THE PRICE OF NASH EQUILIBRIA IN MULTICAST TRANSMISSION GAMES

2010 ◽  
Vol 11 (03n04) ◽  
pp. 97-120 ◽  
Author(s):  
VITTORIO BILÒ
Keyword(s):  
Nash Equilibrium ◽  
Cost Sharing ◽  
Price Of Anarchy ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Price Of Stability ◽  
Common Source ◽  
Cost Share ◽  
Worst Case ◽  
The Cost

We consider the problem of sharing the cost of multicast transmissions in non-cooperative undirected networks where a set of receivers R wants to be connected to a common source s. The set of choices available to each receiver r ∈ R is represented by the set of all (s, r)-paths in the network. Given the choices performed by all the receivers, a public known cost sharing method determines the cost share to be charged to each of them. Receivers are selfish agents aiming to obtain the transmission at the minimum cost share and their interactions create a non-cooperative game. Devising cost sharing methods yielding games whose price of anarchy (price of stability), defined as the worst-case (best-case) ratio between the cost of a Nash equilibrium and that of an optimal solution, is not too high is thus of fundamental importance in non-cooperative network design. Moreover, since cost sharing games naturally arise in socio-economical contests, it is convenient for a cost sharing method to meet some constraining properties. In this paper, we first define several such properties and analyze their impact on the prices of anarchy and stability. We also reconsider all the methods known so far by classifying them according to which properties they satisfy and giving the first non-trivial lower bounds on their price of stability. Finally, we propose a new method, namely the free-riders method, which admits a polynomial time algorithm for computing a pure Nash equilibrium whose cost is at most twice the optimal one. Some of the ideas characterizing our approach have been independently proposed in Ref. 10.

OIL AND THE ENVIRONMENT - CALIFORNIA CASE STUDY

1976 ◽  
Vol 16 (1) ◽  
pp. 137
Author(s):  
D. W. Barnett
Keyword(s):  
Energy Production ◽  
Social Cost ◽  
Shadow Price ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Gulf Of Alaska ◽  
Outer Continental Shelf ◽  
Trade Offs ◽  
The Cost ◽  
Prudhoe Bay

USA environmentalists have tended to oppose all new energy developments. Their efforts may be counterproductive because opposition to, say, offshore oil directly leads to the continued use of other energy sources that may have a higher social cost. Rather than attempting to eliminate all pollution from energy production, which would be prohibitively expensive, one should minimize the social cost of energy production for the given demand.Linear programming is used to rank various oils (California State and Outer Continental Shelf (OCS), Gulf of Alaska, Prudhoe Bay, Athabasca tar sands, oil shale and certain foreign crudes) in terms of their social desirability. The objective is to minimize the cost of supplying the California market, subject to resource, sulphur and oil spill constraints.Social desirability is indicated by the inclusion of the oil in the optimal solution and the size of the associated shadow price. The larger the shadow price, the greater the benefits of increased production. The more negative, the greater the cost associated with forcing consumption of that fuel. The environmental shadow prices indicate the size of the trade-off between a particular environmental standard and minimum cost. The trade-offs can be surprisingly large. Any reasonable spill standard can be achieved by changing the development pattern. Generally, the further offshore, the smaller is the environmental degradation, but the more expensive is the oil. Foreign oils can be economically and environmentally inferior to domestic oils. Crude from the California OCS, San Joaquin Valley and Prudhoe Bay appears a valuable resource, while the Gulf of Alaska, synthetic and foreign crudes appear marginal to submarginal.The methodology could be readily adapted to the Australian scene.

scholarly journals Equilibrium Inefficiency and Computation in Cost-Sharing Games in Real-Time Scheduling Systems

Algorithms ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 103
Author(s):  
Eirini Georgoulaki ◽  
Kostas Kollias ◽  
Tami Tamir
Keyword(s):  
Real Time ◽  
Cost Sharing ◽  
Price Of Anarchy ◽  
Time Slot ◽  
Optimal Solution ◽  
Restricted Class ◽  
Real Time Scheduling ◽  
Payment Mechanism ◽  
Congestion Effect ◽  
Time Scheduling

