My primary research interests are centered around the following two broad themes:

**Cooperative game theory** — In this, I mostly focus on developing methodologies to analyze cooperative games under *group* *externalities* and *risky payoff situations*.

**Operations management** — In this, my focus is on applying game-theoretic and optimization techniques to solve operations management problems. This research can be put under the following sub-themes:

**Inventory management**— shelf-stocking policy, inventory games**Sharing economy**— smart mobility such as*ride-sharing*and*multi-modal transportation***Internet economics**— supply chain structure on the Internet, interactions among Internet service providers and content providers

**1. COOPERATIVE GAME THEORY**

When a group of self-interested players plan to take up a joint action by cooperating with each other, a fundamental problem that arises is to agree upon how to allocate the prospective gain from the cooperation among the group members in a way that satisfies everyone involved. Players break away from the group if they are not satisfied with the allocation. In this research, we are interested in providing solutions to this problem under situations when the prospective gain from cooperation: (i) is *risky* because the participating players are uncertain or ignorant about whether every group member is capable of performing the action or will indeed take the action that benefits the group; and (ii) has *externalities* because the group can also benefit or lose from activities of other players that are not in the group.

**(i) Cooperative games under externalities**

The existing solution concepts for this class of cooperative games can be empty. Using the *partition function form* representation, we propose a new solution concept called *equivalence nucleolus*, which is shown to be unique and always non-empty. To develop this solution concept, we first define the bargaining power of a player to capture its influence over sharing a pie. Next, we define an egalitarian rule for division of payoffs, called *equality of satisfaction values*. We prove that the division rule is an equivalence relation. The existence result is derived using the fundamental theorem of equivalence relation.

**Reference***: *Rajeev R Tripathi, R K Amit, (2016). Equivalence nucleolus for coalitional games with externalities. Operations Research Letters. 44(2), 219-224.

**(ii) Cooperative games under risk and externalities**

In the literature, externalities and stochasticity are studied independently. However, in many real situations, like pre-electoral coalition formation, both co-exist. As there is virtually no discussion on such a setting in the existing literature on game theory to the best of our knowledge, we first propose a theoretical framework to model cooperative games under such a setting. To represent the cooperative games with externalities under stochastic payoffs, we use partition function but the function is defined to be a random variable rather than deterministically known. We assume that the distribution of payoff to a coalition in more refined partition first-order stochastically dominates the distribution of payoff to the same coalition in a less refined partition. In order to use the concept of stochastic dominance, we define a class of games where stochastic ordering is always a strict order. We introduce a notion of stability and propose a new solution concept, called *foresighted nucleolus*. We show that the foresighted nucleolus always exists, but it may not be unique.

**Reference***: *Rajeev R Tripathi, R K Amit, (2019). Analysis of cooperation under risk and externalities. Production and Operations Management (under review)

**(iii) A cooperative game approach to fair pricing in two-sided markets**

We study the pricing decision of a two-sided platform that deals with heterogeneous sellers. Some of the sellers may be owned or operated by the platform. Unlike traditional two-sided platforms, a platform involving heterogeneous sellers faces both *same-side* and *cross-side* externalities. A traditional two-sided platform’s pricing decision necessitates endogenizing cross-side externalities and adopting a strategy where the more elastic side of the platform often subsidizes the less elastic side. A price-subsidization strategy that is based on demand elasticities of the two sides may lead to a pricing structure that is perceived as biased against one side and favoring the other side. This problem further gets amplified when there is heterogeneity among players on the same side and the pricing decision fails to endogenize the same side externalities. In this research, we convert a two-sided platform’s problem into a cooperative game problem which we call a *two-sided platform game*. We analyze the two-sided platform game using a fairness-based solution concept from cooperative game theory to characterize a fair pricing structure.

**Reference***: *Rajeev R Tripathi (2019). Fair pricing on a platform with heterogeneous sellers. (working)

**2. OPERATIONS MANAGEMENT**

**(i) Shelf-stocking policy in retail inventory management**

We develop an optimal shelf-space stocking policy when demand, in addition to the exogenous uncertainty, is influenced by the amount of inventory displayed (supply) on the shelves. Our model exploits stochastic dominance condition; and, we assume that the distribution of realized demand with higher stocking level stochastically dominates the distribution of realized demand with lower stocking level. We show that the critical fractile with endogenous demand may not exceed the critical fractile of the classical newsvendor model. Our computational results validate the optimality of amount of units stocked on the retail shelves.

**Reference**: R K Amit, Peeyush Mehta, Rajeev R Tripathi, (2015). Optimal shelf-space stocking policy using stochastic dominance under supply-driven demand uncertainty. European Journal of Operational Research, 246(1), 339-342.

**(ii) Newsvendor cooperation under ****asymmetric demand information:**** Bayesian inventory game**

When a group of players in a stochastic inventory game or a newsvendor game pool their resources to build a centralized inventory, it is assumed that the individual demand distributions are common knowledge. However, as the players are competitors, they wish to evaluate the benefit that they are likely to get by joining the inventory pooling game before sharing their demand information. This leads to an asymmetric information (ex-interim) scenario where demand distributions are no longer common knowledge. In this research, we model a newsvendor game with asymmetric demand information using cooperative game theory which is termed as Bayesian inventory game (BIG). In BIG, each player has a finite set of possible demand distribution, thereby yielding a set of possible newsvendor games. Each player has private information of his distribution and Bayesian updated belief over possible demands of other players. As payoff is uncertain, we assume players form contracts specifying payoff allocation for each newsvendor game. We show that BIG has a non-empty core if the cost parameters are identical for players. We use the duality approach and obtain weights over every demand profile possibles within a coalition for all coalitions to dene necessary and sufficient condition for non-emptiness of the BIG core.

**Reference**: Aniruda S, Rajeev R Tripathi, Vipin B, R K Amit (2019). Newsvendor cooperation under asymmetric demand information. (preparing for submission)

**3. INTERNET ECONOMICS**

**(i) Revenue models and capacity decisions in the internet value chain**

Net-neutrality refers to a network design principle which states that regardless of the content type, application, hosting site, network carrying the traffic, end-users viewing, charges paid by end-users and the platforms, all data packets have to be treated equally. However, selectively changing network performance leads to differentiation. The internet service providers (ISPs), are capable of giving such preference to a particular content provider (CP), in terms of delivery and can charge different fee to consumers as well in order to discriminate. In 2012, Comcast (ISP) applying unfair caps to content providers such as Netflix is such an example. The formation of consortiums between an ISP and content service providers has been discussed in the literature. Members in the consortium share costs and investments and this seems to be helpful for the players in the market. In this research, we are interested in studying the dynamics of interactions among ISPs and CPs. Some of the questions that we ask are — In the scenario of competition or cooperation, to which content provider should the ISP allocate more capacity? What could be the ISP caching strategies in net-neutrality scenario? Further, what kind of revenue model should the CPs like Netflix opt for? Should they go for subscription model or advertising-based model or hybrid, in such scenarios of competition or cooperation?

**Reference***: *Sudha Madhavi Dastrala, Rajeev R Tripathi (2019). Revenue models and capacity decisions in the internet value chain. (working)