Abstract not found

We present a game-theoretic model that captures many of the intricacies of interdomain routing in today’s Internet. In this model, the strategic agents are source nodes located on a network, who aim to send traffic to a unique destination node. The interaction between the agents is dynamic and complex – asynchronous, sequential, and based on partial information. Best-reply dynamics in this model capture crucial aspects of the only interdomain routing protocol de facto, namely the Border Gateway Protocol (BGP). We study complexity and incentive-related issues in this model. Our main results are showing that in realistic and well-studied settings, BGP is incentive-compatible. I.e., not only does myopic behaviour of all players converge to a “stable ” routing outcome, but no player has motivation to unilaterally deviate from the protocol. Moreover, we show that even coalitions of players of any size cannot improve their routing outcomes by collaborating. Unlike the vast majority of works in mechanism design, our results do not require any monetary transfers (to or by the agents).

In a network with selfish users, designing and deploying a protocol determines the rules of the game by which end users interact with each other and with the network. We study the problem of designing a protocol to optimize the equilibrium behavior of the induced network game. We consider network cost-sharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal costsharing protocols for undirected and directed graphs, single-sink and multicommodity networks, different classes of cost-sharing methods, and different measures of the inefficiency of equilibria. One of our main technical tools is a complete characterization of the uniform cost-sharing protocols—protocols that are designed without foreknowledge of or assumptions on the network in which they will be deployed. We use this characterization result to identify the optimal uniform protocol in several scenarios: for example, the Shapley protocol is optimal in directed graphs, while the optimal protocol in undirected graphs, a simple priority scheme, has exponentially smaller worst-case price of anarchy than the Shapley protocol. We also provide several matching upper and lower bounds on the bestpossible performance of non-uniform cost-sharing protocols.

Abstract. We consider the solution concept of stochastic stability, and propose the price of stochastic anarchy as an alternative to the price of (Nash) anarchy for quantifying the cost of selfishness and lack of coordination in games. As a solution concept, the Nash equilibrium has disadvantages that the set of stochastically stable states of a game avoid: unlike Nash equilibria, stochastically stable states are the result of natural dynamics of computationally bounded and decentralized agents, and are resilient to small perturbations from ideal play. The price of stochastic anarchy can be viewed as a smoothed analysis of the price of anarchy, distinguishing equilibria that are resilient to noise from those that are not. To illustrate the utility of stochastic stability, we study the load balancing game on unrelated machines. This game has an unboundedly large price of Nash anarchy even when restricted to two players and two machines. We show that in the two player case, the price of stochastic anarchy is 2, and that even in the general case, the price of stochastic anarchy is bounded. We conjecture that the price of stochastic anarchy is O(m), matching the price of strong Nash anarchy without requiring player coordination. We expect that stochastic stability will be useful in understanding the relative stability of Nash equilibria in other games where the worst equilibria seem to be inherently brittle.

We give a brief and biased survey of the past, present, and future of research on the interface of theoretical computer science and game theory. 1

To better support interactive applications, individual network operators are decreasing the timers that affect BGP convergence, leading to greater diversity in the timer settings across the Internet. While decreasing timers is intended to improve routing convergence, we show that, ironically, the resulting timer heterogeneity can make routing convergence substantially worse. We examine the widely-used Min Route Advertisement Interval (MRAI) timer that rate-limits update messages to reduce router overhead. We show that, while routing systems with homogeneous MRAI timers have linear convergence time, diverse MRAIs can cause exponential increases in both the number of BGP messages and the convergence time (as measured in “activations”). We prove tight upper bounds on these metrics in terms of MRAI timer diversity in general dispute-wheel-free networks and economically sensible (Gao-Rexford) settings. We also demonstrate significant impacts on the data plane: blackholes sometimes last throughout the route-convergence process, and forwarding changes, at best, are only polynomially less frequent than routing changes. We show that these problems vanish in contiguous regions of the Internet with homogeneous MRAIs or with next-hop-based routing policies, suggesting practical strategies for mitigating the problem, especially when all routers are administered by one institution.

Abstract—We explore BGP safety, the question of whether a BGP system converges to a stable routing, in light of several BGP implementation features that have not been fully included in the previous theoretical analyses. We show that Route Flap Damping, MRAI timers, and other intra-router features can cause a router to briefly send “spurious ” announcements of less-preferred routes. We demonstrate that, even in simple configurations, this short-term spurious behavior may cause long-term divergence in global routing. We then present DPVP, a general model that unifies these sources of spurious announcements in order to examine their impact on BGP safety. In this new, more robust model of BGP behavior, we derive a necessary and sufficient condition for safety, which furthermore admits an efficient algorithm for checking BGP safety in most practical circumstances — two complementary results that have been elusive in the past decade’s worth of classical studies of BGP convergence in more simple models. We also consider the implications of spurious updates for well-known results on dispute wheels and safety under filtering. I.

We consider computational aspects of alternating move games, repeated games in which players take actions at alternating time steps rather than playing simultaneously. We show that alternating move games are more tractable than simultaneous move games: we give an FPTAS for computing an ɛ-approximate equilibrium of an alternating move game with any number of players. In contrast, it is known that for k ≥ 3 players, there is no FPTAS for computing Nash equilibria of simultaneous move repeated games unless P = P P AD. We also consider equilibria in memoryless strategies, which are guaranteed to exist in two player games. We show that for the special case of k = 2 players, all but a negligible fraction of games admit an equilibrium in pure memoryless strategies that can be found in polynomial time. Moreover, we give a PTAS to compute an ɛ-approximate equilibrium in pure memoryless strategies in any 2 player game that admits an exact equilibrium in pure memoryless strategies. 1

Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network costsharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal cost-sharing protocols for undirected and directed graphs, single-sink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the cost-sharing protocols that only induce network games with pure-strategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs, and that simple priority protocols are essentially optimal in undirected graphs.

Abstract. The class of weakly acyclic games, which includes potential games and dominance-solvable games, captures many practical application domains. Informally, a weakly acyclic game is one where natural distributed dynamics, such as better-response dynamics, cannot enter inescapable oscillations. We establish a novel link between such games and the existence of pure Nash equilibria in subgames. Specifically, we show that the existence of a unique pure Nash equilibrium in every subgame implies the weak acyclicity of a game. In contrast, the possible existence of multiple pure Nash equilibria in every subgame is insufficient for weak acyclicity. 1