We study cost-sharing games in real-time scheduling systems where the server’s activation cost in every time slot is a function of its load. We focus on monomial cost functions and consider both the case when the degree is less than one (inducing positive congestion effect for the jobs) and when it is greater than one (inducing negative congestion effect for the jobs). For the former case, we provide tight bounds on the price of anarchy, and show that the price of anarchy grows to infinity as a polynomial of the number of jobs in the game. For the latter, we observe that existing results provide constant and tight (asymptotically in the degree of the monomial) bounds on the price of anarchy. We then turn to analyze payment mechanism with arbitrary cost-sharing, that is, when the strategy of a player includes also its payment. We show that our mechanism reduces the price of anarchy of games with n jobs and unit server costs from Θ(n) to 2. We also show that, for a restricted class of instances, a similar improvement is achieved for monomial server costs. This is not the case, however, for unrestricted instances of monomial costs, for which we prove that the price of anarchy remains super-constant for our mechanism. For systems with load-independent activation costs, we show that our mechanism can produce an optimal solution which is stable against coordinated deviations.

scholarly journals Optimization of open flow controller placement in software defined networks

2021 ◽  
Vol 11 (4) ◽  
pp. 3145
Author(s):  
Raghda Salam Al mahdawi ◽  
Huda M. Salih
Keyword(s):  
Network Architecture ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Open Flow ◽  
Processing Power ◽  
Input Size ◽  
Different Types ◽  
Network Topologies ◽  
High Level ◽  
The Cost

The world is entering into the era of Big Data where computer networks are an essential part. However, the current network architecture is not very convenient to configure such leap. Software defined network (SDN) is a new network architecture which argues the separation of control and data planes of the network devices by centralizing the former in high level, centralised devices and efficient supervisors, called controllers. This paper proposes a mathematical model that helps optimizing the locations of the controllers within the network while minimizing the overall cost under realistic constrains. Our method includes finding the minimum cost of placing the controllers; these costs are the network latency, controller processing power and link bandwidth. Different types of network topologies have been adopted to consider the data profile of the controllers, links of controllers and locations of switches. The results showed that as the size of input data increased, the time to find the optimal solution also increased in a non-polynomial time. In addition, the cost of solution is increased linearly with the input size. Furthermore, when increasing allocating possible locations of the controllers, for the same number of switches, the cost was found to be less.

scholarly journals Cost of cooperation for scheduling meetings

2010 ◽  
Vol 7 (3) ◽  
pp. 551-568 ◽  
Author(s):  
Alon Grubshtein ◽  
Amnon Meisels
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Price Of Anarchy ◽  
Distributed Optimization ◽  
Objective Functions ◽  
Game Theoretic ◽  
The Cost ◽  
Global Objective

Scheduling meetings among agents can be represented as a game - the Meetings Scheduling Game (MSG). In its simplest form, the two-person MSG is shown to have a price of anarchy (PoA) which is bounded by 0.5. The PoA bound provides a measure on the efficiency of the worst Nash Equilibrium in social (or global) terms. The approach taken by the present paper introduces the Cost of Cooperation (CoC) for games. The CoC is defined with respect to different global objective functions and provides a measure on the efficiency of a solution for each participant (personal). Applying an ?egalitarian? objective, that maximizes the minimal gain among all participating agents, on our simple example results in a CoC which is non positive for all agents. This makes the MSG a cooperation game. The concepts are defined and examples are given within the context of the MSG. Although not all games are cooperation games, a game may be revised by adding a mediator (or with a slight change of its mechanism) so that it behaves as a cooperation game. Rational participants can cooperate (by taking part in a distributed optimization protocol) and receive a payoff which will be at least as high as the worst gain expected by a game theoretic equilibrium point.

Prices of Anarchy of Selfish 2D Bin Packing Games

2019 ◽  
Vol 30 (03) ◽  
pp. 355-374
Author(s):  
Cristina G. Fernandes ◽  
Carlos E. Ferreira ◽  
Flávio K. Miyazawa ◽  
Yoshiko Wakabayashi
Keyword(s):  
Nash Equilibrium ◽  
Bin Packing ◽  
Price Of Anarchy ◽  
Dimensional Case ◽  
Theoretical Problem ◽  
Single Item ◽  
Strong Nash Equilibrium ◽  
Square Packing ◽  
The Cost

We consider a game-theoretical problem called selfish 2-dimensional bin packing game, a generalization of the 1-dimensional case already treated in the literature. In this game, the items to be packed are rectangles, and the bins are unit squares. The game starts with a set of items arbitrarily packed in bins. The cost of an item is defined as the ratio between its area and the total occupied area of the respective bin. Each item is a selfish player that wants to minimize its cost. A migration of an item to another bin is allowed only when its cost is decreased. We show that this game always converges to a Nash equilibrium (a stable packing where no single item can decrease its cost by migrating to another bin). We show that the pure price of anarchy of this game is unbounded, so we address the particular case where all items are squares. We show that the pure price of anarchy of the selfish square packing game is at least [Formula: see text] and at most [Formula: see text]. We also present analogous results for the strong Nash equilibrium (a stable packing where no nonempty set of items can simultaneously migrate to another common bin and decrease the cost of each item in the set). We show that the strong price of anarchy when all items are squares is at least [Formula: see text] and at most [Formula: see text].

