Rajeev R Tripathi, R K Amit, (2016). Equivalence nucleolus for coalitional games with externalities. Operations Research Letters. 44(2), 219-224.
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.
WORK IN PROGRESS:
Who gets how much: Sharing gain from cooperation under risk and coalitional externalities [preparing for submission]
Abstract: In this paper, we develop a theoretical framework for coalitional games in partition function form with stochastic payoffs, and define a solution concept for stability of this class of games.
Operationalizing the interplays of self-interest, trust and fairness in cooperative sharing [working]
Abstract: We propose a measure of trust. Using the core and the Shapley value to capture the notions of self-interest and fairness respectively, we model the interplays of the three constructs.
Stable allocation of profit in a Bayesian inventory game [preparing for submission]
Abstract: We study a single-echelon inventory sharing system under stochastic inventory game setting in which a set of retailers form coalitions to gain from inventory pooling. The retailers only share their inventories but privately hold their demand information. We introduce a cooperative game with Bayesian approach to model this situation, which we term as Bayesian inventory game (BIG).
Cooperation in service systems with impatient customers [working]
Abstract: We model sharing of resources using cooperative game theory in a service system when customers are impatient. In such a system many independent service providers collaborate through capacity pooling to serve their customers. We also consider that a customer quits or abandons the system whenever his waiting time exceeds his threshold patience for services provided by a service provider. We analyze the profitability of the collaboration and propose a benefit-sharing model.
A pricing framework for ridesharing game [preparing for submission]
Abstract: We propose a game theoretic model for ridesharing game with sequential fairness, and develop an algorithm to balance the trade-off between fairness, stability and optimality.
- Balancing stability and fairness in ridesharing game. 5th PAN IIM World Management Conference (PAN-IIM WMC), Dec 14 – 16, 2017, Lucknow, India
- A cost-sharing mechanism in ridesharing using cooperative game. 11th ISDSI International Conference (ISDSI 2017), Dec 27 – 30, 2017, Tiruchirappalli, India
- Cooperation in service systems with impatient customers. 11th ISDSI International Conference (ISDSI 2017), Dec 27 – 30, 2017, Tiruchirappalli, India
- Application of cooperative game theory to 5G spectrum sharing. 11th ISDSI International Conference (ISDSI 2017), Dec 27 – 30, 2017, Tiruchirappalli, India
- On stability of coalitions when externalities and stochasticity co-exist. 28th International Conference on Game Theory at Stony Brook (ICGT 2017), July 17 – 21, 2017, New York, USA
- Stable allocation of profit in a Bayesian inventory game. East Asian Game Theory Conference 2017 (EAGT 2017), July 31 – Aug 2, 2017, Singapore
- A pricing scheme in ridesharing game. East Asian Game Theory Conference 2017 (EAGT 2017), July 31 – Aug 2, 2017, Singapore
- Stability of partition function games with stochastic payoffs. 4th PAN IIM World Management Conference (PAN-IIM WMC), December 13 – 15, 2016, Ahmedabad, India (best doctoral research paper award)
- Partition function games with stochastic payoffs. 5th World Congress of the Game Theory Society (GAMES 2016), July 24 – 28, 2016, Maastricht, The Netherlands (accepted, did not attend)
- A Cooperative model under risk and externalities. European Meeting on Game Theory (SING11-GTM2015), July 8 – 10, 2015, Saint Petersburg, Russia. [Slides]
- Equivalence nucleolus for coalitional games with externalities. 10th Annual Conference on Economic Growth and Development (10th ACEGD), December 18 – 20, 2014, New Delhi, India. [Slides]
- Equivalence nucleolus – an application to code sharing alliance in airline industry. 18th Annual International Conference of the Society of Operations Management (XVIII SOM), December 12 – 14, 2014, Roorkee, India. [Slides]
- Equivalence nucleolus for partition function games. 14th Consortium of Students in Management Research (COSMAR’14), November 21 – 22, 2014, Bangalore, India.
- Modified bargaining set for coalitional games with externalities. 17th Annual International Conference of the Society of Operations Management (XVII SOM), December 20 – 22, 2013, Chennai, India. [Slides]
- Stability of coalitional games in partition function form. 9th Spain-Italy-Netherlands Meeting on Game Theory (SING9), July 8 – 10, 2013, Vigo, Spain. [Slides]
ABOUT MY DOCTORAL DISSERTATION
Title: Stability of coalitional games with externalities
Abstract: Many real life situations involve non-hierarchical and non-centralized decision making among rational players. Players form coalitions when there is gain from cooperation. In such a situation, a fundamental issue arises—how to divide the coalitional gains so that the coalition remains stable? This issue becomes complex when the payoffs are under externalities and stochasticity. Externality is a situation when the payoff to a coalition is also a function of the overall coalition structure in which the considered coalition is embedded. Stochasticity allows to capture a situation when payoff to a coalition is known only after the coalition is formed and the action is taken. Robust models are required in game theory to analyze such situations. This is where my thesis contributes to the current research state of the art in coalitional game theory. It deals with the coalitional games with externalities under both deterministic and stochastic payoffs. The focus is on developing solution concepts which characterize stability. Solution concepts, like the core and the nucleolus, which characterize stability of games in characteristic function form have been well studied in the literature. Two basic assumptions in the characteristic function form games are—the payoff to a coalition is independent of the coalition structure, and are deterministic. These assumptions have been relaxed in the literature of coalitional games with externalities and stochastic coalitional games. There have been attempts to extend the solution concepts of characteristic function form games to partition function form games. However, the core-class of solution concepts for partition function form games, which capture stability of coalition structures, can be empty.
We use partition function to represent the payoffs in coalitional games with externalities under deterministic payoffs, and propose a new solution concept for the stability, called equivalence nucleolus. One of the significant contributions of this new solution concept is that it guarantees the existence of solution for such games. The solution concept also has another goodness property of uniqueness. 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.
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 coalitional games under such a setting. To represent the coalitional 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. The thesis also describes computational methods for the proposed solution concepts, the equivalence nucleolus and the foresighted nucleolus.