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Replicator Dynamics (replicator + dynamics)

Distribution by Scientific Domains
Business, Economics, Finance and Accounting60%

Selected Abstracts

Expedient and Monotone Learning Rules

ECONOMETRICA, Issue 2 2004
Tilman Börgers
This paper considers learning rules for environments in which little prior and feedback information is available to the decision maker. Two properties of such learning rules are studied: absolute expediency and monotonicity. Both require that some aspect of the decision maker's performance improves from the current period to the next. The paper provides some necessary, and some sufficient conditions for these properties. It turns out that there is a large variety of learning rules that have the properties. However, all learning rules that have these properties are related to the replicator dynamics of evolutionary game theory. For the case in which there are only two actions, it is shown that one of the absolutely expedient learning rules dominates all others. [source]

Two Competing Models of How People Learn in Games

ECONOMETRICA, Issue 6 2002
Ed Hopkins
Reinforcement learning and stochastic fictitious play are apparent rivals as models of human learning. They embody quite different assumptions about the processing of information and optimization. This paper compares their properties and finds that they are far more similar than were thought. In particular, the expected motion of stochastic fictitious play and reinforcement learning with experimentation can both be written as a perturbed form of the evolutionary replicator dynamics. Therefore they will in many cases have the same asymptotic behavior. In particular, local stability of mixed equilibria under stochastic fictitious play implies local stability under perturbed reinforcement learning. The main identifiable difference between the two models is speed: stochastic fictitious play gives rise to faster learning. [source]

Meta-analysis of functional imaging data using replicator dynamics

HUMAN BRAIN MAPPING, Issue 1 2005
Jane Neumann
Abstract Despite the rapidly growing number of meta-analyses in functional neuroimaging, the field lacks formal mathematical tools for the quantitative and qualitative evaluation of meta-analytic data. We propose to use replicator dynamics in the meta-analysis of functional imaging data to address an important aspect of neuroimaging research, the search for functional networks of cortical areas that underlie a specific cognitive task. The replicator process requires as input only a list of activation locations, and it results in a network of locations that jointly show significant activation in most studies included in the meta-analysis. These locations are likely to play a critical role in solving the investigated cognitive task. Our method was applied to a meta-analysis of the Stroop interference task using data provided by the publicly accessible database BrainMap DBJ. Hum Brain Mapp 25:165,173, 2005. © 2005 Wiley-Liss, Inc. [source]

Stability and instability of the unbeatable strategy in dynamic processes

INTERNATIONAL JOURNAL OF ECONOMIC THEORY, Issue 1 2006
Fuhito Kojima
C72; C73 A strategy is unbeatable if it is immune to any entrant strategy of any size. This paper investigates static and dynamic properties of unbeatable strategies. We give equivalent conditions for a strategy to be unbeatable and compare it with related equilibrium concepts. An unbeatable strategy is globally stable under replicator dynamics. In contrast, an unbeatable strategy can fail to be globally stable under best response dynamics even if it is also a unique and strict Nash equilibrium. [source]