Prompted by a real-life observation in the UK retail market, a two-player Prisoners’ Dilemma model of an alliance between two firms is adapted to include the response of a rival firm, resulting in a version of a three-player Prisoners’ Dilemma. We use this to analyse the impact on the stability of the alliance of the rival’s competition, either with the alliance or with the individual partners....

The United Nations Framework Convention on Climate Change (unfccc) has the potential to become one the most important instruments to-date for addressing urgent global and local environmental and developmental priorities. It is also one of the most inclusive in that it incorporates important actors from government as well as private sector and civil society. Because of the importance of their fu...

For any simple connected graph $G=(V,E)$, a defensive alliance is a subset $S$ of $V$ satisfying the condition that every vertex $vin S$ has at most one more neighbour in $V-S$ than it has in $S$. The minimum cardinality of any defensive alliance in $G$ is called the alliance number of $G$, denoted $a(G)$. In this paper, we introduce a new type of alliance number called $k$-strong alliance numb...