Reinforcement Learning Dynamics in Social Dilemmas

In this paper we replicate and advance Macy and Flache\'s (2002; Proc. Natl. Acad. Sci. USA, 99, 7229–7236) work on the dynamics of reinforcement learning in 2�2 (2-player 2-strategy) social dilemmas. In particular, we provide further insight into the solution concepts that they describe, illustrate some recent analytical results on the dynamics of their model, and discuss the robustness of such results to occasional mistakes made by players in choosing their actions (i.e. trembling hands). It is shown here that the dynamics of their model are strongly dependent on the speed at which players learn. With high learning rates the system quickly reaches its asymptotic behaviour; on the other hand, when learning rates are low, two distinctively different transient regimes can be clearly observed. It is shown that the inclusion of small quantities of randomness in players\' decisions can change the dynamics of the model dramatically.Reinforcement Learning; Replication; Game Theory; Social Dilemmas; Agent-Based; Slow Learning

Techniques to Understand Computer Simulations: Markov Chain Analysis

The aim of this paper is to assist researchers in understanding the dynamics of simulation models that have been implemented and can be run in a computer, i.e. computer models. To do that, we start by explaining (a) that computer models are just input-output functions, (b) that every computer model can be re-implemented in many different formalisms (in particular in most programming languages), leading to alternative representations of the same input-output relation, and (c) that many computer models in the social simulation literature can be usefully represented as time-homogeneous Markov chains. Then we argue that analysing a computer model as a Markov chain can make apparent many features of the model that were not so evident before conducting such analysis. To prove this point, we present the main concepts needed to conduct a formal analysis of any time-homogeneous Markov chain, and we illustrate the usefulness of these concepts by analysing 10 well-known models in the social simulation literature as Markov chains. These models are: • Schelling\'s (1971) model of spatial segregation • Epstein and Axtell\'s (1996) Sugarscape • Miller and Page\'s (2004) standing ovation model • Arthur\'s (1989) model of competing technologies • Axelrod\'s (1986) metanorms models • Takahashi\'s (2000) model of generalized exchange • Axelrod\'s (1997) model of dissemination of culture • Kinnaird\'s (1946) truels • Axelrod and Bennett\'s (1993) model of competing bimodal coalitions • Joyce et al.\'s (2006) model of conditional association In particular, we explain how to characterise the transient and the asymptotic dynamics of these computer models and, where appropriate, how to assess the stochastic stability of their absorbing states. In all cases, the analysis conducted using the theory of Markov chains has yielded useful insights about the dynamics of the computer model under study.Computer Modelling, Simulation, Markov, Stochastic Processes, Analysis, Re-Implementation

Is Your Model Susceptible to Floating-Point Errors?

This paper provides a framework that highlights the features of computer models that make them especially vulnerable to floating-point errors, and suggests ways in which the impact of such errors can be mitigated. We focus on small floating-point errors because these are most likely to occur, whilst still potentially having a major influence on the outcome of the model. The significance of small floating-point errors in computer models can often be reduced by applying a range of different techniques to different parts of the code. Which technique is most appropriate depends on the specifics of the particular numerical situation under investigation. We illustrate the framework by applying it to six example agent-based models in the literature.Floating Point Arithmetic, Floating Point Errors, Agent Based Modelling, Computer Modelling, Replication

Kink fluctuation asymptotics and zero modes

In this paper we propose a refinement of the heat kernel/zeta function treatment of kink quantum fluctuations in scalar field theory, further analyzing the existence and implications of a zero energy fluctuation mode. Improved understanding of the interplay between zero modes and the kink heat kernel expansion delivers asymptotic estimations of one-loop kink mass shifts with remarkably higher precision than previously obtained by means of the standard Gilkey-DeWitt heat kernel expansion.Comment: 21 pages, 8 figures, to be published in The European Physical Journal

Strategy sets closed under payoff sampling

Producción CientíficaWe consider population games played by procedurally rational players who, when revising their current strategy, test each of their available strategies independently in a series of random matches –i.e., a battery of tests–, and then choose the strategy that performed best in this battery of tests. This revision protocol leads to the so-called payoff-sampling dynamics (aka test-all Best Experienced Payoff dynamics). In this paper we characterize the support of all the rest points of these dynamics in any game and analyze the asymptotic stability of the faces to which they belong. We do this by defining strategy sets closed under payoff sampling, and by proving that the identification of these sets can be made in terms of simple comparisons between some of the payoffs of the game

Stability of strict equilibria in best experienced payoff dynamics: Simple formulas and applications

Producción CientíficaWe consider a family of population game dynamics known as Best Experienced Payoff Dynamics. Under these dynamics, when agents are given the opportunity to revise their strategy, they test some of their possible strategies a fixed number of times. Crucially, each strategy is tested against a new randomly drawn set of opponents. The revising agent then chooses the strategy whose total payoff was highest in the test, breaking ties according to a given tie-breaking rule. Strict Nash equilibria are rest points of these dynamics, but need not be stable. We provide some simple formulas and algorithms to determine the stability or instability of strict Nash equilibria.Agencia Estatal de Investigación (project PID2020-118906GB-I00/AEI/10.13039/501100011033)Ministerio de Ciencia, Innovación y Universidades (projects PRX19/00113 and PRX21/00295)Fulbright Program (projects PRX19/00113 and PRX21/00295

Compact UWB Monopole for Multilayer Applications

A novel compact, dual layer UWB monopole antenna is presented. This low profile ultra-wideband antenna is fed by a 50 ? shielded strip-line with an array of metal vias making the conducting walls. A printed disc monopole with a circular cut is the radiating element. The dual layer, shielded strip line feed allows for integration in multilayer technologies. The ultra-wideband, monopole characteristics of the antenna are confirmed experimentally

Millimeter Wave Substrate Integrated Waveguide Antennas: Design and Fabrication Analysis

The paper presents a new concept in antenna design, whereby a photo-imageable thick-film process is used to integrate a waveguide antenna within a multilayer structure. This has yielded a very compact, high performance antenna working at high millimeter-wave (mm-wave) frequencies, with a high degree of repeatability and reliability in antenna construction. Theoretical and experimental results for 70 GHz mm-wave integrated antennas, fabricated using the new technique are presented. The antennas were formed from miniature slotted waveguide arrays using up to 18 layers of photo-imageable material. To enhance the electrical performance a novel folded waveguide array was also investigated. The fabrication process is analysed in detail and the critical issues involved in the fabrication cycle are discussed. The losses in the substrate integrated waveguide have been calculated. The performance of the new integrated antenna is compared to conventional metallic, air-filled waveguide antennas, and also to conventional microstrip antenna arrays operating at the same frequencies

A visualization of the damage in Lead Tungstate calorimeter crystals after exposure to high-energy hadrons

The anticipated performance of calorimeter crystals in the environment expected after the planned High-Luminosity upgrade of the Large Hadron Collider (HL-LHC) at CERN has to be well understood, before informed decisions can be made on the need for detector upgrades. Throughout the years of running at the HL-LHC, the detectors will be exposed to considerable fluences of fast hadrons, that have been shown to cause cumulative transparency losses in Lead Tungstate scintillating crystals. In this study, we present direct evidence of the main underlying damage mechanism. Results are shown from a test that yields a direct insight into the nature of the hadron-specific damage in Lead Tungstate calorimeter crystals exposed to 24 GeV/c protons.Comment: 8 pages, 6 figure