5,655 research outputs found
Designing Network Protocols for Good Equilibria
Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network cost-sharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal cost-sharing protocols for undirected and directed graphs, single-sink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the cost-sharing protocols that induce only network games with pure-strategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs
Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems
Recently, significant attention has been dedicated to the models of opinion
dynamics in which opinions are described by real numbers, and agents update
their opinions synchronously by averaging their neighbors' opinions. The
neighbors of each agent can be defined as either (1) those agents whose
opinions are in its "confidence range," or (2) those agents whose "influence
range" contain the agent's opinion. The former definition is employed in
Hegselmann and Krause's bounded confidence model, and the latter is novel here.
As the confidence and influence ranges are distinct for each agent, the
heterogeneous state-dependent interconnection topology leads to a
poorly-understood complex dynamic behavior. In both models, we classify the
agents via their interconnection topology and, accordingly, compute the
equilibria of the system. Then, we define a positive invariant set centered at
each equilibrium opinion vector. We show that if a trajectory enters one such
set, then it converges to a steady state with constant interconnection
topology. This result gives us a novel sufficient condition for both models to
establish convergence, and is consistent with our conjecture that all
trajectories of the bounded confidence and influence models eventually converge
to a steady state under fixed topology.Comment: 22 pages, Submitted to SIAM Journal on Control and Optimization
(SICON
“Driving While Black”: A Theory for Interethnic Integration and Evolution of Prejudice
This paper studies the evolution of interethnic attitudes, the integration or segregation dynamics of ethnic minorities and the conditions for the rising of ethnic-based social hierarchies. By means of a cultural evolution framework, a dynamics of interethnic attitudes is provided and conditions for their convergence derived. Steady states implying a constant role of racism and no role for racism are identified. Deriving sufficient conditions for convergence, we find that the way in which Oblique Socialization Schemes (the way children react to out-of-family stimuli when forming their cultural values) are defined and modelled becomes crucial for the structure of the derived long run equilibria. In particular, we find that Steady States implying an Ethnic-based social ranking or full integration of ethnicities may be reached depending on whether or not agents use Reciprocity and/or Ethnocentrism in their interethnic attitudes formation schemes. Allowing different groups for asymmetric use of reciprocity and Ethnocentrism, we explain why different ethnic minorities may show different integration patterns, and what are the different roles (Cultural bridge, cultural hub) an ethnic group may play in the integration process. Moreover, in this way, we explain why attitudes of some groups towards others converge to the same values, while other groups seems to be excluded from this process. At last, we provide the first steps for the endogeneization of socialization structures.Cultural transmission, Minority integration, Evolution of preferences
A revised model of fluid transport optimization in Physarum polycephalum
Optimization of fluid transport in the slime mold Physarum polycephalum has
been the subject of several modeling efforts in recent literature. Existing
models assume that the tube adaptation mechanism in P. polycephalum's tubular
network is controlled by the sheer amount of fluid flow through the tubes. We
put forward the hypothesis that the controlling variable may instead be the
flow's pressure gradient along the tube. We carry out the stability analysis of
such a revised mathematical model for a parallel-edge network, proving that the
revised model supports the global flow-optimizing behavior of the slime mold
for a substantially wider class of response functions compared to previous
models. Simulations also suggest that the same conclusion may be valid for
arbitrary network topologies.Comment: To appear in Journal of Mathematical Biolog
Pure Nash Equilibria and Best-Response Dynamics in Random Games
In finite games mixed Nash equilibria always exist, but pure equilibria may
fail to exist. To assess the relevance of this nonexistence, we consider games
where the payoffs are drawn at random. In particular, we focus on games where a
large number of players can each choose one of two possible strategies, and the
payoffs are i.i.d. with the possibility of ties. We provide asymptotic results
about the random number of pure Nash equilibria, such as fast growth and a
central limit theorem, with bounds for the approximation error. Moreover, by
using a new link between percolation models and game theory, we describe in
detail the geometry of Nash equilibria and show that, when the probability of
ties is small, a best-response dynamics reaches a Nash equilibrium with a
probability that quickly approaches one as the number of players grows. We show
that a multitude of phase transitions depend only on a single parameter of the
model, that is, the probability of having ties.Comment: 29 pages, 7 figure
On Nash Dynamics of Matching Market Equilibria
In this paper, we study the Nash dynamics of strategic interplays of n buyers
in a matching market setup by a seller, the market maker. Taking the standard
market equilibrium approach, upon receiving submitted bid vectors from the
buyers, the market maker will decide on a price vector to clear the market in
such a way that each buyer is allocated an item for which he desires the most
(a.k.a., a market equilibrium solution). While such equilibrium outcomes are
not unique, the market maker chooses one (maxeq) that optimizes its own
objective --- revenue maximization. The buyers in turn change bids to their
best interests in order to obtain higher utilities in the next round's market
equilibrium solution.
This is an (n+1)-person game where buyers place strategic bids to gain the
most from the market maker's equilibrium mechanism. The incentives of buyers in
deciding their bids and the market maker's choice of using the maxeq mechanism
create a wave of Nash dynamics involved in the market. We characterize Nash
equilibria in the dynamics in terms of the relationship between maxeq and mineq
(i.e., minimum revenue equilibrium), and develop convergence results for Nash
dynamics from the maxeq policy to a mineq solution, resulting an outcome
equivalent to the truthful VCG mechanism.
Our results imply revenue equivalence between maxeq and mineq, and address
the question that why short-term revenue maximization is a poor long run
strategy, in a deterministic and dynamic setting
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