Search Talks

We present a model of opinion formation game resource limited utility-maximizing agents interacting over a social network. The opinion dynamics is the result of each agent simultaneously revising its opinion by gradient ascent of its utility function. We analyze the evolution of opinions, including boundedness of opinions, convergence to an equilibrium and oscillatory behavior. In some special cases, we comment on the relative dominance of the agents on the steady state opinions. We also establish connections to Nash equilibria and prices of anarchy.

Bio: Pavan Tallapragada is an Associate Prof. in the Robert Bosch Centre for Cyber Physical Systems at the Indian Institute of Science. His research interests are broadly in multi-agent systems and control, including in multi-robot control, multi-agent reinforcement learning and dynamics of social systems.

Animals in the natural world face many choices, and their decisions with respect to food and habitat have major consequences for their fitness. Many factors influence these behavioural decisions, including the ecological and life history context of individuals. I will present our work analysing how females of a cosmopolitan and generalist pest — the red flour beetle Tribolium castaneum — choose where and how to lay eggs. When presented with a choice of an optimal (wheat flour) vs. a non-optimal resource (finger millet), females sometimes allocate more eggs in finger millet. However, we find that this preference depends on their age and density context, and is tuned to optimize distinct fitness components for their offspring, likely mediated via differential nutrient provisioning. During laboratory evolution in wheat-finger millet habitats, the founder female context also determines evolutionary changes in decision-making, though these maternal effects decline over time. Importantly, founder context also influenced population size and the effect of an inadvertent parasitic infection in our experiment. Our work highlights the role of ecological context in driving female decision-making, and demonstrates some wide-ranging effects of founder context on adaptation and trait evolution.

Beginning with the intimate relationship between recursive algorithms and dynamical systems, I shall describe some common dynamics that serve as templates for `stateless' learning. This will be followed by reinforcement learning for dynamic systems, using Markov decision processes as a test case.

In a series of four lectures, I give an introduction to evolutionary game theory and the literature on the evolution of cooperation. This series covers
(i) Evolutionary game theory in infinite and finite populations (Replicator dynamics, Moran process);
(ii) Evolution of cooperation and direct reciprocity
(iii) Social norms and the evolution of indirect reciprocity
(iv) Some current research directions (e.g., direct reciprocity in complex environments).

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.

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 a series of four lectures, I give an introduction to evolutionary game theory and the literature on the evolution of cooperation. This series covers
(i) Evolutionary game theory in infinite and finite populations (Replicator dynamics, Moran process);
(ii) Evolution of cooperation and direct reciprocity
(iii) Social norms and the evolution of indirect reciprocity
(iv) Some current research directions (e.g., direct reciprocity in complex environments).

In a series of four lectures, I give an introduction to evolutionary game theory and the literature on the evolution of cooperation. This series covers
(i) Evolutionary game theory in infinite and finite populations (Replicator dynamics, Moran process);
(ii) Evolution of cooperation and direct reciprocity
(iii) Social norms and the evolution of indirect reciprocity
(iv) Some current research directions (e.g., direct reciprocity in complex environments).

We will consider further applications in game theory and economics, such as bargaining problems, coalitional processes, bounded rationality, matching problems, housing markets. More detail will be provided on useful tricks and techniques used to prove these kinds of results.

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.

Cooperation is vital in both human and animal behavior, allowing individuals to achieve goals that would be difficult alone, such as hunting large, elusive prey. This cooperation has been integral to the evolution of conformity and group norms. However, it is unclear whether individuals conform primarily to acquire valuable information (informational conformity) or to blend in with the group (normative compliance), and under what conditions each form of conformity is exhibited. The degree of conformity may depend on factors like the nature of the activity, an individual’s expertise, and the reward structure. In activities such as foraging, where individuals often exhibit nearly optimal behaviors, one might expect informational conformity, as foragers likely know what is best for them. However, whether individuals conform in this way or are motivated by the desire to conform to group norms remains uncertain. This question forms the basis of our study. While patch foraging has been well studied in both wild and lab settings, most research has focused on individual foraging behavior, overlooking the role of group dynamics. In patchy environments, animals and humans typically behave in ways that align with the Marginal Value Theorem (MVT), but little attention has been given to how group foraging might influence individual behavior. Can suboptimal foragers influence others, leading to less optimal group outcomes? This study explores the social dynamics of group foraging through a novel task, examining whether collective behavior can lead individuals away from optimal foraging, indicating normative conformity. Additionally, our research aims to develop process-level models of learning and decision-making, enhancing our understanding of the mechanisms underlying conformity in group foraging.