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*. I am also interested in studying pricing in two-sided markets using cooperative games.

**Operations management** — In this, my focus is on applying game theoretic and optimization techniques to solve operations management problem. 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 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 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. European Journal of Operational Research (under review)

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

Pricing is one of the important strategic decisions in two-sided markets. A key finding of prior research is that the pricing structure necessitates endogenizing network externalities and adopting a pricing strategy where one side of the market often subsidizes the other side. In effect, the prices charged on one side does not usually reflect the costs incurred to serve that side. This gives rise to a popular opinion that many two-sided market platforms often adopt a pricing structure that is biased against one side and favors the other side. A fundamental question arises in such a setting: How much subsidization is fair in two-sided markets? We analyze the question of fair pricing structure in two-sided markets from the point of view of coalitional game theory. We model two-sided markets using coalitional games, and develop pricing models using various fairness-based solution concepts. This study has an implication on how competition policy can be applied in two-sided markets.

**Reference***: *Rajeev R Tripathi (2019). Fair pricing in a two-sided market game. (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**

Industries which face stochastic demand centralize their inventory to take advantage of the reduced cost, due to dampening of variances in the pooled demand (risk pooling). In such inventory pooling situations in a decentralized supply chain, the central question is how to divide this profit among the agents in the coalition such that the coalition is stable. Cooperative game theory (CGT) serves as an appropriate tool for designing such payoff allocation mechanisms. Modelling this scenario is an extension of classical newsvendor models to CGT settings and are termed as stochastic inventory games or newsvendor games. The common assumption made for these games is that the demand distribution of players are common knowledge. But in a decentralized supply chain, the players who are individual units (may be competitors) would wish to evaluate the possibility of getting profit from such an inventory centralization before sharing their demand information and joining the scheme. This evaluation leads to an asymmetric information (ex-interim) scenario where demand distribution of players is no longer a common knowledge. Hence, our work models newsvendor games with asymmetric demand information using CGT which we term as Bayesian Inventory Games (BIG). In BIG, each player has a nite 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 non-empty core if the cost parameters are identical for players. We use 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: Bayesian inventory game. (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)

**4. SHARING ECONOMY**

**(i) A ****benefit-allocation mechanism to improve vehicle occupancy in ridesharing**

Individuals benefit economically by sharing a ride. But they also experience some inconvenience by being a part of a shared ride. The inconvenience is caused due to extra distance one has to travel to pick- up or drop-off another participant and sharing of personal space with strangers. To avoid excess inconvenience, participants prefer ridesharing in smaller groups rather than larger ones. Ridesharing in smaller groups, however, reduces the occupancy levels of the vehicle, in-turn reducing the economic benefit of ridesharing. To address this trade-off between inconvenience and occupancy, we propose a mechanism that shares the economic benefit generated by ridesharing amongst the participants by considering the inconvenience experienced by them. The proposed mechanism ensures participants gain more by joining a large-size ridesharing group than a smaller one. It also ensures that no single participant benefits at the expense of the others. We use cooperative game theory to develop the mechanism. Further, we propose a decision rule to help ridesharing service firms identify potential participants for a shared ride. The benefit-allocation mechanism along with the decision rule can aid ridesharing service firms to achieve high occupancy.

**Reference***: *Srikanth Krishnaprasad, Rajeev R Tripathi (2019). A benefit allocation mechanism to improve vehicle occupancy in ride-sharing. (re-submitting)