This page contains ongoing research projects and working papers on pure and applied game theory, in particular cooperative game theory and its applications.
A Generalised 𝜆-Core Concept for Normal Form Games
by Subhadip Chakrabarti, Robert P Gilles and Lina Mallozzi
August 2024
Abstract:
In this note, we develop a generalisation of the 𝜆-Core solution for non-cooperative games in normal form. We show that this generalised 𝜆-Core is non-empty for the class of separable games that admit a socially optimal Nash equilibrium. Examples are provided that indicate that non-emptiness of the generalised 𝜆-Core cannot be expected for large classes of normal form games.
Available on arXiv as 2408.06086
Gately Values of Cooperative Games
by Robert P. Gilles and Lina Mallozzi
July 2023 – Revised: June 2024
Abstract:
We investigate Gately’s solution concept for cooperative games with transferable utilities. Gately’s conception introduced a bargaining solution that minimises the maximal quantified “propensity to disrupt” the negotiation process of the players over the allocation of the generated collective payoffs. We show that Gately’s solution concept is well-defined for a broad class of games and that it can be interpreted as a compromise solution. We also consider a gener- alisation based on a parameter-based quantification of the propensity to disrupt. We provide an axiomatic characterisation of the original Gately value as well as these generalised Gately values. Furthermore, we investigate the relationship of these Gately values with the Core and the Nucleolus and show that Gately’s solution is in the Core for all regular 3-player games, but is fundamentally different from the Nucleolus. We identify exact conditions under which these Gately values are Core imputations for arbitrary regular cooperative games. Finally, we investigate the relationship of the Gately value with the Shapley value.
Available on arXiv as 2208.10189
An older version is also available on the SSRN QMS Working Paper Series.
Emergent Collaboration in Social Purpose Games
by Robert P. Gilles, Lina Mallozzi and Roberta Messalli
September 2021
Abstract:
We study a class of non-cooperative aggregative games—denoted as social purpose games—in which the payoffs depend separately on a player’s own strategy (individual benefits) and on a function of the strategy profile which is common to all players (social benefits) weighted by an individual benefit parameter. This structure allows for an asymmetric assessment of the social benefit across players.
We show that these games have a potential and we investigate its properties. We investigate the payoff structure and the uniqueness of Nash equilibria and social optima. Furthermore, following the literature on partial cooperation, we investigate the leadership of a single coalition of cooperators while the rest of players act as non-cooperative followers. In particular, we show that social purpose games admit the emergence of a stable coalition of cooperators for the subclass of strict social purpose games. Due to the nature of the partial cooperative leadership equilibrium, stable coalitions of cooperators reflect a limited form of farsightedness in their formation.
As a particular application, we study the tragedy of the commons game. We show that there emerges a single stable coalition of cooperators to curb the over-exploitation of the resource.
Published in Dynamic Games and Applications
Stability of Cartels in Multimarket Cournot Oligopolies
by Subhadip Chakrabarti, Robert P. Gilles and Emiliya Lazarova
January 2018; Revised: August 2020
Abstract:
We investigate the stability of cooperation agreements, such as those agreed by cartels, among firms in a Cournot model of oligopolistic competition embedded in a multimarket contact setting. Our analysis considers a broad array of 64 potential market structural configurations under linear demand and quadratic production costs. We establish that for an appropriate range of parameter values there exists a unique core stable market configuration in which an identical two-firm cartel is sustained in both markets. Our result highlights the significance of multimarket presence for cartel formation in light of the well-known result from the single-market setting where cartels are non-profitable.
Published in The Manchester School.
Partial Cooperation in Strategic Multi-sided Decision Situations
by Subhadip Chakrabarti, Robert P. Gilles and Emiliya Lazarova
May 2018
Abstract:
We consider a normal form game in which there is a single exogenously given coalition of cooperating players that can write a binding agreement on pre-selected actions. The actions representing other dimensions of the strategy space remain under the sovereign, individual control of the players.
We consider a standard extension of the Nash equilibrium concept denoted as a partial cooperative equilibrium as well as an equilibrium concept in which the coalition of cooperators has a leadership position. Existence results are stated and we identify conditions under which the various equilibrium concepts are equivalent.
We apply this framework to existing models of multi-market oligopolies and international pollution abatement. In a multi-market oligopoly typically a merger paradox emerges in the partial cooperative equilibrium the paradox vanishes if the cartel attains a leadership position. For international pollution abatement treaties, cooperation by a sufficiently large group of countries results in a Pareto improvement over the standard tragedy of the commons outcome described by the Nash equilibrium.
Published in Theory & Decision
Local Conventions in Game Play in an Evolving Dual Social Network Framework
by Zhengzheng Pan and Robert P. Gilles
December 2010
Abstract:
People usually perform economic interactions within the social setting of a small group, while they obtain relevant information from a broader source. We capture this feature with a dynamic interaction model based on two separate social networks. Individuals play a coordination game in an interaction network, while updating their strategies using information from a separate influence network through which information is disseminated. In each time period, the interaction and influence networks co-evolve, and the individuals’ strategies are updated through a modified naive learning process. We show that both network structures and players’ strategies always reach a steady state, in which players form fully connected groups and converge to local conventions. We also analyze the influence exerted by a minority group of strongly opinionated players on these outcomes.