Game Theory

The Special Issue “Game Theory” of the journal Mathematics provides a collection of papers that represent modern trends in mathematical game theory and its applications. The works address the problem of constructing and implementation of solution concepts based on classical optimality principles in different classes of games. In the case of non-cooperative behavior of players, the Nash equilibrium as a basic optimality principle is considered in both static and dynamic game settings. In the case of cooperative behavior of players, the situation is more complicated. As is seen from presented papers, the direct use of cooperative optimality principles in dynamic and differential games may bring time or subgame inconsistency of a solution which makes the cooperative schemes unsustainable. The notion of time or subgame consistency is crucial to the success of cooperation in a dynamic framework. In the works devoted to dynamic or differential games, this problem is analyzed and the special regularization procedures proposed to achieve time or subgame consistency of cooperative solutions. Among others, special attention in the presented book is paid to the construction of characteristic functions which determine the power of coalitions in games. The book contains many multi-disciplinary works applied to economic and environmental applications in a coherent manner

Nonlinear Interval Parameter Programming Combined with Cooperative Games: a Tool for Addressing Uncertainty in Water Allocation Using Water Diplomacy Framework

This paper shows the utility of a new interval cooperative game theory as an effective water diplomacy tool to resolve competing and conflicting needs of water users from different sectors including agriculture, domestic, industry and environment. Interval parameter programming is applied in combination with cooperative game theoretic concepts such as Shapley values and the Nucleolus to provide mutually beneficial solutions for water allocation problems under uncertainty. The allocation problem consists of two steps: water resources are initially allocated to water users based on the Nash bargaining model and the achieved nonlinear interval parameter model is solved by transforming it into a problem with a deterministic weighted objective function. Water amounts and net benefits are reallocated to achieve efficient water usage through net benefit transfers. The net benefit reallocation is done by the application of different cooperative game theoretical methods. Then, the optimization problem is solved by linear interval programming and by converting it into a problem with two deterministic objective functions. The suggested model is then applied to the Zarrinehrud sub-basin, within Urmia Lake basin in Northwestern Iran. Findings suggest that a reframing of the problem using cooperative strategies within the context of water diplomacy framework - creating flexibility in water allocation using mutual gains approach - provides better outcomes for all competing users of water

Energy Access Scenarios to 2030 for the Power Sector in Sub-Saharan Africa

In order to reach a goal of universal access to modern energy services in Africa by 2030, consideration of various electricity sector pathways is required to help inform policy-makers and investors, and help guide power system design. To that end, and building on existing tools and analysis, we present several ‘high-level’, transparent, and economy-wide scenarios for the sub-Saharan African power sector to 2030. We construct these simple scenarios against the backdrop of historical trends and various interpretations of universal access. They are designed to provide the international community with an indication of the overall scale of the effort required. We find that most existing projections, using typical long-term forecasting methods for power planning, show roughly a threefold increase in installed generation capacity occurring by 2030, but more than a tenfold increase would likely be required to provide for full access – even at relatively modest levels of electricity consumption. This equates to approximately a 13% average annual growth rate, compared to a historical one (in the last two decades) of 1.7%.Energy Access, Power System Planning, Sub-Saharan Africa

Decision support systems for large dam planning and operation in Africa

Decision support systems/ Dams/ Planning/ Operations/ Social impact/ Environmental effects