Strategy Updates Research Articles

Fixation and escape times in stochastic game learning

Evolutionary dynamics in finite populations is known to fixate eventually in the absence of mutation. We here show that a similar phenomenon can be found in stochastic game dynamical batch learning, and investigate fixation in learning processes in a simple 2×2 game, for two-player games with cyclic interaction, and in the context of the best-shot network game. The analogues of finite populations in evolution are here finite batches of observations between strategy updates. We study when and how such fixation can occur, and present results on the average time-to-fixation from numerical simulations. Simple cases are also amenable to analytical approaches and we provide estimates of the behaviour of so-called escape times as a function of the batch size. The differences and similarities with escape and fixation in evolutionary dynamics are discussed.

Evaluating fitness by integrating the highest payoff within the neighborhood promotes cooperation in social dilemmas

In this paper, we propose a modified fitness evaluation mechanism, which integrates the environmental factors into the focal player’s fitness calculation, to investigate the evolution of cooperative behaviors in the prisoner’s dilemma game. Here, the fitness of a player is computed by combining the individual raw payoff and the highest payoff within the neighborhood, which is regulated by a single parameter termed as trust level η. We show, compared to the traditional version (η=0), that the cooperation level can be highly enhanced for η>0. Meanwhile, we illustrate the dynamical evolution of cooperators on the square lattice, and for different defection parameters b the FC−K curves are utilized to investigate the impact of noise during the strategy updates. Likely, the role of pursuing the highest payoff within the neighborhood also favors the survival of cooperators in the spatial snowdrift game. In addition, the sensibility of knowing the external factors is often not identical for all individuals and we consider the distributed trust level in which η is a distributed parameter, and the results indicate that pursuing the highest payoff in the neighborhood is also inspiring as a consequence of its positive effect on cooperation. The current results are highly instructive for us to further understand the maintenance and emergence of cooperation under the framework of evolutionary game theory.

Conditional imitation might promote cooperation under high temptations to defect

In this paper we introduce a conditional imitation rule into an evolutionary game, in which the imitation probabilities of individuals are determined by a function of payoff difference and two crucial parameters μ and σ. The parameter μ characterizes the most adequate goal for individuals and the parameter σ characterizes the tolerance of individuals. By using the pair approximation method and numerical simulations, we find an anomalous cooperation enhancement in which the cooperation level shows a nonmonotonic variation with the increase of temptation. The parameter μ affects the regime of the payoff parameter which supports the anomalous cooperation enhancement, whereas the parameter σ plays a decisive role on the appearance of the nonmonotonic variation of the cooperation level. Furthermore, to give explicit implications for the parameters μ and σ we present an alterative form of the conditional imitation rule based on the benefit and the cost incurred to individuals during strategy updates. In this way, we also provide a phenomenological interpretation for the nonmonotonic behavior of cooperation with the increase of temptation. The results give a clue that a higher cooperation level could be obtained under adverse environments for cooperation by applying the conditional imitation rule, which is possible to be manipulated in real life. More generally, the results in this work might point out an efficient way to maintain cooperation in the risky environments to cooperators.

Selfishness, fraternity, and other-regarding preference in spatial evolutionary games

Spatial evolutionary games are studied with myopic players whose payoff interest, as a personal character, is tuned from selfishness to other-regarding preference via fraternity. The players are located on a square lattice and collect income from symmetric two-person two-strategy (called cooperation and defection) games with their nearest neighbors. During the elementary steps of evolution a randomly chosen player modifies her strategy in order to maximize stochastically her utility function composed from her own and the co-players' income with weight factors 1−Q and Q. These models are studied within a wide range of payoff parameters using Monte Carlo simulations for noisy strategy updates and by spatial stability analysis in the low noise limit. For fraternal players (Q=1/2) the system evolves into ordered arrangements of strategies in the low noise limit in a way providing optimum payoff for the whole society. Dominance of defectors, representing the “tragedy of the commons”, is found within the regions of prisoner's dilemma and stag hunt game for selfish players (Q=0). Due to the symmetry in the effective utility function the system exhibits similar behavior even for Q=1 that can be interpreted as the “lovers' dilemma”.

