(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

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 paper, we propose a solution to this problem under a situation 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. To address this issue, we propose a cooperative game model in stochastic partition function form. We propose a solution concept called foresighted nucleolus that characterizes an equitable allocation of payoffs among players. Players do not break away from the group if the allocation lies in the “foresighted nucleolus”. We provide a computational method for determining the allocation. We prove that the foresighted nucleolus always exists, and 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)

2. INVENTORY 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

In operations management, risk pooling using inventory centralization is one of the strategies to reduce demand risk. In this paper, we study an inventory centralization situation when the retailers face the newsvendor game under asymmetric demand information. We model this situation as a coalitional game under Bayesian setting,and name it Bayesian inventory game (BIG). The fundamental question is how to allocate the profits due to inventory sharing among the players in such a way that the grand coalition is stable. The core is one of the solution concepts in coalitional games to compute such an allocation. An extension of the core to Bayesian settings is called the ex-interim core. We characterize the ex-interim core for BIG, and show that it is nonempty if the cost and price parameters are identical and retailers are risk-neutral.

Reference: Aniruda S, Rajeev R Tripathi, Vipin B, R K Amit (2019). Bayesian inventory game (BIG) — Newsvendor cooperation under asymmetric demand information. Annals of Operations Research (under review)

3. PLATFORM ECONOMICS

(i) Fair pricing on a two-sided platform with heterogeneous sellers

A two-sided platform that enables economic transaction between sellers and buyers enters into the sellers’ space with its own product or services offerings. This creates heterogeneity among the sellers on the basis of their competitive position on the platform, and they are categorized into independent sellers and platform-owned sellers. The sellers face positive cross-side externalities from a higher participation level of buyers (and vice versa), and negative same-side externalities from a higher participation level of other sellers on the platform. We model the utility structure of the platform which shows that the utility of the platform declines if more sellers are added beyond a point. Next, we study the issue of fairness in pricing decision of the platform in presence of the independent and the platform-owned sellers. To develop the pricing model, we convert the pricing decision problem of the platform into a cooperative game-based payoff allocation problem. We characterize a fair pricing structure using a solution concept from cooperative games that allocates the payoff in an equitable manner.

Reference: Rajeev R Tripathi (2019). Fair pricing on a two-sided platform with heterogeneous sellers.

4. SHARING ECONOMY

(i) On the interplays of self-interest and trust in sharing economy

An important activity in a sharing economy involves a group of players cooperating with each other to generate a gain through joint actions, and then sharing the gain among themselves according to a commonly agreed payoff allocation mechanism. We examine this activity assuming that the players are self-interested  and may or may not have complete trust on other players involved in cooperation. We present a cooperative game model on the effects of self-interest and trust on cooperation.

Reference: Rajeev R Tripathi (2018). On the interplays of self-interest and trust in sharing economy.

(ii) Pricing in a ridesharing game

Low vehicle occupancy is an issue faced by many ridesharing platforms. One of the ways to address this issue is to design a pricing mechanism that incentivises riders to join large-size pools. In this study, we propose a pricing mechanism and a decision rule to aid the platforms in achieving high capacity utilisation (forming large-size pools), even in the presence of rider inconveniences. 

Reference: Srikanth Krishnaprasad, Rajeev R Tripathi, (2020). A pricing mechanism to improve capacity utilization in ridesharing. Journal of the Operational Research Society. (under review)