Evolutionary Games in Complex Topologies: Interplay between Structure and Dynamics

En este estudio exploramos la interrelación entre la estructura subyacente de una cierta población de individuos y el resultado de la dinámica que está teniendo lugar en ella, específicamente, el Dilema del Prisionero. En la primera parte de este trabajo analizamos el caso de una topología estática, en la que la red de conexiones no cambia en el tiempo. En la segunda parte, desarrollamos dos modelos para crecer redes, donde dicho crecimiento esta íntimamente relacionado con la dinámica

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

Analysis of game playing agents with fingerprints

Evolutionary computation (EC) can create a vast number of strategies for playing simple games in a short time. Analysis of these strategies is typically more time-consuming than their production. As a result, analysis of strategies produced by an EC system is often lacking or restricted to the extraction of superficial summary Statistics and Probability; This thesis presents a technique for extracting a functional signature from evolved agents that play games. This signature can be used as a visualization of agent behavior in games with two moves and also provides a numerical target for clustering and other forms of automatic analysis. The fingerprint can be used to induce a similarity measure on the space of game strategies. This thesis develops fingerprints in the context of the iterated prisoner\u27s dilemma; we note that they can be computed for any two player simultaneous game with a finite set of moves. When using a clustering algorithm, the results are strongly influenced by the choice of the measure used to find the distance between or to compare the similarity of the data being clustered. The Euclidean metric, for example, rates a convex polytope as the most compact type of object and builds clusters that are contained in compact polytopes. Presented here is a general method, called multi-clustering, that compensates for the intrinsic shape of a metric or similarity measure. The method is tested on synthetic data sets that are natural for the Euclidean metric and on data sets designed to defeat k-means clustering with the Euclidean metric. Multi-clustering successfully discovers the designed cluster structure of all the synthetic data sets used with a minimum of parameter tuning. We then use multi-clustering and filtration on fingerprint data. Cellular representation is the practice of evolving a set of instructions for constructing a desired structure. This thesis presents a cellular encoding for finite state machines and specializes it to play the iterated prisoner\u27s dilemma. The impact on the character and behavior of finite state agents of using the cellular representation is investigated. For the cellular representation resented a statistically significant drop in the level of cooperation is found. Other differences in the character of the automaton generated with a direct and cellular representation are reported

Leave and let leave: A sufficient condition to explain the evolutionary emergence of cooperation

The option to leave your current partner in response to his behavior, also known as conditional dissociation, is a mechanism that has been shown to promote the emergence and stability of cooperation in many social interactions. This mechanism, nevertheless, has always been studied in combination with other factors that are known to support cooperation by themselves. In this paper, we isolate the effect of conditional dissociation on the evolution of cooperation and show that this mechanism is enough to sustain a significant level of cooperation if the expected lifetime of individuals is sufficiently longACCESS (EU, 12-120610), SIMULPAST (MICINN, CSD2010-00034) and SPPORT (JCyL, VA056A12-2). L.R.I. Spanish Ministry of Education for grant JC2009-0026

Pairwise Interaction on Random Graphs

We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph) can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph) cannot change over time.

Density games

The basic idea of evolutionary game theory is that payoff determines reproductive rate. Successful individuals have a higher payoff and produce more offspring. But in evolutionary and ecological situations there is not only reproductive rate but also carrying capacity. Individuals may differ in their exposure to density limiting effects. Here we explore an alternative approach to evolutionary game theory by assuming that the payoff from the game determines the carrying capacity of individual phenotypes. Successful strategies are less affected by density limitation (crowding) and reach higher equilibrium abundance. We demonstrate similarities and differences between our framework and the standard replicator equation. Our equation is defined on the positive orthant, instead of the simplex, but has the same equilibrium points as the replicator equation. Linear stability analysis produces the classical conditions for asymptotic stability of pure strategies, but the stability properties of internal equilibria can differ in the two frameworks. For example, in a two-strategy game with an internal equilibrium that is always stable under the replicator equation, the corresponding equilibrium can be unstable in the new framework resulting in a limit cycle

On Agent Communication in Large Groups

The problem is fundamental and natural, yet deep - to simulate the simplest possible form of communication that can occur within a large multi-agent system. It would be prohibitive to try and survey all of the research on communication in general so we must restrict our focus. We will devote our efforts to synthetic communication occurring within large groups. In particular, we would like to discover a model for communication that will serve as an abstract model, a prototype, for simulating communication within large groups of biological organisms

Stochastic models for biological evolution

In this work, we deal with the problem of creating a model that describes a population of agents undergoing Darwinian Evolution, which takes into account the basic phenomena of this process. According to the principles of evolutionary biology, Evolution occurs if there is selection and adaptation of phenotypes, mutation of genotypes, presence of physical space. The evolution of a biological population is then described by a system of ordinary stochastic differential equations; the basic model of dynamics represents the trend of a population divided into different types, with relative frequency in a simplex. The law governing this dynamics is called Replicator Dynamics: the growth rate of type k is measured in terms of evolutionary advantage, with its own fitness compared to the average in the population. The replicator dynamics model turns into a stochastic process when we consider random mutations that can transform fractions of individuals into others. The two main forces of Evolution, selection and mutation, act on different layers: the environment acts on the phenotype, selecting the fittest, while the randomness of the mutations affects the genotype. This difference is underlined in the model, where each genotype express a phenotype, and fitness influences emerging traits, not explicitly encoded in genotypes. The presence of a potentially infinite space of available genomes makes sure that variants of individuals with characteristics never seen before can be generated. In conclusion, numerical simulations are provided for some applications of the model, such as a variation of Conway's Game of Lif