The Present and Future of Game Theory

A broad nontechnical coverage of many of the developments in game theory since the 1950s is given together with some comments on important open problems and where some of the developments may take place. The nearly 90 references given serve only as a minimal guide to the many thousands of books and articles that have been written. The purpose here is to present a broad brush picture of the many areas of study and application that have come into being. The use of deep techniques flourishes best when it stays in touch with application. There is a vital symbiotic relationship between good theory and practice. The breakneck speed of development of game theory calls for an appreciation of both the many realities of conflict, coordination and cooperation and the abstract investigation of all of them.Game theory, Application and theory, Social sciences, Law, Experimental gaming, conflict, Coordination and cooperation

Cooperation, Stability and Self-Enforcement in International Environmental Agreements: A Conceptual Discussion

In essence, any international environmental agreement (IEA) implies cooperation of a form or another. The paper seeks for logical foundations of this. It first deals with how the need for cooperation derives from the public good aspect of the externalities involved, as well as with where the source of cooperation lies in cooperative game theory. In either case, the quest for efficiency is claimed to be at the root of cooperation. Next, cooperation is considered from the point of view of stability. After recalling the two competing concepts of stability in use in the IEA literature, new insights on the nature of the gamma core in general are given as well as of the Chander-Tulkens solution within the gamma core. Free riding is also evaluated in relation with the alternative forms of stability under scrutiny. Finally, it is asked whether with the often mentioned virtue of “self enforcement” any conceptual gain is achieved, different from what is meant by efficiency and stability. A skeptical answer is offered, as a reply to Barrett’s (2003) attempt at giving the notion a specific content.International Environmental Agreements, Cooperation, Stability, Self-enforcement

An FPTAS for Bargaining Networks with Unequal Bargaining Powers

Bargaining networks model social or economic situations in which agents seek to form the most lucrative partnership with another agent from among several alternatives. There has been a flurry of recent research studying Nash bargaining solutions (also called 'balanced outcomes') in bargaining networks, so that we now know when such solutions exist, and also that they can be computed efficiently, even by market agents behaving in a natural manner. In this work we study a generalization of Nash bargaining, that models the possibility of unequal 'bargaining powers'. This generalization was introduced in [KB+10], where it was shown that the corresponding 'unequal division' (UD) solutions exist if and only if Nash bargaining solutions exist, and also that a certain local dynamics converges to UD solutions when they exist. However, the bound on convergence time obtained for that dynamics was exponential in network size for the unequal division case. This bound is tight, in the sense that there exists instances on which the dynamics of [KB+10] converges only after exponential time. Other approaches, such as the one of Kleinberg and Tardos, do not generalize to the unsymmetrical case. Thus, the question of computational tractability of UD solutions has remained open. In this paper, we provide an FPTAS for the computation of UD solutions, when such solutions exist. On a graph G=(V,E) with weights (i.e. pairwise profit opportunities) uniformly bounded above by 1, our FPTAS finds an \eps-UD solution in time poly(|V|,1/\eps). We also provide a fast local algorithm for finding \eps-UD solution, providing further justification that a market can find such a solution.Comment: 18 pages; Amin Saberi (Ed.): Internet and Network Economics - 6th International Workshop, WINE 2010, Stanford, CA, USA, December 13-17, 2010. Proceedings

Supply chain collaboration

In the past, research in operations management focused on single-firm analysis. Its goal was to provide managers in practice with suitable tools to improve the performance of their firm by calculating optimal inventory quantities, among others. Nowadays, business decisions are dominated by the globalization of markets and increased competition among firms. Further, more and more products reach the customer through supply chains that are composed of independent firms. Following these trends, research in operations management has shifted its focus from single-firm analysis to multi-firm analysis, in particular to improving the efficiency and performance of supply chains under decentralized control. The main characteristics of such chains are that the firms in the chain are independent actors who try to optimize their individual objectives, and that the decisions taken by a firm do also affect the performance of the other parties in the supply chain. These interactions among firms’ decisions ask for alignment and coordination of actions. Therefore, game theory, the study of situations of cooperation or conflict among heterogenous actors, is very well suited to deal with these interactions. This has been recognized by researchers in the field, since there are an ever increasing number of papers that applies tools, methods and models from game theory to supply chain problems

Distributed Game Theoretic Optimization and Management of Multichannel ALOHA Networks

The problem of distributed rate maximization in multi-channel ALOHA networks is considered. First, we study the problem of constrained distributed rate maximization, where user rates are subject to total transmission probability constraints. We propose a best-response algorithm, where each user updates its strategy to increase its rate according to the channel state information and the current channel utilization. We prove the convergence of the algorithm to a Nash equilibrium in both homogeneous and heterogeneous networks using the theory of potential games. The performance of the best-response dynamic is analyzed and compared to a simple transmission scheme, where users transmit over the channel with the highest collision-free utility. Then, we consider the case where users are not restricted by transmission probability constraints. Distributed rate maximization under uncertainty is considered to achieve both efficiency and fairness among users. We propose a distributed scheme where users adjust their transmission probability to maximize their rates according to the current network state, while maintaining the desired load on the channels. We show that our approach plays an important role in achieving the Nash bargaining solution among users. Sequential and parallel algorithms are proposed to achieve the target solution in a distributed manner. The efficiencies of the algorithms are demonstrated through both theoretical and simulation results.Comment: 34 pages, 6 figures, accepted for publication in the IEEE/ACM Transactions on Networking, part of this work was presented at IEEE CAMSAP 201