The Shapley value for airport and irrigation games

In this paper cost sharing problems are considered. We focus on problems given by rooted trees, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, called irrigation games. A formal notion of irrigation games is introduced, and the characterization of the class of these games is provided. The well-known class of airport games Littlechild and Thompson (1977) is a subclass of irrigation games. The Shapley value Shapley (1953) is probably the most popular solution concept for transferable utility cooperative games. Dubey (1982) and Moulin and Shenker (1992) show respectively, that Shapley's Shapley (1953) and Young (1985)'s axiomatizations of the Shapley value are valid on the class of airport games. In this paper we show that Dubey (1982)'s and Moulin and Shenker (1992)'s results can be proved by applying Shapley (1953)'s and Young (1985)'s proofs, that is those results are direct consequences of Shapley (1953)'s and Young (1985)'s results. Furthermore, we extend Dubey (1982)'s and Moulin and Shenker (1992)'s results to the class of irrigation games, that is we provide two characterizations of the Shapley value for cost sharing problems given by rooted trees. We also note that for irrigation games the Shapley value is always stable, that is it is always in the core Gillies (1959).

Climate change impacts on migration and labour market

Floods, droughts and monsoons have always disturbed human settlements, but there are more settlements now and more people in the world. Therefore, if a natural disaster happens, more will suffer than ever before. Moreover, climate in the past several decades has been greatly degraded by anthropogenic activity. In some cases, the chain of causality of human influence on the climate is direct and unambiguous (e.g. the effects of irrigation on local humidity), though there are instances where it is less clear. Presently, the scientific consensus (IPCC, 2007) on climate change is that human activity is very likely the cause for the rapid increase of global average temperatures, more generally known as global warming.