Feasibility analysis: Evaluating sites for possible renewable energy options and their implications to minimize the cost

2020 ◽  
pp. 002072092092853 ◽  
Author(s):  
Eklas Hossain ◽  
Feng Shi ◽  
Ramazan Bayindir ◽  
Jakir Hossain
Keyword(s):  
Renewable Energy ◽  
Alternative Energy ◽  
Renewable Energy Sources ◽  
Minimum Cost ◽  
Energy Sources ◽  
Case Scenario ◽  
Worst Case ◽  
Bad Weather ◽  
Energy Options ◽  
The Cost

Renewable energy sources are replacing other energy sources to minimize the cost of due to the conventional sources of energy. Solar and wind are readily available sources which will minimize the cost of electricity if implemented properly. Considering the weather and other relevant advantages, solar energy is a favorable option for a particular site. But it is extremely difficult for the implementation of the suggested renewable energy in a site which already has specific resources and existing infrastructure to replace. Several factors should be counted in for the selection and implementation of appropriate renewable source for fulfilling the demand. As a possible energy option, on-grid infrastructure is selected looking at its low necessity of development and hardware cost. This paper aims to impart the detailed designs of alternative energy options that will offset the annual irrigation costs of the Rainbow Youth Golf Education Program in Klamath County. Using simulator, a practical modeling of the system is performed to look at the cost associated with each case. After selecting a combination with the minimum cost, it is shown that the model decreases the irrigation cost compared to previous year. Other technological implications are also evaluated. Finally, worst case scenario is modeled using the simulator to show that even in the bad weather, the site’s energy supply model serves well both electrically and economically.

scholarly journals Selfishness Level of Strategic Games

2014 ◽  
Vol 49 ◽  
pp. 207-240 ◽  
Author(s):  
K. R. Apt ◽  
G. Schaefer
Keyword(s):  
Nash Equilibrium ◽  
Social Welfare ◽  
Price Of Anarchy ◽  
Congestion Games ◽  
Price Of Stability ◽  
Social Optimum ◽  
Potential Game ◽  
Strategic Games ◽  
The Social ◽  
The Impact

We introduce a new measure of the discrepancy in strategic games between the social welfare in a Nash equilibrium and in a social optimum, that we call selfishness level. It is the smallest fraction of the social welfare that needs to be offered to each player to achieve that a social optimum is realized in a pure Nash equilibrium. The selfishness level is unrelated to the price of stability and the price of anarchy and is invariant under positive linear transformations of the payoff functions. Also, it naturally applies to other solution concepts and other forms of games. We study the selfishness level of several well-known strategic games. This allows us to quantify the implicit tension within a game between players' individual interests and the impact of their decisions on the society as a whole. Our analyses reveal that the selfishness level often provides a deeper understanding of the characteristics of the underlying game that influence the players' willingness to cooperate. In particular, the selfishness level of finite ordinal potential games is finite, while that of weakly acyclic games can be infinite. We derive explicit bounds on the selfishness level of fair cost sharing games and linear congestion games, which depend on specific parameters of the underlying game but are independent of the number of players. Further, we show that the selfishness level of the $n$-players Prisoner's Dilemma is c/(b(n-1)-c), where b and c are the benefit and cost for cooperation, respectively, that of the n-players public goods game is (1-c/n)/(c-1), where c is the public good multiplier, and that of the Traveler's Dilemma game is (b-1)/2, where b is the bonus. Finally, the selfishness level of Cournot competition (an example of an infinite ordinal potential game), Tragedy of the Commons, and Bertrand competition is infinite.

