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Selfish Algorithms. Juan Jose Jaramillo CS 598 IG. The Tragedy of the Commons. Garret Hardin. Tragedy of the Commons.
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Selfish Algorithms Juan Jose Jaramillo CS 598 IG
The Tragedy of the Commons Garret Hardin
Tragedy of the Commons The parable shows how unrestricted access to a resource ultimately dooms the resource because of over-exploitation. This occurs because the benefits of exploitation accrue to individuals, while the costs of exploitation are distributed between all those exploiting the resource.
The Pasture and the Herdsmen • There is a pasture open to all herdsmen. • Every herdsman tries to maximize its gain by incrementing the count of his cattle. • Adding more animals will eventually lead to overgrazing, which is a cost shared by all. • Since the gain is personal and the cost is shared among all, the rational herdsman will conclude that the best is to increase his cattle. • The tragedy is that the action of every rational herdsman will lead to the destruction of the pasture.
Free Riding on Gnutella • Almost 70% of Gnutella users share no files, and nearly 50% of all responses are returned by the top 1% of sharing hosts. • Free riding is distributed evenly between domains, so that no one group contributes significantly more than others, and that peers that volunteer to share files are not necessarily those who have desirable ones. • Thus, free riding leads to degradation of the system performance and adds vulnerability to the system. Source: “Free Riding on Gnutella” by E. Adar and B. A. Huberman
Statistics on Gnutella Source: “Free Riding on Gnutella” by E. Adar and B. A. Huberman
Discussion • Can you think of other scenarios with same problem? E.g., non-cooperative ad-hoc networks. • Why the model of the commons works in certain scenarios, like the Linux community? • Is the privatization of commonly owned resources the solution to all our problems? Are there any other solutions? What about defining rights of use?
Characterizing Selfishly Constructed Overlay Routing Networks B.-G. Chun, R. Fonseca, I. Stoica, and J. Kubiatowicz
Motivation • Overlay networks are easy to deploy, flexible, and resilient to faults, but most systems assume nodes cooperate. • In reality, nodes may behave selfishly, maximizing their own benefit even at the expense of the global optimum behavior. • This paper studies selfishly constructed networks by modeling network formation as a non-cooperative game.
Routing Network Creation Game • Modeled as a non-cooperative game with n nodes whose strategies are to select which nodes to connect to. • Cost model: • The cost to connect to node j is a function of j. • The distance between two nodes may be represented by other functions rather than the number of hopes (e.g., latency). • The possible neighbors a node can connect are a subset of all the nodes.
Definitions • The strategy of a node is the subset of nodes in the graph the node chooses to connect to. • The cost incurred by node i given the strategy is given by: • Total cost of the graph G:
Game Optimization Process • Exhaustive search: • One node at a time examines all possible configuration of links that it can add/drop and chooses the one with the least cost, given the current configuration of the network. • At each step nodes take turns in adding/dropping links links, using a fixed ordering of action.
Game Optimization Process • Randomized local search: • Same procedure as the exhaustive search, but when searching for a link to be added, node randomly chooses a node and checks whether the cost diminishes or not. • In addition, every node has a maximum degree bound: if the chosen node has reached the maximum degree, the link cannot be established.
Importance of • To add a link: • To drop a link:
Simple Scenario • All pairs of physical nodes are connected and the distance between them is one. • Different link cost functions (tj) used: • Unit-Countout: tj=1 j • Exp-Countout: linking costs are generated from an exponential distribution of mean 1.0: tj ~ exp(1) • Unit-Nodedegree: cost incurred by a node to create a link depends on the node degree of the node to connect to, i.e., tj=degree(j)
Realistic Scenario • Underlying topology is 1000 node transit-stub physical network generated by the GT-ITM. • Overlay nodes are randomly chosen from the stub domains. • Distance dG(i,j) is the sum of the latencies in the overlay path between node i and node j. • Linking cost tj is defined as:
Performance Metrics • Graph Cost. • Node Degree Distribution. • Characteristic Path Length: average shortest distance among all pairs of nodes. • Stretch: average ratio of the shortest path latency in the overlay network to the shortest path latency in the physical network. (Measures efficiency of overlay paths.)
Failure and Attack Tolerance • K: ratio of all connected node-pairs in the network over the total number of distinct node-pairs in the network. • Failures: remove a fraction of randomly selected nodes. • Attacks: remove a fraction of nodes, starting from the node with the largest degree.
Conclusions • Exp-Countout creates graphs with cores comprising nodes with small linking cost values. • Unit-Nodedegree can produce graphs with balanced node degrees without hot spots and nodes vulnerable to attacks. • Unit-Nodedegree with small creats k-regular graphs with the MaxDegree bound.
Conclusions • There is a tradeoff between performance and resilience in the networks. • Networks obtained can present desirable properties with respect to stretch and resilience, even though nodes are selfish.
Discussion • What would happen if different users have different cost functions? Will it lead to instability? • Will results significantly change if the distance metric is changed for the same physical topology?
Final Discussion • What do you think about potential selfish behavior in the following systems? • RON • PlanetLab • The Grid • Sensor networks • Ad-hoc networks • Mesh networks • How would you cope with selfishness in these networks?
