108 research outputs found
Designing Networks with Good Equilibria under Uncertainty
We consider the problem of designing network cost-sharing protocols with good
equilibria under uncertainty. The underlying game is a multicast game in a
rooted undirected graph with nonnegative edge costs. A set of k terminal
vertices or players need to establish connectivity with the root. The social
optimum is the Minimum Steiner Tree. We are interested in situations where the
designer has incomplete information about the input. We propose two different
models, the adversarial and the stochastic. In both models, the designer has
prior knowledge of the underlying metric but the requested subset of the
players is not known and is activated either in an adversarial manner
(adversarial model) or is drawn from a known probability distribution
(stochastic model).
In the adversarial model, the designer's goal is to choose a single,
universal protocol that has low Price of Anarchy (PoA) for all possible
requested subsets of players. The main question we address is: to what extent
can prior knowledge of the underlying metric help in the design? We first
demonstrate that there exist graphs (outerplanar) where knowledge of the
underlying metric can dramatically improve the performance of good network
design. Then, in our main technical result, we show that there exist graph
metrics, for which knowing the underlying metric does not help and any
universal protocol has PoA of , which is tight. We attack this
problem by developing new techniques that employ powerful tools from extremal
combinatorics, and more specifically Ramsey Theory in high dimensional
hypercubes.
Then we switch to the stochastic model, where each player is independently
activated. We show that there exists a randomized ordered protocol that
achieves constant PoA. By using standard derandomization techniques, we produce
a deterministic ordered protocol with constant PoA.Comment: This version has additional results about stochastic inpu
Approximately Fair Cost Allocation in Metric Traveling Salesman Games
A traveling salesman game is a cooperative game . Here N, the set of players, is the set of cities (or the vertices of the complete graph) andc D is the characteristic function where D is the underlying cost matrix. For all S⊆N, define c D (S) to be the cost of a minimum cost Hamiltonian tour through the vertices of S∪{0} where is called as the home city. Define Core ({\mathcal{G}})=\{x\in \Re^{|N|}:x(N)=c_{D}(N)\ \mbox{and}\ \forall S\subseteq N,x(S)\le c_{D}(S)\} as the core of a traveling salesman game . Okamoto (Discrete Appl. Math. 138:349-369, [2004]) conjectured that for the traveling salesman game with D satisfying triangle inequality, the problem of testing whether Core is empty or not is -hard. We prove that this conjecture is true. This result directly implies the -hardness for the general case when D is asymmetric. We also study approximately fair cost allocations for these games. For this, we introduce the cycle cover games and show that the core of a cycle cover game is non-empty by finding a fair cost allocation vector in polynomial time. For a traveling salesman game, let \epsilon\mbox{-Core}({\mathcal{G}})=\{x\in \Re^{|N|}:x(N)\ge c_{D}(N) and ∀ S⊆N, x(S)≤ε⋅c D (S)} be an ε-approximate core, for a given ε>1. By viewing an approximate fair cost allocation vector for this game as a sum of exact fair cost allocation vectors of several related cycle cover games, we provide a polynomial time algorithm demonstrating the non-emptiness of the log 2(|N|−1)-approximate core by exhibiting a vector in this approximate core for the asymmetric traveling salesman game. We improve it further by finding a -approximate core in polynomial time for some constantc. We also show that there exists an ε 0>1 such that it is -hard to decide whether ε 0-Core is empty or no
Generating greenhouse gas cutting incentives when allocating carbon dioxide emissions to shipments in road freight transportation
Road freight transportation accounts for a great share of the anthropogenic greenhouse gas (GHG) emissions. In order to provide a common methodology for carbon accounting related to transport activities, the European Committee for Standardization has published the European Norm EN-16258. Unfortunately, EN-16258 contains gaps and ambiguities and leaves room for interpretation, which makes the comparison of the environmental performance of different logistics networks still difficult and hinders the identification of best practices. This research contributes to the identification of particularly meaningful principles for the allocation of GHG to shipments in road freight transportation by presenting an analytical framework for studying the performance of the EN-16258 allocation schemes with respect to accuracy, fairness, and the GHG minimizing incentive. In doing so, we continue previous studies that analyzed two important aspects of the EN-16258 allocation rules: accuracy and fairness. This study provides further insights into this allocation problem by investigating the incentive power of the different allocation schemes to opt for the GHG minimal way of running a road freight network. First, we complement the list of transport scenarios introduced in prior studies and present two novel scenarios. Second, we carry out a series of numerical experiments to compare the EN-16258 allocation rules with respect to accuracy, fairness, and the GHG minimizing incentive. We find that the results may differ significantly for the two scenarios, suggesting a case-by-case recommendation. This is particularly interesting because the first scenario confirms the results of the prior studies, while the second scenario rather contradicts them
Modelling interactive behaviour, and solution concepts
The final chapter of this thesis extensively studies fall back equilibrium. This equilibrium concept is a refinement of Nash equilibrium, which is the most fundamental solution concept in non-cooperative game theory.
Modelling interactive behaviour, and solution concepts.
The final chapter of this thesis extensively studies fall back equilibrium. This equilibrium concept is a refinement of Nash equilibrium, which is the most fundamental solution concept in non-cooperative game theory.
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