We propose a model of evolutionary snowdrift game with N -person interactions and study the effects of multi-person interactions on the emergence of cooperation. An exact N -th-order equation for the equilibrium density of cooperators x * is derived for a well-mixed population using the approach of replicator dynamics. The results show that the extent of cooperation drops with increasing cost-to-benefit ratio and the number N of interaction persons in a group, with x * ∼ 1/N for large N . An algorithm for numerical simulations is constructed for the model. The simulation results are in good agreements with theoretical results of the replicator dynamics.

We propose a model of weighted scale-free networks incorporating a stochastic scheme for weight assignments to the links, taking into account both the popularity and fitness of a node. As the network grows, the weights of links are driven either by the connectivity with probability p or by the fitness with probability 1-p. Numerical results show that the total weight exhibits a power-law distribution with an exponent sigma that depends on the probability p. The exponent sigma decreases continuously as p increases. For p=0, the scaling behavior is the same as that of the connectivity distribution. An analytical expression for the total weight is derived so as to explain the features observed in the numerical results. Numerical results are also presented for a generalized model with a fitness-dependent link formation mechanism.

We explore various extensions of Challet and Zhang's Minority Game in an attempt to gain insight into the dynamics underlying financial markets. First we consider a heterogeneous population where individual traders employ differing "time horizons" when making predictions based on historical data. The resulting average winnings per trader is a highly non-linear function of the population's composition. Second, we introduce a threshold confidence level among traders below which they will not trade. This can give rise to large fluctuations in the "volume" of market participants and the resulting market "price".

The effects of networking on the extent of cooperation emerging in a competitive setting are studied. The evolutionary snowdrift game, which represents a realistic alternative to the well-known Prisoner's Dilemma, is studied in the Watts-Strogatz network that spans the regular, small-world, and random networks through random re-wiring. Over a wide range of payoffs, a re-wired network is found to suppress cooperation when compared with a well-mixed or fully connected system. Two extinction payoffs, that characterize the emergence of a homogeneous steady state, are identified. It is found that, unlike in the Prisoner's Dilemma, the standard deviation of the degree distribution is the dominant property in a re-wired network that governs the extinction payoffs.