Stochastic learning dynamics and speed of convergence in population games

We study how long it takes for large populations of interacting agents to come close to Nash equilibrium when they adapt their behavior using a stochastic better reply dynamic. Prior work considers this question mainly for 2 × 2 games and potential games; here we characterize convergence times for general weakly acyclic games, including coordination games, dominance solvable games, games with strategic complementarities, potential games, and many others with applications in economics, biology, and distributed control. If players' better replies are governed by idiosyncratic shocks, the convergence time can grow exponentially in the population size; moreover, this is true even in games with very simple payoff structures. However, if their responses are sufficiently correlated due to aggregate shocks, the convergence time is greatly accelerated; in fact, it is bounded for all sufficiently large populations. We provide explicit bounds on the speed of convergence as a function of key structural parameters including the number of strategies, the length of the better reply paths, the extent to which players can influence the payoffs of others, and the desired degree of approximation to Nash equilibrium

Long-term legacy implications for Olympic Games

Celebrations have been occurring throughout history from the commemoration of phases of the moon, to historical and cultural festivals in addition to life cycle celebrations of birth, marriage and death. Events came about through the commercialisation of popular celebrations and in the UK as our population becomes more culturally diverse, so do the events appearing showing diversifying into the leisure and every aspect of people’s everyday lives. All these events have impacts and legacies and the larger the size of event the greater these ‘consequences’, with the Olympics having the greatest impacts and legacies. These large scale events also have major benefits including destination image and urban developments, the legacy left behind after the event is held. In order for these benefits to maximise the long-term potential, legacy planning as early as possible is paramount. Case studies of the Sydney Games show that whilst they have been known as ‘the best games ever’ their legacy planning post the games, beginning in 2000, were negligible and the consequences of this are on-going. For the organisers of the Barcelona 1992 Games, their built environment and the re-modelling of the city, was part of a larger scale long-term redevelopment and their legacy planning was part of an overall vision for the city. What appears to be a long-term strategic plan for London, especially in relation to the social impacts of the four main boroughs involved in the staging of the 2012 Games, could become known as the ‘London’ model of urban rejuvenation for future mega-event planners, particularly in relation to the long-term future legacy. This chapter sets put to evaluate the lessons learned from the past Games of Sydney and Barcelona in relation to legacy planning, especially the social consequences, and the ‘best-practice’ lessons to be incorporated within the London 2012 planning in relation to future long-term legacies. London won the right to host the 2012 games on the basis of their regeneration plans for an area of London in socially deprived conditions. All the ‘paper’ promises within the bid document talk of the major regeneration project with the associated large scale spend on infrastructure, it is vital that the promises are turned into long-term viable legacy

Evolutionary games and spatial periodicity

We establish a theoretical framework to address evolutionary dynamics of spatial games under strong selection. As the selection intensity tends to infinity, strategy competition unfolds in the deterministic way of winners taking all. We rigorously prove that the evolutionary process soon or later either enters a cycle and from then on repeats the cycle periodically, or stabilizes at some state almost everywhere. This conclusion holds for any population graph and a large class of finite games. This framework suffices to reveal the underlying mathematical rationale for the kaleidoscopic cooperation of Nowak and May's pioneering work on spatial games: highly symmetric starting configuration causes a very long transient phase covering a large number of extremely beautiful spatial patterns. For all starting configurations, spatial patterns transit definitely over generations, so cooperators and defectors persist definitely. This framework can be extended to explore games including the snowdrift game, the public goods games (with or without loner, punishment), and repeated games on graphs. Aspiration dynamics can also be fully addressed when players deterministically switch strategy for unmet aspirations by virtue of our framework. Our results have potential implications for exploring the dynamics of a large variety of spatially extended systems in biology and physics.Comment: 35 pages, 10 figures, and supplementary informatio

Improving games AI performance using grouped hierarchical level of detail

Computer games are increasingly making use of large environments; however, these are often only sparsely populated with autonomous agents. This is, in part, due to the computational cost of implementing behaviour functions for large numbers of agents. In this paper we present an optimisation based on level of detail which reduces the overhead of modelling group behaviours, and facilitates the population of an expansive game world. We consider an environment which is inhabited by many distinct groups of agents. Each group itself comprises individual agents, which are organised using a hierarchical tree structure. Expanding and collapsing nodes within each tree allows the efficient dynamic abstraction of individuals, depending on their proximity to the player. Each branching level represents a different level of detail, and the system is designed to trade off computational performance against behavioural fidelity in a way which is both efficient and seamless to the player. We have developed an implementation of this technique, and used it to evaluate the associated performance benefits. Our experiments indicate a significant potential reduction in processing time, with the update for the entire AI system taking less than 1% of the time required for the same number of agents without optimisation

On Influence, Stable Behavior, and the Most Influential Individuals in Networks: A Game-Theoretic Approach

We introduce a new approach to the study of influence in strategic settings where the action of an individual depends on that of others in a network-structured way. We propose \emph{influence games} as a \emph{game-theoretic} model of the behavior of a large but finite networked population. Influence games allow \emph{both} positive and negative \emph{influence factors}, permitting reversals in behavioral choices. We embrace \emph{pure-strategy Nash equilibrium (PSNE)}, an important solution concept in non-cooperative game theory, to formally define the \emph{stable outcomes} of an influence game and to predict potential outcomes without explicitly considering intricate dynamics. We address an important problem in network influence, the identification of the \emph{most influential individuals}, and approach it algorithmically using PSNE computation. \emph{Computationally}, we provide (a) complexity characterizations of various problems on influence games; (b) efficient algorithms for several special cases and heuristics for hard cases; and (c) approximation algorithms, with provable guarantees, for the problem of identifying the most influential individuals. \emph{Experimentally}, we evaluate our approach using both synthetic influence games as well as several real-world settings of general interest, each corresponding to a separate branch of the U.S. Government. \emph{Mathematically,} we connect influence games to important game-theoretic models: \emph{potential and polymatrix games}.Comment: Accepted to AI Journal, subject to addressing the reviewers' points (which are addressed in this version). An earlier version of the article appeared in AAAI-1

Internet gaming disorder: investigating the clinical relevance of a new phenomenon

The American Psychiatric Association identified Internet Gaming Disorder as a new potential psychiatric disorder and has recognized that little is known about the prevalence, validity, or cross-cultural robustness of proposed Internet Gaming Disorder criteria. In response to this gap in our understanding, this project estimated the period prevalence of this new potential psychiatric disorder using APA guidance, examined the validity of its proposed indicators, evaluated reliability cross-culturally and across genders, compared it to gold-standard research on gambling addiction and problem gaming, and estimated its impact on physical, social, and mental health. To do so, in a first for this research topic, four survey studies (n = 18,932) with large international cohorts employed an open-science methodology wherein the analysis plans for confirmatory hypotheses were registered prior to data collection. Results showed that of those who play games, more than 2 in 3, did not report any symptoms of Internet Gaming Disorder, and findings showed a very small proportion of the general population – between 0.3% and 1.0% – might qualify for a potential acute diagnosis of Internet Gaming Disorder. Comparison to Gambling Disorder revealed that Internet-based games may be significantly less addictive than gambling and similarly dysregulating as electronic games more generally. The evidence linking Internet Gaming Disorder to game engagement was strong, but links to physical, social, and mental health outcomes were decidedly mixed

Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics

We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of decay of the probability that the sample path of the evolutionary process lies in a prespecified set as the population size approaches infinity. We use these results to describe excursion rates and stationary distribution asymptotics in settings where the mean dynamic admits a globally attracting state, and we compute these rates explicitly for the case of logit choice in potential games