Bugra Caskurlu

Exact and Approximate Equilibria for Optimal Group Network Formation

We consider a process called Group Network Formation Game, which represents the scenario when strategic agents are building a network together. In our game, agents can have extremely varied connectivity requirements, and attempt to satisfy those requirements by purchasing links in the network. We show a variety of results about equilibrium properties in such games, including the fact that the price of stability is 1 when all nodes in the network are owned by players, and that doubling the number of players creates an equilibrium as good as the optimum centralized solution. For the most general case, we show the existence of a 2-approximate Nash equilibrium that is as good as the centralized optimum solution, as well as how to compute good approximate equilibria in polynomial time. Our results essentially imply that for a variety of connectivity requirements, giving agents more freedom can paradoxically result in more efficient outcomes.

Price of Stability in Survivable Network Design

We study the survivable version of the game theoretic network formation model known as the Connection Game, originally introduced in [4]. In this model, players attempt to connect to a common source node in a network by purchasing edges, and sharing their costs with other players. We introduce the survivable version of this game, where each player desires 2 edge-disjoint connections between her pair of nodes instead of just a single connecting path, and analyze the quality of exact and approximate Nash equilibria. For the special case where each node represents a player, we show that Nash equilibria are guaranteed to exist and price of stability is 1. For the general version of the Survivable Connection Game, we show that there always exists a 2-approximate Nash equilibrium that is as cheap as the socially optimal solution.

Capacity allocation games for network-coded multicast streaming

In this paper, we formulate and study a capacity allocation game between a set of receivers (players) that are interested in receiving multicast data (video/multimedia) being streamed from a server through a multihop network. We consider fractional multicast streaming, where the multicast stream from the source (origin-server) to any particular receiver (end-user) can be split over multiple paths. The receivers are selfish and noncooperative, but must collaboratively purchase capacities of links in the network, as necessary for delivery of the multicast stream from the source to the individual receivers, assuming that the multicast stream is network-coded. For this multicast capacity allocation (network formation) game, we show that the Nash equilibrium is guaranteed to exist in general. For a 2-tier network model where the receivers must obtain the multicast data from the source through a set of relay nodes, we show that the price of stability is at most 2, and provide a polynomial-time algorithm that computes a Nash equilibrium whose social cost is within a factor of 2 of the socially optimum solution. For more general network models, we show that there exists a 2-approximate Nash equilibrium, whose cost is at most two times the social optimum. We also give a polynomial-time algorithm that computes a (2+∈)-approximate Nash equilibrium for any ∈ > 0, whose cost is at most two times the social optimum. Simulation studies show that our algorithms generate efficient Nash equilibrium allocation solutions for a vast majority of randomly generated network topologies.

Exact and approximate equilibria for optimal group network formation

Abstract We consider a process called the Group Network Formation Game, which represents the scenario when strategic agents are building a network together. In our game, agents can have extremely varied connectivity requirements, and attempt to satisfy those requirements by purchasing links in the network. We show a variety of results about equilibrium properties in such games, including the fact that the price of stability is 1 when all nodes in the network are owned by players, and that doubling the number of players creates an equilibrium as good as the optimum centralized solution. For the general case, we show the existence of a 2-approximate Nash equilibrium that is as good as the centralized optimum solution, as well as how to compute good approximate equilibria in polynomial time. Our results essentially imply that for a variety of connectivity requirements, giving agents more freedom can paradoxically result in more efficient outcomes.

Strategic Multiway Cut and Multicut Games

We consider cut games where players want to cut themselves off from different parts of a network. These games arise when players want to secure themselves from areas of potential infection. For the game-theoretic version of Multiway Cut, we prove that the price of stability is 1, i.e., there exists a Nash equilibrium as good as the centralized optimum. For the game-theoretic version of Multicut, we show that there exists a 2-approximate equilibrium as good as the centralized optimum. We also give poly-time algorithms for finding exact and approximate equilibria in these games.

Strategic multiway cut and multicut games

We consider cut games where players want to cut themselves off from different parts of a network. These games arise when players want to secure themselves from areas of potential infection. For the game-theoretic version of Multiway Cut, we prove that the price of stability is 1, i.e., there exists a Nash equilibrium as good as the centralized optimum. For the game-theoretic version of Multicut, we show that there exists a 2-approximate equilibrium as good as the centralized optimum. We also give poly-time algorithms for finding exact and approximate equilibria in these games.

Partition equilibrium always exists in resource selection games

We consider the existence of Partition Equilibrium in Resource Selection Games. Super-strong equilibrium, where no subset of players has an incentive to change their strategies collectively, does not always exist in such games. We show, however, that partition equilibrium (introduced in [4] to model coalitions arising in a social context) always exists in general resource selection games, as well as how to compute it efficiently. In a partition equilibrium, the set of players has a fixed partition into coalitions, and the only deviations considered are by coalitions that are sets in this partition. Our algorithm to compute a partition equilibrium in any resource selection game (i.e., load balancing game) settles the open question from [4] about existence of partition equilibrium in general resource selection games. Moreover, we show how to always find a partition equilibrium which is also a Nash equilibrium. This implies that in resource selection games, we do not need to sacrifice the stability of individual players when forming solutions stable against coalitional deviations. In addition, while super-strong equilibrium may not exist in resource selection games, we show that its existence can be decided efficiently, and how to find one if it exists.