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

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

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

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

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

Repeated games with endogenous separation

Producción CientíficaWe consider repeated games with endogenous separation – also known as voluntarily separable or voluntary partnership games – and their evolutionary dynamics. We formulate the replicator dynamics for games with endogenous separation, and provide a definition of neutral stability that guarantees Lyapunov stability in the replicator dynamics. We also provide existence results for monomorphic neutrally stable states in games with endogenous separation.Organización de Empresas y CI

Errors and Artefacts in Agent-Based Modelling

The objectives of this paper are to define and classify different types of errors and artefacts that can appear in the process of developing an agent-based model, and to propose activities aimed at avoiding them during the model construction and testing phases. To do this in a structured way, we review the main concepts of the process of developing such a model – establishing a general framework that summarises the process of designing, implementing, and using agent-based models. Within this framework we identify the various stages where different types of errors and artefacts may appear. Finally we propose activities that could be used to detect (and hence eliminate) each type of error or artefact.Verification, Replication, Artefact, Error, Agent-Based Modelling, Modelling Roles

Three-dimensional range imaging apparatus and method

A three-dimensional range imager includes a light source for providing a modulated light signal, a multiplexer, an optical fiber connecting the light source to the multiplexer, a plurality of optical fibers connected at first ends to the multiplexer and at second ends to a first fiber array, and a transmitter optic disposed adjacent the first fiber array for projecting a pixel pattern of the array onto a target

Sugar nucleotide quantification by liquid chromatography tandem mass spectrometry reveals a distinct profile in Plasmodium falciparum sexual stage parasites

The obligate intracellular lifestyle of Plasmodium falciparum and the difficulties to obtain sufficient amounts of biological material has hampered the study of specific metabolic pathways in the malaria parasite. Thus, for example, the pools of sugar nucleotides required to fuel glycosylation reactions have never been studied in-depth in well-synchronized asexual parasites or in other stages of its life cycle. These metabolites are of critical importance, especially considering the renewed interest in the presence of N -, O - and other glycans in key parasite proteins. In this work, we adapted a liquid chromatography tandem mass spectrometry method based on the use of porous graphitic carbon (PGC) columns and MS-friendly solvents to quantify sugar nucleotides in the malaria parasite. We report on the thorough quantification of the pools of these metabolites throughout the intraerythrocytic cycle of P. falciparum The sensitivity of the method enabled for the first time the targeted analysis of these glycosylation precursors in gametocytes, the parasite sexual stages that are transmissible to the mosquito vector