THE PRICE OF ANARCHY FOR RESTRICTED PARALLEL LINKS

2006 ◽  
Vol 16 (01) ◽  
pp. 117-131 ◽  
Author(s):  
MARTIN GAIRING ◽  
THOMAS LÜCKING ◽  
MARIOS MAVRONICOLAS ◽  
BURKHARD MONIEN
Keyword(s):  
Nash Equilibrium ◽  
System Performance ◽  
Nash Equilibria ◽  
Price Of Anarchy ◽  
Pure Nash Equilibrium ◽  
Worst Case ◽  
Comprehensive Collection ◽  
Parallel Links ◽  
Special Case

In the model of restricted parallel links, n users must be routed on m parallel links under the restriction that the link for each user be chosen from a certain set of allowed links for the user. In a (pure) Nash equilibrium, no user may improve its own Individual Cost (latency) by unilaterally switching to another link from its set of allowed links. The Price of Anarchy is a widely adopted measure of the worst-case loss (relative to optimum) in system performance (maximum latency) incurred in a Nash equilibrium. In this work, we present a comprehensive collection of bounds on Price of Anarchy for the model of restricted parallel links and for the special case of pure Nash equilibria. Specifically, we prove: • For the case of identical users and identical links, the Price of Anarchy is [Formula: see text]. • For the case of identical users, the Price of Anarchy is [Formula: see text]. • For the case of identical links, the Price of Anarchy is [Formula: see text], which is asymptotically tight. • For the most general case of arbitrary users and related links, the Price of Anarchy is at least m – 1 and less than m. The shown bounds reveal the dependence of the Price of Anarchy on n and m for all possible assumptions on users and links.

scholarly journals Additively Separable Hedonic Games with Social Context

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 71
Author(s):  
Gianpiero Monaco ◽  
Luca Moscardelli ◽  
Yllka Velaj
Keyword(s):  
Nash Equilibrium ◽  
Social Context ◽  
Nash Equilibria ◽  
Price Of Anarchy ◽  
Strategic Interaction ◽  
Price Of Stability ◽  
Fundamental Class ◽  
New Model ◽  
Hedonic Games ◽  
And Performance

In hedonic games, coalitions are created as a result of the strategic interaction of independent players. In particular, in additively separable hedonic games, every player has valuations for all other ones, and the utility for belonging to a coalition is given by the sum of the valuations for all other players belonging to it. So far, non-cooperative hedonic games have been considered in the literature only with respect to totally selfish players. Starting from the fundamental class of additively separable hedonic games, we define and study a new model in which, given a social graph, players also care about the happiness of their friends: we call this class of games social context additively separable hedonic games (SCASHGs). We focus on the fundamental stability notion of Nash equilibrium, and study the existence, convergence and performance of stable outcomes (with respect to the classical notions of price of anarchy and price of stability) in SCASHGs. In particular, we show that SCASHGs are potential games, and therefore Nash equilibria always exist and can be reached after a sequence of Nash moves of the players. Finally, we provide tight or asymptotically tight bounds on the price of anarchy and the price of stability of SCASHGs.

scholarly journals On Non-Cooperativeness in Social Distance Games

2019 ◽  
Vol 66 ◽  
pp. 625-653
Author(s):  
Alkida Balliu ◽  
Michele Flammini ◽  
Giovanna Melideo ◽  
Dennis Olivetti
Keyword(s):  
Nash Equilibrium ◽  
Polynomial Time ◽  
Social Distance ◽  
Price Of Anarchy ◽  
Cluster Formation ◽  
Solution Concept ◽  
Price Of Stability ◽  
The Social ◽  
Np Complete ◽  
Inverse Distance

We consider Social Distance Games (SDGs), that is cluster formation games in which the utility of each agent only depends on the composition of the cluster she belongs to, proportionally to her harmonic centrality, i.e., to the average inverse distance from the other agents in the cluster. Under a non-cooperative perspective, we adopt Nash stable outcomes, in which no agent can improve her utility by unilaterally changing her coalition, as the target solution concept. Although a Nash equilibrium for a SDG can always be computed in polynomial time, we obtain a negative result concerning the game convergence and we prove that computing a Nash equilibrium that maximizes the social welfare is NP-hard by a polynomial time reduction from the NP-complete Restricted Exact Cover by 3-Sets problem. We then focus on the performance of Nash equilibria and provide matching upper bound and lower bounds on the price of anarchy of Θ(n), where n is the number of nodes of the underlying graph. Moreover, we show that there exists a class of SDGs having a lower bound on the price of stability of 6/5 − ε, for any ε > 0. Finally, we characterize the price of stability 5 of SDGs for graphs with girth 4 and girth at least 5, the girth being the length of the shortest cycle in the graph.

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