1,347 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
Navigable networks as Nash equilibria of navigation games
Common sense suggests that networks are not random mazes of purposeless connections,
but that these connections are organized so that networks can perform their functions well.
One function common to many networks is targeted transport or navigation. Here, using
game theory, we show that minimalistic networks designed to maximize the navigation
efficiency at minimal cost share basic structural properties with real networks. These
idealistic networks are Nash equilibria of a network construction game whose purpose is to
find an optimal trade-off between the network cost and navigability. We show that these
skeletons are present in the Internet, metabolic, English word, US airport, Hungarian road
networks, and in a structural network of the human brain. The knowledge of these skeletons
allows one to identify the minimal number of edges, by altering which one can efficiently
improve or paralyse navigation in the network
Complex network analysis and nonlinear dynamics
This chapter aims at reviewing complex network and nonlinear dynamical
models and methods that were either developed for or applied to socioeconomic
issues, and pertinent to the theme of New Economic Geography. After an introduction
to the foundations of the field of complex networks, the present summary
introduces some applications of complex networks to economics, finance, epidemic
spreading of innovations, and regional trade and developments. The chapter also
reviews results involving applications of complex networks to other relevant
socioeconomic issue
Atomic Splittable Flow Over Time Games
In an atomic splittable flow over time game, finitely many players route flow dynamically through a network, in which edges are equipped with transit times, specifying the traversing time, and with capacities, restricting flow rates. Infinitesimally small flow particles controlled by the same player arrive at a constant rate at the player's origin and the player's goal is to maximize the flow volume that arrives at the player's destination within a given time horizon. Here, the flow dynamics are described by the deterministic queuing model, i.e., flow of different players merges perfectly, but excessive flow has to wait in a queue in front of the bottle-neck. In order to determine Nash equilibria in such games, the main challenge is to consider suitable definitions for the players' strategies, which depend on the level of information the players receive throughout the game. For the most restricted version, in which the players receive no information on the network state at all, we can show that there is no Nash equilibrium in general, not even for networks with only two edges. However, if the current edge congestions are provided over time, the players can adapt their route choices dynamically. We show that a profile of those strategies always lead to a unique feasible flow over time. Hence, those atomic splittable flow over time games are well-defined. For parallel-edge networks Nash equilibria exists and the total flow arriving in time equals the value of a maximum flow over time leading to a price of anarchy of 1.ISSN:1868-896
Collective navigation of complex networks: Participatory greedy routing
Many networks are used to transfer information or goods, in other words, they
are navigated. The larger the network, the more difficult it is to navigate
efficiently. Indeed, information routing in the Internet faces serious
scalability problems due to its rapid growth, recently accelerated by the rise
of the Internet of Things. Large networks like the Internet can be navigated
efficiently if nodes, or agents, actively forward information based on hidden
maps underlying these systems. However, in reality most agents will deny to
forward messages, which has a cost, and navigation is impossible. Can we design
appropriate incentives that lead to participation and global navigability?
Here, we present an evolutionary game where agents share the value generated by
successful delivery of information or goods. We show that global navigability
can emerge, but its complete breakdown is possible as well. Furthermore, we
show that the system tends to self-organize into local clusters of agents who
participate in the navigation. This organizational principle can be exploited
to favor the emergence of global navigability in the system.Comment: Supplementary Information and Videos:
https://koljakleineberg.wordpress.com/2016/11/14/collective-navigation-of-complex-networks-participatory-greedy-routing
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