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).

The impact of airport shopping environments and dwell time on consumer spending

This article provides new insight into how the ambience and design of shopping environments impact onspending behaviour. Environmental cues in a retail area influence emotional states of by-passers, which in turn influence spending levels. Past research suggested that this effect only applies to shops with moderate arousal level. Also, several studies failed to confirm a relationship between emotions and spending levels. This is surprising, since high arousal environments (e.g., amusement parks, sports stadiums and airports) often feature a wide range of retail outlets. Based on survey data collected in a live airport shopping area, this study finds a relationship between pleasure emotions associated with the retail area and recalled consumer spending, but also the time available for shopping (which in an airport is constrained). Also, visitors’ emotional state was influenced by the ambience (e.g., cleanliness, noise levels, lighting) as well as the design (e.g., easy wayfinding, seating areas) of the retail area. Shopper’s arousal levels did not explain variations in spending level. Implications for researchers and managers are discussed as well as suggestions for future research.