Greys Sošić

In a non-negative profit game that possesses a Population Monotonic Allocation Scheme (PMAS), being a member of a larger coalition implies that your profit cannot decrease. In this paper, we refer to such games as PMAS profit games. As population monotonicity is a nice and desirable property that encourages formation of larger coalitions and implies stability of the grand coalition, we explore if this special feature of PMAS games can help in identifying additional stable coalition structures under different stability concepts in cooperative game---namely, core partitions, the von Neumann--Morgenstern (vNM) stable set, the largest consistent set, and the equilibrium process of coalition formation (EPCF)---and in developing relationships between coalition structures that are stable under these different stability concepts.

We first define two special classes of players for PMAS profit games---extreme and strong players---and use them to develop an algorithm for construction of stable (core) partitions. We also use extreme players to identify absorbing states for equilibrium processes of coalition formation with high level of farsightedness.

We then explore the impact of population monotonicity on the relationship between stable coalition structures under abovementioned stability concepts. While we are able to obtain some results related to stability of the grand coalition and to establish relationships between stable coalition structures under different stability notions that are consistent with the existing body of knowledge, population monotonicity in general does not add enough for strengthening of the existing results. However, we are able to show a couple of more general result that hold for arbitrary cooperative TU profit games. That is, we show that the members of vNM farsighted stable sets are core partitions, and that core partitions are members of a vNM stable sets. Moreover, we show that the members of vNM farsighted stable sets are EPCF-stable partitions.

We study a special class of cooperative games with transferable utility (TU), called m-attribute games. Every player in an m-attribute game is endowed with a vector of attributes that can be combined in an additive fashion; that is, if players form a coalition, the attribute vector of this coalition is obtained by adding the attributes of its members. Another fundamental feature of m-attribute games is that their characteristic function is defined by a continuous attribute function—the value of a coalition depends only on evaluation of on the attribute vector possessed by the coalition, and not on the identity of coalition members. This class of games encompasses many well-known examples, such as queueing games and economic lot-sizing games. We believe that by studying attribute function and its properties, instead of specific examples of games, we are able to develop a common platform for studying different situations and obtain more general results with wider applicability. In this paper, we first show the relationship between nonemptiness of the core and identification of attribute prices that can be used to calculate core allocations. We then derive necessary and sufficient conditions under which every m-attribute game embedded in attribute function has a nonempty core, and a set of necessary and sufficient conditions that should satisfy for the embedded game to be convex. We also develop several sufficient conditions for nonemptiness of the core of m-attribute games, which are easier to check, and show how to find a core allocation when these conditions hold. Finally, we establish natural connections between TU games and m-attribute games.

Is it feasible to build desalination plants for the co-production of salt and freshwater from U.S. seawater that could lead to a restructuring of supply chains for salt imports? As it is predicted that climate change will increase water stress worldwide, an increasing number of countries are using desalination plants to generate freshwater. In most such cases, residual concentrates must be disposed of, and the disposal cost is increasing as countries are becoming more environmentally conscious. Selective salt recovery can help to alleviate this issue, as it reduces the need for concentrate disposal and generates additional revenue.

To gain some insights into the costs and benefits of co-production plants, we have collected data on current desalination practices and salt imports in the U.S., along with the manufacturing costs and energy requirements for co-production plants. We have used this data to build an optimization model to determine an optimal number and location of co-production plants in the U.S. and their potential markets for the sale of co-produced salt. In our analysis, we have considered a different total number of co-production facilities, and for each configuration we evaluated the resulting net water cost and carbon emissions impact. Our results indicate that there exists the potential for building several co-production plants in the U.S. that would be both financially competitive with existing desalination plants and lead to a reduction in carbon emissions. This information might be of use to both governments and businesses when they make decisions about the type of desalination facilities built and the implemented “polluter pays” policies.

A recently emerging concept, Extended Producer Responsibility (EPR), is being adopted by the government in more and more countries and regions. It shifts the burden of proper disposal of end-of-life consumer products from (local) governments to the producers that bring the products to the market. To comply with governments’ EPR-type legislation, producers form coalitions to have their products recycled in a more efficient way. In this paper, we study how two important determinants of recycling costs, fixed recycling costs and material-stream heterogeneity, influence producers’ recycling network (structure of producers’ recycling coalitions). On one hand, large fixed recycling costs make the coalitions typically larger, due to the economies of scale. On the other hand, large coalitions generate typically more heterogeneous material streams, which increase the variable recycling costs due to additional separation and disassembly efforts. This paper discusses two currently existing scenarios: one exists prior to EPR-type legislation (referred to as the Disparate Problem, or DP) and the other is motivated by EPR-type legislation (referred to as the Endogenous Problem, or EP). In DP, the recycling of end-of-life products is not the responsibility of any producer but the government. Therefore, the recycling network is determined to minimize the total recycling cost, which also maximizes the social welfare, while the outputs are determined by producers without concerns about recycling. In EP, producers who compete in a horizontally differentiated primary market may also collaborate at the same time to organize proper disposal of their products. As each producer is only interested in maximizing its own payoff and there may exist conflict of interests, we use the game-theoretical methodology to analyze the endogenous process of coalition-formation. We find structural differences in these two scenarios and conclude by discussing implications for social welfare of imposing tax or subsidy.

Because greenhouse-gas (GHG) emissions from the supply chains of just the 2,500 largest global corporations account for more than 20% of global emissions, rationalizing emissions in supply chains could make an important contribution toward meeting the global CO2 emission-reduction targets agreed upon in the 2015 Paris Climate Agreement. Accordingly, in this paper, we consider supply chains with joint production of GHG emissions, operating under either a carbon-tax regime, wherein a regulator levies a penalty on the emissions generated by the firms in the supply chain, or an internal carbon-pricing scheme. Supply chain leaders, such as Walmart, are assumed to be environmentally motivated to induce their suppliers to abate their emissions. We adopt a cooperative game-theory methodology to derive a footprint-balanced scheme for reapportioning the total carbon emissions amongst the firms in the supply chain. This emission responsibility-allocation scheme, which is the Shapley value of an associated cooperative game, is shown to have several desirable characteristics. In particular, (i) it is transparent and easy to compute; (ii) when the abatement-cost functions of the firms are private information, it incentivizes suppliers to exert pollution-abatement efforts that, among all footprint-balanced allocation schemes, minimize the maximum deviation from the socially optimal pollution level; and (iii) the Shapley value is the unique allocation mechanism satisfying certain contextually desirable properties.