Cooperation in two-person evolutionary games with complex personality profiles.

We propose a theory of evolution of social systems which generalizes the standard proportional fitness rule of the evolutionary game theory. The formalism is applied to describe the dynamics of two-person one-shot population games. In particular it predicts the non-zero level of cooperation in the long run for the Prisoner's Dilemma games, the increase of the fraction of cooperators for general classes of the Snow-Drift game, and stable nonzero cooperation level for coordination games.

A mechanism of dynamical interactions for two-person social dilemmas.

We propose a new mechanism of interactions between game-theoretical agents in which the weights of the connections between interacting individuals are dynamical, payoff-dependent variables. Their evolution depends on the difference between the payoff of the agents from a given type of encounter and their average payoff. The mechanism is studied in the frame of two models: agents distributed on a random graph, and a mean field model. Symmetric and asymmetric connections between the agents are introduced. Long time behavior of both systems is discussed for the Prisoner's Dilemma and the Snow Drift games.

Cooperation in aspiration-based N -person prisoner's dilemmas.

We propose a mathematical model of the N -person prisoner's dilemma game played by a continuous population of agents with a time-dependent aspiration level. The model-a system of differential equations-takes into account the evolution of the aspiration level and of the mean frequency of the cooperators in the population. The dependence of the asymptotic level of cooperation on the individual payoffs and on the transition rates determining the agent's reaction to the received payoffs is studied. In general the existence and the magnitude of the asymptotic level of cooperation depends on N , the payoffs and the transition rates, and decreases with increasing N .

Population dynamics with a stable efficient equilibrium.

We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider symmetric two-player games with two evolutionarily stable strategies: the efficient one in which the population is in a state with a maximal payoff and the risk-dominant one where players are averse to risk. We show that for a large range of parameters of our dynamics, even if the initial conditions in both habitats are in the basin of attraction of the risk-dominant equilibrium (with respect to the standard replication dynamics without migration), in the long run most individuals play the efficient strategy.

Physics, stability, and dynamics of supply networks.

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed "bullwhip effect" in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.