Ordering in spatial evolutionary games for pairwise collective strategy updates

Evolutionary 2×2 games are studied with players located on a square lattice. During the evolution the randomly chosen neighboring players try to maximize their collective income by adopting a random strategy pair with a probability dependent on the difference of their summed payoffs between the final and initial states assuming quenched strategies in their neighborhood. In the case of the anticoordination game this system behaves like an antiferromagnetic kinetic Ising model. Within a wide region of social dilemmas this dynamical rule supports the formation of similar spatial arrangement of the cooperators and defectors ensuring the optimum total payoff if the temptation to choose defection exceeds a threshold value dependent on the sucker's payoff. The comparison of the results with those achieved for pairwise imitation and myopic strategy updates has indicated the relevant advantage of pairwise collective strategy update in the maintenance of cooperation.

A game-theoretic analysis of denial of service attacks in wireless random access

In wireless access, transmitter nodes need to make individual decisions for distributed operation and do not necessarily cooperate with each other. We consider a single-receiver random access system of non-cooperative transmitters with the individual objectives of optimizing their throughput rewards, transmission energy costs and delay costs. The non-cooperative transmitter behavior may be purely selfish or may also reflect malicious objectives of generating interference to prevent the successful transmissions of the other nodes as a form of denial of service attack. Our goal is to evaluate the interactions between selfish and malicious nodes that have the dual objectives of optimizing their individual performance measures and blocking the packet transmissions of the other selfish nodes. We assume saturated packet queues of infinite buffer capacities and consider a general multi-packet reception channel that allows packet captures in the presence of simultaneous transmissions. In this context, we formulate a non-cooperative random access game of selecting the individual probabilities of transmitting packets to a common receiver. We derive the non-cooperative transmission strategies in Nash equilibrium. The analysis provides insights for the optimal strategies to block random access of selfish nodes as well as the optimal defense mechanisms against the possible denial of service attacks of malicious nodes in wireless networks. The results are also compared with the cooperative equilibrium strategies that optimize the total system utility (separately under random access and scheduled access). A pricing scheme is presented to improve the non-cooperative operation. For distributed implementation, we formulate a repeated game of the best-response strategy updates and introduce adaptive heuristics (based on the channel feedback only) provided that the system parameters are not explicitly known at the individual transmitters.

Rock-scissors-paper and the survival of the weakest.

In the children's game of rock-scissors-paper, players each choose one of three strategies. A rock beats a pair of scissors, scissors beat a sheet of paper and paper beats a rock, so the strategies form a competitive cycle. Although cycles in competitive ability appear to be reasonably rare among terrestrial plants, they are common among marine sessile organisms and have been reported in other contexts. Here we consider a system with three species in a competitive loop and show that this simple ecology exhibits two counter-intuitive phenomena. First, the species that is least competitive is expected to have the largest population and, where there are oscillations in a finite population, to be the least likely to die out. As a consequence an apparent weakening of a species leads to an increase in its population. Second, evolution favours the most competitive individuals within a species, which leads to a decline in its population. This is analogous to the tragedy of the commons, but here, rather than leading to a collapse, the 'tragedy' acts to maintain diversity.

WORLD-CLASS OIL SPILL PREVENTION AND RESPONSE FOR THE ALASKAN: TRANS-ALASKA PIPELINE SYSTEM TANKER TRADE

ABSTRACT Alyeska Pipeline Service Company, Ship Escort Response Vessel System (SERVS) is the primary response action contractor for Trans-Alaska Pipeline System (TAPS) laden tankers within Prince William Sound and an oil spill removal organization for the Gulf of Alaska. During the past five years, SERVS has implemented a world-class spill prevention and response organization for this region. The activities of the SERVS prevention and response organization include escort prevention service, spill prevention activities, response equipment, contingency planning, nearshore response, community involvement, fishing vessels program, citizen oversight, and training. Plans have been made for dispersant use, in-situ burning, waste management, coastal resource and sensitive environment inventory, wildlife protection and rehabilitation, and other response strategies. Response equipment and strategy updates are closely coordinated with ship operators/charters (planholders), agencies, and the public, including the Prince William Sound Regional Citizen Advisory Council.