3,905 research outputs found
A Dynamic Game Model of Collective Choice in Multi-Agent Systems
Inspired by successful biological collective decision mechanisms such as
honey bees searching for a new colony or the collective navigation of fish
schools, we consider a mean field games (MFG)-like scenario where a large
number of agents have to make a choice among a set of different potential
target destinations. Each individual both influences and is influenced by the
group's decision, as well as the mean trajectory of all the agents. The model
can be interpreted as a stylized version of opinion crystallization in an
election for example. The agents' biases are dictated first by their initial
spatial position and, in a subsequent generalization of the model, by a
combination of initial position and a priori individual preference. The agents
have linear dynamics and are coupled through a modified form of quadratic cost.
Fixed point based finite population equilibrium conditions are identified and
associated existence conditions are established. In general multiple equilibria
may exist and the agents need to know all initial conditions to compute them
precisely. However, as the number of agents increases sufficiently, we show
that 1) the computed fixed point equilibria qualify as epsilon Nash equilibria,
2) agents no longer require all initial conditions to compute the equilibria
but rather can do so based on a representative probability distribution of
these conditions now viewed as random variables. Numerical results are
reported
The Opinion Game: Stock price evolution from microscopic market modelling
We propose a class of Markovian agent based models for the time evolution of
a share price in an interactive market. The models rely on a microscopic
description of a market of buyers and sellers who change their opinion about
the stock value in a stochastic way. The actual price is determined in
realistic way by matching (clearing) offers until no further transactions can
be performed. Some analytic results for a non-interacting model are presented.
We also propose basic interaction mechanisms and show in simulations that these
already reproduce certain particular features of prices in real stock markets.Comment: 14 pages, 5 figure
- …