11,991 research outputs found
Penalty-regulated dynamics and robust learning procedures in games
Starting from a heuristic learning scheme for N-person games, we derive a new
class of continuous-time learning dynamics consisting of a replicator-like
drift adjusted by a penalty term that renders the boundary of the game's
strategy space repelling. These penalty-regulated dynamics are equivalent to
players keeping an exponentially discounted aggregate of their on-going payoffs
and then using a smooth best response to pick an action based on these
performance scores. Owing to this inherent duality, the proposed dynamics
satisfy a variant of the folk theorem of evolutionary game theory and they
converge to (arbitrarily precise) approximations of Nash equilibria in
potential games. Motivated by applications to traffic engineering, we exploit
this duality further to design a discrete-time, payoff-based learning algorithm
which retains these convergence properties and only requires players to observe
their in-game payoffs: moreover, the algorithm remains robust in the presence
of stochastic perturbations and observation errors, and it does not require any
synchronization between players.Comment: 33 pages, 3 figure
Evolutionary Poisson Games for Controlling Large Population Behaviors
Emerging applications in engineering such as crowd-sourcing and
(mis)information propagation involve a large population of heterogeneous users
or agents in a complex network who strategically make dynamic decisions. In
this work, we establish an evolutionary Poisson game framework to capture the
random, dynamic and heterogeneous interactions of agents in a holistic fashion,
and design mechanisms to control their behaviors to achieve a system-wide
objective. We use the antivirus protection challenge in cyber security to
motivate the framework, where each user in the network can choose whether or
not to adopt the software. We introduce the notion of evolutionary Poisson
stable equilibrium for the game, and show its existence and uniqueness. Online
algorithms are developed using the techniques of stochastic approximation
coupled with the population dynamics, and they are shown to converge to the
optimal solution of the controller problem. Numerical examples are used to
illustrate and corroborate our results
A Mathematical Analysis of the Long-run Behavior of Genetic Algorithms for Social Modeling
We present a mathematical analysis of the long-run behavior of genetic algorithms that are used for modeling social phenomena. The analysis relies on commonly used mathematical techniques in evolutionary game theory. Assuming a positive but infinitely small mutation rate, we derive results that can be used to calculate the exact long-run behavior of a genetic algorithm. Using these results, the need to rely on computer simulations can be avoided. We also show that if the mutation rate is infinitely small the crossover rate has no effect on the long-run behavior of a genetic algorithm. To demonstrate the usefulness of our mathematical analysis, we replicate a well-known study by Axelrod in which a genetic algorithm is used to model the evolution of strategies in iterated prisonerââŹâ˘s dilemmas. The theoretically predicted long-run behavior of the genetic algorithm turns out to be in perfect agreement with the long-run behavior observed in computer simulations. Also, in line with our theoretically informed expectations, computer simulations indicate that the crossover rate has virtually no long-run effect. Some general new insights into the behavior of genetic algorithms in the prisonerââŹâ˘s dilemma context are provided as well.genetic algorithm;economics;evolutionary game theory;long-run behavior;social modeling
Learning in Evolutionary Environments
The purpose of this work is to present a sort of short selective guide to an enormous and diverse literature on learning processes in economics. We argue that learning is an ubiquitous characteristic of most economic and social systems but it acquires even greater importance in explicitly evolutionary environments where: a) heterogeneous agents systematically display various forms of "bounded rationality"; b) there is a persistent appearance of novelties, both as exogenous shocks and as the result of technological, behavioural and organisational innovations by the agents themselves; c) markets (and other interaction arrangements) perform as selection mechanisms; d) aggregate regularities are primarily emergent properties stemming from out-of-equilibrium interactions. We present, by means of examples, the most important classes of learning models, trying to show their links and differences, and setting them against a sort of ideal framework of "what one would like to understand about learning...". We put a signifiphasis on learning models in their bare-bone formal structure, but we also refer to the (generally richer) non-formal theorising about the same objects. This allows us to provide an easier mapping of a wide and largely unexplored research agenda.Learning, Evolutionary Environments, Economic Theory, Rationality
Learning in evolutionary environments
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Modeling the Use of Nonrenewable Resources Using a Genetic Algorithm
This paper shows, how a genetic algorithm (GA) can be used to model an economic process: the interaction of profit-maximizing oil-exploration firms that compete with each other for a limited amount of oil. After a brief introduction to the concept of multi-agent-modeling in economics, a GA-based resource-economic model is developed. Several model runs based on different economic policy assumptions are presented and discussed in order to show how the GA-model can be used to gain insight into the dynamic properties of economic systems. The remainder outlines deficiencies of GA-based multi-agent approaches and sketches how the present model can be improved.
Fashion, Cooperation, and Social Interactions
Fashion plays such a crucial rule in the evolution of culture and society
that it is regarded as a second nature to the human being. Also, its impact on
economy is quite nontrivial. On what is fashionable, interestingly, there are
two viewpoints that are both extremely widespread but almost opposite:
conformists think that what is popular is fashionable, while rebels believe
that being different is the essence. Fashion color is fashionable in the first
sense, and Lady Gaga in the second. We investigate a model where the population
consists of the afore-mentioned two groups of people that are located on social
networks (a spatial cellular automata network and small-world networks). This
model captures two fundamental kinds of social interactions (coordination and
anti-coordination) simultaneously, and also has its own interest to game
theory: it is a hybrid model of pure competition and pure cooperation. This is
true because when a conformist meets a rebel, they play the zero sum matching
pennies game, which is pure competition. When two conformists (rebels) meet,
they play the (anti-) coordination game, which is pure cooperation. Simulation
shows that simple social interactions greatly promote cooperation: in most
cases people can reach an extraordinarily high level of cooperation, through a
selfish, myopic, naive, and local interacting dynamic (the best response
dynamic). We find that degree of synchronization also plays a critical role,
but mostly on the negative side. Four indices, namely cooperation degree,
average satisfaction degree, equilibrium ratio and complete ratio, are defined
and applied to measure people's cooperation levels from various angles. Phase
transition, as well as emergence of many interesting geographic patterns in the
cellular automata network, is also observed.Comment: 21 pages, 12 figure
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