arXiv subjects

Tushar Shankar Walunj

Publications and source records attributed to Tushar Shankar Walunj.

5 recordsLinked to original sources

arXiv2025

Equilibrium Cycle: A "Dynamic" Equilibrium

In this paper, we introduce a novel equilibrium concept, called the equilibrium cycle, which seeks to capture the outcome of oscillatory game dynamics. Unlike the (pure) Nash equilibrium, which defines a fixed point of mutual best responses, an equilibrium cycle is a set-valued solution concept that can be demonstrated even in games where best responses do not exist (for example, in discontinuous games). The equilibrium cycle identifies a Cartesian product set of action profiles that satisfies three important properties: stability against external deviations, instability against internal deviations, and minimality. This set-valued equilibrium concept generalizes the classical notion of the minimal curb set to discontinuous games. In finite games, the equilibrium cycle is related to strongly connected sink components of the best response graph.

econ.TH↗

arXiv2025

Strategic Pricing and Ranking in Recommendation Systems with Seller Competition

We study a recommendation system where sellers compete for visibility by strategically offering commissions to a platform that optimally curates a ranked menu of items and their respective prices for each customer. Customers interact sequentially with the menu following a cascade click model, and their purchase decisions are influenced by price sensitivity and positions of various items in the menu. We model the seller-platform interaction as a Stackelberg game with sellers as leaders and consider two different games depending on whether the prices are set by the platform or prefixed by the sellers. It is complicated to find the optimal policy of the platform in complete generality; hence, we solve the problem in an important asymptotic regime. The core contribution of this paper lies in characterizing the equilibrium structure of the limit game. We show that when sellers are of different strengths, the standard Nash equilibrium does not exist due to discontinuities in utilities. We instead establish the existence of a novel equilibrium solution, namely `$μ$-connected equilibrium cycle' ($μ$-EC), which captures oscillatory strategic responses at the equilibrium. Unlike the (pure) Nash equilibrium, which defines a fixed point of mutual best responses, this is a set-valued solution concept of connected components. This novel equilibrium concept identifies a Cartesian product set of connected action profiles in the continuous action space that satisfies four important properties: stability against external deviations, no external chains, instability against internal deviations, and minimality. We extend a recently introduced solution concept equilibrium cycle to include stability against measure-zero violations and, by avoiding topological difficulties to propose $μ$-EC.

econ.TH↗

arXiv2024

On the interplay between pricing, competition and QoS in ride-hailing

We analyse a non-cooperative game between two competing ride-hailing platforms, each of which is modeled as a two-sided queueing system, where drivers (with a limited level of patience) are assumed to arrive according to a Poisson process at a fixed rate, while the arrival process of (price-sensitive) passengers is split across the two platforms based on Quality of Service (QoS) considerations. As a benchmark, we also consider a monopolistic scenario, where each platform gets half the market share irrespective of its pricing strategy. The key novelty of our formulation is that the total market share is fixed across the platforms. The game thus captures the competition between the platforms over market share, with pricing being the lever used by each platform to influence its share of the market. The market share split is modeled via two different QoS metrics: (i) probability that an arriving passenger obtains a ride, and (ii) the average passenger pick-up time. The platform aims to maximize the rate of revenue generated from matching drivers and passengers. In each of the above settings, we analyse the equilibria associated with the game in certain limiting regimes. We also show that these equilibria remain relevant in the more practically meaningful 'pre-limit.' Interestingly, we show that for a certain range of system parameters, no pure Nash equilibrium exists. Instead, we demonstrate a novel solution concept called an \textit{equilibrium cycle}, which has interesting dynamic connotations. Our results highlight the interplay between competition, passenger-side price sensitivity, and passenger/driver arrival rates.

math.OC↗

arXiv2024

Partition-form Cooperative Games in Two-Echelon Supply Chains

Competition and cooperation are inherent features of any multi-echelon supply chain. The interactions among the agents across the same echelon and that across various echelons influence the percolation of market demand across echelons. The agents may want to collaborate with others in pursuit of attracting higher demand and thereby improving their own revenue. We consider one supplier (at a higher echelon) and two manufacturers (at a lower echelon and facing the customers) and study the collaborations that are `stable'; the main differentiator from the existing studies in supply chain literature is the consideration of the following crucial aspect -- the revenue of any collaborative unit also depends upon the way the opponents collaborate. Such competitive scenarios can be modeled using what is known as partition form games. Our study reveals that the grand coalition is not stable when the product is essential and the customers buy it from any of the manufacturers without a preference. The supplier prefers to collaborate with only one manufacturer, the one stronger in terms of market power; further, such collaboration is stable only when the stronger manufacturer is significantly stronger. Interestingly, no stable collaborative arrangements exist when the two manufacturers are nearly equal in market power.

econ.TH↗

arXiv2022

Pricing, competition and market segmentation in ride hailing

We analyse a non-cooperative strategic game among two ride-hailing platforms, each of which is modeled as a two-sided queueing system, where drivers (with a certain patience level) are assumed to arrive according to a Poisson process at a fixed rate, while the arrival process of passengers is split across the two providers based on QoS considerations. We also consider two monopolistic scenarios: (i) each platform has half the market share, and (ii) the platforms merge into a single entity, serving the entire passenger base using their combined driver resources. The key novelty of our formulation is that the total market share is fixed across the platforms. The game thus captures the competition among the platforms over market share, which is modeled using two different Quality of Service (QoS) metrics: (i) probability of driver availability, and (ii) probability that an arriving passenger takes a ride. The objective of the platforms is to maximize the profit generated from matching drivers and passengers. In each of the above settings, we analyse the equilibria associated with the game. Interestingly, under the second QoS metric, we show that for a certain range of parameters, no Nash equilibrium exists. Instead, we demonstrate a new solution concept called an equilibrium cycle. Our results highlight the interplay between competition, cooperation, passenger-side price sensitivity, and passenger/driver arrival rates.

math.OC↗