This paper gives a formulation of a theory of n‐person cooperative games with side payments in terms of a partition function which is defined on the set of all partitions of the set of players. The results for all games with n ≤ 3 are presented. This development generalizes the von Neumann‐Morgenstern theory of games in characteristic function form.

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Post-starburst galaxies can be identified via the presence of prominent Hydrogen Balmer absorption lines in their spectra. We present a comprehensive study of the origin of strong Balmer lines in a volume-limited sample of 189 galaxies with 0.01 < z < 0.05, log(M /M ) > 9.5 and projected axis ratio b/a > 0.32. We explore their structural properties, environments, emission lines and star formation histories, and compare them to control samples of star-forming and quiescent galaxies, and simulated galaxy mergers. Excluding contaminants, in which the strong Balmer lines are most likely caused by dust-star geometry, we find evidence for three different pathways through the post-starburst phase, with most events occurring in intermediate-density environments: (1) a significant disruptive event, such as a gas-rich major merger, causing a starburst and growth of a spheroidal component, followed by quenching of the star formation (70% of post-starburst galaxies at 9.5 < log(M /M ) < 10.5 and 60% at log(M /M ) > 10.5); (2) at 9.5 < log(M /M ) < 10.5, stochastic star formation in blue-sequence galaxies, causing a weak burst and subsequent return to the blue sequence (30%); (3) at log(M /M ) > 10.5, cyclic evolution of quiescent galaxies which gradually move towards the high-mass end of the red sequence through weak starbursts, possibly as a result of a merger with a smaller gas-rich companion (40%). Our analysis suggests that AGN are 'on' for 50% of the duration of the post-starburst phase, meaning that traditional samples of post-starburst galaxies with strict emission line cuts will be at least 50% incomplete due to the exclusion of narrow-line AGN.

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Feedback from supernovae is often invoked as an important process in limiting star formation, removing gas from galaxies and hence as a determining process in galaxy formation. Here we report on numerical simulations investigating the interaction between supernova explosions and the natal molecular cloud. We also consider the cases with and without previous feedback from the high-mass star in the form of ionising radiation and stellar winds. The supernova is able to find weak points in the cloud and create channels through which it can escape, leaving much of the well shielded cloud largely unaffected. This effect is increased when the channels are pre-existing due to the effects of previous stellar feedback. The expanding supernova deposits its energy in the gas that is in these exposed channels, and hence sweeps up less mass when feedback has already occurred, resulting in faster outflows with less radiative losses. The full impact of the supernova explosion is then able to impact the larger scale of the galaxy in which it abides. We conclude that supernova explosions only have moderate effects on their dense natal environments but that with pre-existing feedback, the energetic effects of the supernova are able to escape and affect the wider scale medium of the galaxy.

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