arXiv subjects

Raghupati Vyas

Publications and source records attributed to Raghupati Vyas.

4 recordsLinked to original sources

arXiv2026

Multi-type random game dynamics: limits at discontinuities and cyclic limits

We consider (random) strategic interactions in a large population consisting of a variety of players. A rational player chooses actions that maximise certain utility functions, while a behavioural player chooses actions based on preferences such as avoid-the-crowd or follow-the-majority. We specifically study a turn-by-turn dynamic process in which players choose their actions sequentially and once; the utilities are realised either immediately or at the end of the game. In the literature, such dynamical systems are often analysed using an appropriate approximating ordinary differential equation (ODE). However, the ODEs approximating the dynamics with pure actions are typically discontinuous. We adopt a differential inclusion (DI) based stochastic-approximation framework to derive the limiting analysis. The limits of the dynamics are characterised through the internally chain transitive (ICT) sets. We identify the presence of non-classical zeros as potential limits of the dynamics, a phenomenon not observed in classical settings involving continuous ODEs. These new limits arise precisely at the points of discontinuity of the dynamics. We further provide the conditions under which cyclic outcomes may occur at the limit. Finally, we study a queuing game with differential priority-based services and examine the impact of the proportions of avoid-the-crowd and two types of rational populations on the long-run outcomes of the strategic interactions. We identify potential point limits and establish the possibility of cyclic outcomes for certain parameter configurations.

math.OC↗

arXiv2026

Balancing Morality and Economics: Population Games with Herding and Inertia

The adoption of clean technologies (CTs) plays an important role in reducing carbon dioxide (CO$_2$) emissions. We study CT adoption in a large population of consumers with heterogeneous behavioral tendencies. We model the interaction among the agents as a multi-type mean-field game in which the agents choose between clean and polluting technology based products and may either behave as rationals (trading off price and moral incentives), herding agents (just follow the majority), or lethargic agents exhibiting inertia toward adopting the new technologies. We characterize equilibrium CT adoption levels using the recently introduced notion of $\boldsymbolα$-Rational Nash Equilibrium ($\boldsymbolα$-RNE) and its multi-type extension. We then identify a stable subset using the limits of a stochastic turn-by-turn behavioral dynamics. Our results highlight the role of population composition in determining CT adoption. In particular, widespread adoption requires either a sufficiently small price disadvantage for CTs or the presence of a sufficiently large herding population that can be influenced through social awareness programs. Surprisingly, we could prove that environmental damages do not provide sufficient incentives to increase CT adoption.

math.OC↗

arXiv2026

Games with Rational and Herding Players

Classical game theory is a powerful framework to analyze the strategic interactions among rational players. However, in many real-life scenarios, players choose actions based on their inherent natural tendencies rather than deliberate reasoning. In this paper, we develop an analytical framework to study large population games with an alpha-fraction of rational and (1-alpha)-fraction of herding players. We introduce a new notion of equilibrium called alpha-Rational Nash Equilibrium (in short, alpha-RNE) and discuss its interpretations. Some classical equilibria may disappear, and some new ones may emerge, but only for smaller alpha >0. Interestingly, rational players benefit from the presence of herding and may even achieve utility exceeding the socially optimum. Even more strikingly, in some cases, the herding players also benefit, attaining utility close to the social optimum. We further study the effect of the herding fraction on system performance using measures such as the Price of Anarchy (PoA). In transportation networks, a well-known paradox first studied by Pigou and later by Braess typically arises from rational decision-making: adding an extra link can reduce overall efficiency. Our analysis leads to a different conclusion. When a substantial fraction of users exhibit herding behavior, introducing a new link can increase efficiency, provided herding choices can be suitably influenced. The gains are larger when the herding fraction is higher and/or congestion is lower. By contrast, when herding decisions cannot be influenced, the added link may become detrimental. We also study a bandwidth sharing game in which herding tendencies improve system efficiency. Finally, we discuss the mechanism or influence design in the presence of herding, highlighting both opportunities and risks.

math.OC↗

arXiv2024

Balancing rationality and social influence: Alpha-rational Nash equilibrium in games with herding

The classical game theory models rational players and proposes Nash equilibrium (NE) as the solution. However, real-world scenarios rarely feature rational players; instead, players make inconsistent and irrational decisions. Often, irrational players exhibit herding behaviour by simply following the majority. In this paper, we consider the mean-field game with $α$-fraction of rational players and the rest being herding-irrational players. For such a game, we introduce a novel concept of equilibrium named $α$-Rational NE (in short, $α$-RNE). The $α$-RNEs and their implications are extensively analyzed in the game with two actions. Due to herding-irrational players, new equilibria may arise, and some classical NEs may be deleted. The rational players are not harmed but benefit from the presence of irrational players. Notably, we demonstrate through examples that rational players leverage upon the herding behaviour of irrational players and may attain higher utility (under $α$-RNE) than social optimal utility (in the classical setting). Interestingly, the irrational players may also benefit by not being rational. We observe that irrational players do not lose compared to some classical NEs for participation and bandwidth sharing games. More importantly, in bandwidth sharing game, irrational players receive utility that approaches the social optimal utility. Such examples indicate that it may sometimes be `rational' to be irrational.

cs.GT↗