Rajnish Kumar

We introduce the notion of committee-structured games (CSG) in a cooperative framework to analyze situations where committees affect players in generating their coalitional values. We represent the sets of committees by hypergraphs and obtain values as a function of both coalitions and hypergraphs. Based on how committee structures affect value generation, we present two models within the CSG framework. In the first model, the total value is generated by the committee set as a whole, while in the second model, it is obtained by aggregating contributions from all subsets of the set of committees. Accordingly, we define the Shapley value for the first model and the Aggregated Shapley value for the second, providing axiomatic characterizations for both. Further, we propose bidding mechanisms to show that the Shapley value and the Aggregated Shapley value for the class of CSG is a subgame perfect Nash equilibrium (SPNE) of the induced strategic game. Finally, we study an alternative Exchange Economy model by incorporating committees instead of commodities.

We study the class of probabilistic cooperative games and obtain the Expected Shapley value as a solution concept. This is an extension of the classical cooperative games with transferable utilities where we assume that each coalition has an ex-ante probability of being formed. The Expected Shapley value is the expectation of the Shapley values of all the coalitions with respect to their probability distribution and is calculated before the realization of the state. We present five characterizations of our proposed value. Finally, we introduce a bidding mechanism under a non-cooperative setup and show that the Expected Shapley value is a subgame perfect Nash equilibrium under this setup.

In this paper, we introduce the concept of a multilayer network game in a cooperative setup. We consider the notion of simultaneous contribution of individual players or links to two different networks (say, X and Z). Our model nests both classical network games and bi-cooperative network games. The calculation of the utility of players within a specific network in the presence of an additional/alternative network provides a broader spectrum of real-world decision dynamics. The subsequent challenge involves achieving an optimal distribution of payoffs among the players forming the networks. The link-based rule best fits to our model as it delves into the influence of the alternative links in the network. We have designed an extended Position value to address the complexities arising from scenarios where networks overlap. Further, it is shown that the Position value is uniquely characterized by the Efficiency and Balanced Link Contribution axioms.

A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting. We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payoff to the players in a variable network game. We establish two axiomatizations of the Expected Myerson Value, originally formulated and proven on the class of communication situations, based on the well-established component balance, equal bargaining power and balanced contributions properties. Furthermore, we extend an established axiomatization of the Position Value based on the balanced link contribution property to the Expected Position Value.

A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting. We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payoff to the players in a variable network game. We establish two axiomatizations of the Expected Myerson Value, originally formulated and proven on the class of communication situations, based on the well-established component balance, equal bargaining power and balanced contributions properties. Furthermore, we extend an established axiomatization of the Position Value based on the balanced link contribution property to the Expected Position Value.