152 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Essays on the economics of networks
Networks (collections of nodes or vertices and graphs capturing their linkages) are a common object of study across a range of fields includ- ing economics, statistics and computer science. Network analysis is often based around capturing the overall structure of the network by some reduced set of parameters. Canonically, this has focused on the notion of centrality. There are many measures of centrality, mostly based around statistical analysis of the linkages between nodes on the network. However, another common approach has been through the use of eigenfunction analysis of the centrality matrix. My the- sis focuses on eigencentrality as a property, paying particular focus to equilibrium behaviour when the network structure is fixed. This occurs when nodes are either passive, such as for web-searches or queueing models or when they represent active optimizing agents in network games. The major contribution of my thesis is in the applica- tion of relatively recent innovations in matrix derivatives to centrality measurements and equilibria within games that are function of those measurements. I present a series of new results on the stability of eigencentrality measures and provide some examples of applications to a number of real world examples
Computer Aided Verification
This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book
The Complexity of Infinite-Horizon General-Sum Stochastic Games
We study the complexity of computing stationary Nash equilibrium (NE) in
n-player infinite-horizon general-sum stochastic games. We focus on the problem
of computing NE in such stochastic games when each player is restricted to
choosing a stationary policy and rewards are discounted. First, we prove that
computing such NE is in PPAD (in addition to clearly being PPAD-hard). Second,
we consider turn-based specializations of such games where at each state there
is at most a single player that can take actions and show that these
(seemingly-simpler) games remain PPAD-hard. Third, we show that under further
structural assumptions on the rewards computing NE in such turn-based games is
possible in polynomial time. Towards achieving these results we establish
structural facts about stochastic games of broader utility, including
monotonicity of utilities under single-state single-action changes and
reductions to settings where each player controls a single state
On the Emergence of Cooperation in the Repeated Prisoner's Dilemma
This article explores which parameters of the repeated Prisoner's Dilemma
lead to cooperation. Using simulations, I demonstrate that the potential
function of the stochastic evolutionary dynamics of the Grim Trigger strategy
is useful to predict cooperation between Q-learners. The frontier separating
the parameter spaces that induce either cooperation or defection can be
determined based on the kinetic energy exerted by the respective basins of
attraction. When the incentive compatibility constraint of the Grim Trigger
strategy is slack, a sudden increase in the observed cooperation rates occurs
when the ratio of the kinetic energies approaches a critical value, which
itself is a function of the discount factor, multiplied by a correction factor
to account for the effect of the algorithms' exploration probability. Using
metadata from laboratory experiments, I provide evidence that the insights
obtained from the simulations are also useful to explain the emergence of
cooperation between humans. The observed cooperation rates show a positive
gradient at the frontier characterized by an exploration probability of
approximately five percent. In the context of human-to-human interaction, the
exploration probability can be viewed as the belief about the opponent's
probability to deviate from the equilibrium action
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
Geometric aspects of linear programming : shadow paths, central paths, and a cutting plane method
Most everyday algorithms are well-understood; predictions made theoretically
about them closely match what we observe in practice. This is not the case for
all algorithms, and some algorithms are still poorly understood on a theoretical level.
This is the case for many algorithms used for solving optimization problems from operations reserach.
Solving such optimization problems is essential in many industries and is done every day.
One important example of such optimization problems are Linear Programming problems.
There are a couple of different algorithms that are popular in practice,
among which is one which has been in use for almost 80 years.
Nonetheless, our theoretical understanding of these algorithms is limited.
This thesis makes progress towards a better understanding of these key algorithms
for lineair programming, among which are the simplex method, interior point methods,
and cutting plane methods
Dynamic traffic equilibria with route and departure time choice
This thesis studies the dynamic equilibrium behavior in traffic networks and it is motivated by rush-hour congestion. It is well understood that one of the key causes of traffic congestion relies on the behavior of road users. These do not coordinate their actions in order to avoid the creation of traffic jams, but rather make choices that favor only themselves and not the community. An equilibrium occurs when everyone is satisfied with his own choices and would not benefit from changing them. We focus on dynamic mathematical models where the congestion delay of a road varies over time, depending on the amount of traffic that has crossed it up to that specific moment and independently on the pattern of traffic that will cross it at a later time. We mainly consider settings with arbitrary network topologies where users choose both the route and departure time and we tackle questions such as the followings: - Does an equilibrium always exist? - Can there be different equilibria? - How can an equilibrium behavior be computed? - How can one set tolls on roads so that, in an equilibrium, there is no congestion and social welfare is maximized
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