent years the mechanisms of collective decisions of ants under a variety of situations have attracted the attention of physicists. In this talk I will present a brief overview of the individual and collective decisions of ants (a) during transport of a "large" cargo, (b) in a "traffic" on trails, and (c) while selecting a new site for "migration" of the colony.

Infectious diseases or epidemics spread through human society via social interactions among infected and healthy individuals. In this talk, we explore the coupled evolution of the epidemic and protection adoption behavior of humans.

In the first part of the talk, we focus on the class of susceptible-infected-susceptible (SIS) epidemic model where individuals choose whether to adopt protection or not based on the trade-off between the cost of adopting protection and the risk of infection; the latter depends on the current prevalence of the epidemic and the fraction of individuals who adopt protection in the entire population. We define the coupled epidemic-behavioral dynamics by modeling the evolution of individual protection adoption behavior according to the replicator dynamics. We fully characterize the equilibria and their stability properties. We further analyze the coupled dynamics under timescale separation when individual behavior evolves faster than the epidemic, and characterize the equilibria of the resulting discontinuous hybrid dynamical system. Numerical results illustrate how the coupled dynamics exhibits oscillatory behavior and convergence to sliding mode solutions under suitable parameter regimes.

In the second part of the talk, we discuss a dynamic population game model to capture individual behavior against susceptible-asymptomatic-infected-recovered (SAIR) epidemic model. Each node chooses whether to activate (i.e., interact with others), how many other individuals to interact with, and which zone to move to in a time-scale which is comparable with the epidemic evolution. We define and analyze the notion of equilibrium in this game, and investigate the transient behavior of the epidemic spread in a range of numerical case studies, providing insights on the effects of the agents' degree of future awareness, strategic migration decisions, as well as different levels of lockdown and other interventions.

 In this era of omnipresent social media, social contagions are becoming a growing matter of interest. Our work integrates insights from systematic survey data, the tool of choice for social opinion exploration, with computational models to demonstrate a novel framework for deriving compartmental models from open-ended questions. By analyzing free-form survey responses and qualitative narratives, we systematically map individual opinions and behaviors into discrete compartments that mirror the stages of influence and adoption observed in various peer influenced dynamics, like public health and marketing campaigns. In the vaccine perception domain, respondents’ descriptions of peer interactions and protective behavior are classified into states analogous to susceptible, influenced, and resistant, capturing the dynamics of opinion formation and behavioral change. Similarly, in the referral marketing scenario, open-ended responses reveal latent engagement stages that inform a compartmental structure reflective of awareness, participation, and advocacy. Our quantitative treatment shows that these data-driven compartments can be effectively incorporated into dynamical systems models, giving rise to interesting opinion diffusion patterns. The proposed framework not only bridges qualitative insights with rigorous mathematical modeling but also highlights the broader applicability of compartmental approaches in deciphering complex social processes from open-ended inquiry.