No abstract

In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric N-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other individuals in the group play a given strategy. As a consequence, the gain function determining the gradient of selection can be a polynomial of degree N − 1. In order to deal with the intricacy of the resulting evolutionary dynamics, we make use of the theory of polynomials in Bernstein form. This theory implies a tight link between the sign pattern of the gains from switching on the one hand and the number and stability of the rest points of the replicator dynamics on the other hand. While this relationship is a general one, it is most informative if gains from switching have at most two sign changes, as is the case for most multi-player matrix games considered in the literature. We demonstrate that previous results for * Correspondence to: Research Group for Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Str. 2, 24306 Plön, Germany.Email addresses: pena@evolbio.mpg.de (Jorge Peña), laurent.lehmann@unil.ch (Laurent Lehmann), georg.noeldeke@unibas.ch (Georg Nöldeke) Preprint submitted to Journal of Theoretical BiologyDecember 26, 2013 public goods games are easily recovered and extended using this observation.Further examples illustrate how focusing on the sign pattern of the gains from switching obviates the need for a more involved analysis.

We present new break-up and coherent data for h meson photoproduction on the deuteron, using a deuterium target and tagged bremsstrahlung photons up to 1 GeV. The differential cross sections for the coherent process were measured from threshold to 800 MeV. They are much smaller than those previously reported. The break-up channel provides a direct measurement of the neutron to proton differential cross section ratios. At the S 11 ͑1535͒ resonance peak, s n ͞s p 0.68 6 0.06 leading to an isoscalar to isovector amplitude ratio of A s ͞A y 0.096 6 0.02. [S0031-9007 (97)03324-3]

Contingent ownership structures are prevalent in joint ventures. We offer an explanation based on the investment incentives provided by such an arrangement. We consider a holdup problem in which two parties make relationship-specific investments sequentially to generate a joint surplus in the future. In our model, the following ownership structure implements first-best investments: one party owns the firm initially, while the other party has the option to buy the firm at a set price at a later date. This result is robust to the possibility of renegotiation and uncertainty.

Many models proposed to study the evolution of collective action rely on a formalism that represents social interactions as n-player games between individuals adopting discrete actions such as cooperate and defect. Despite the importance of spatial structure in biological collective action, the analysis of n-player games games in spatially structured populations has so far proved elusive.We address this problem by considering mixed strategies and by integrating discrete-action n-player games into the direct fitness approach of social evolution theory. This allows to conveniently identify convergence stable strategies and to capture the effect of population structure by a single structure coefficient, namely, the pairwise (scaled) relatedness among interacting individuals. As an application, we use our mathematical framework to investigate collective action problems associated with the provision of three different kinds of collective goods, paradigmatic of a vast array of helping traits in nature: "public goods" (both providers and shirkers can use the good, e.g., alarm calls), "club goods" (only providers can use the good, e.g., participation in collective hunting), and "charity goods" (only shirkers can use the good, e.g., altruistic sacrifice). We show that relatedness promotes the evolution of collective action in different ways depending on the kind of collective good and its economies of scale. Our findings highlight the importance of explicitly accounting for relatedness, the kind of collective good, and the economies of scale in theoretical and empirical studies of the evolution of collective action.