The power of mediation in an extended El Farol game

A mediator implements a correlated equilibrium when it pro- poses a strategy to each player con dentially such that the mediator's proposal is the best interest for every player to follow. In this paper, we present a mediator that implements the best correlated equilibrium for an extended El Farol game with symmetric players. The extended El Farol game we consider incorporates both negative and positive network e ffects. We study the degree to which this type of mediator can decrease the overall social cost. In particular, we give an exact characterization of Mediation Value (MV) and Enforcement Value (EV) for this game. MV is the ratio of the minimum social cost over all Nash equilibria to the minimum social cost over all mediators of this type, and EV is the ratio of the minimum social cost over all mediators of this type to the optimal social cost. This sort of exact characterization is uncommon for games with both kinds of network e ffects. An interesting outcome of our results is that both the MV and EV values can be unbounded for our game

Selfishness and Malice in Distributed Systems

Large-scale distributed systems are increasingly prevalent. Two issues can impact the performance of such systems: selfishness and malice. Selfish players can reduce social welfare of games, and malicious nodes can disrupt networks. In this dissertation, we provide algorithms to address both of these issues. One approach to ameliorating selfishness in large networks is the idea of a mediator. A mediator implements a correlated equilibrium when it proposes a strategy to each player privately such that the mediators proposal is the best interest for every player to follow. In this dissertation, we present a mediator that implements the best correlated equilibrium for an extended El Farol game. The extended El Farol game we consider has both positive and negative network effects. We study the degree to which this type of mediator can decrease the social cost. In particular, we give an exact characterization of Mediation Value (MV) and Enforcement Value (EV) for this game. MV measures the efficiency of our mediator compared to the best Nash equilibrium, and EV measures the efficiency of our mediator compared to the optimal social cost. This sort of exact characterization is uncommon for games with both kinds of network effects. An interesting outcome of our results is that both the MV and EV values can be unbounded for our game. Recent years have seen significant interest in designing networks that are self-healing in the sense that they can automatically recover from adversarial attacks. Previous work shows that it is possible for a network to automatically recover, even when an adversary repeatedly deletes nodes in the network. However, there have not yet been any algorithms that self-heal in the case where an adversary takes over nodes in the network. In this dissertation, we address this gap. In particular, we describe a communication network over n nodes that ensures the following properties, even when an adversary controls up to t ≤ (1/4 − ε)n nodes, for any constant ε \u3e 0. First, the network provides point-to-point communication with message cost and latency that are asymptotically optimal in an amortized sense. Second, the expected total number of message corruptions is O(t(log* n)^2), after which the adversarially controlled nodes are effectively quarantined so that they cause no more corruptions. In the problem of reliable multiparty computation (RMC), there are n parties, each with an individual input, and the parties want to jointly and reliably compute a function f over n inputs, assuming that it is not necessary to maintain the privacy of the inputs. The problem is complicated by the fact that an omniscient adversary controls a hidden fraction of the parties. We describe a self-healing algorithm for this problem. In particular, for a fixed function f, with n parties and m gates, we describe how to perform RMC repeatedly as the inputs to f change. Our algorithm maintains the following properties, even when an adversary controls up to t ≤ (1/4 − ε)n parties, for any constant ε \u3e 0. First, our algorithm performs each reliable computation with the following amortized resource costs: O(m + n log n) messages, O(m + n log n) computational operations, and O(\ell) latency, where \ell is the depth of the circuit that computes f. Second, the expected total number of corruptions is O(t(log* n)^2). Our empirical results show that the message cost reduces by up to a factor of 60 for communication and a factor of 65 for computation, compared to algorithms of no self-healing

Complexity results for some classes of strategic games

Game theory is a branch of applied mathematics studying the interaction of self-interested entities, so-called agents. Its central objects of study are games, mathematical models of real-world interaction, and solution concepts that single out certain outcomes of a game that are meaningful in some way. The solutions thus produced can then be viewed both from a descriptive and from a normative perspective. The rise of the Internet as a computational platform where a substantial part of today's strategic interaction takes place has spurred additional interest in game theory as an analytical tool, and has brought it to the attention of a wider audience in computer science. An important aspect of real-world decision-making, and one that has received only little attention in the early days of game theory, is that agents may be subject to resource constraints. The young field of algorithmic game theory has set out to address this shortcoming using techniques from computer science, and in particular from computational complexity theory. One of the defining problems of algorithmic game theory concerns the computation of solution concepts. Finding a Nash equilibrium, for example, i.e., an outcome where no single agent can gain by changing his strategy, was considered one of the most important problems on the boundary of P, the complexity class commonly associated with efficient computation, until it was recently shown complete for the class PPAD. This rather negative result for general games has not settled the question, however, but immediately raises several new ones: First, can Nash equilibria be approximated, i.e., is it possible to efficiently find a solution such that the potential gain from a unilateral deviation is small? Second, are there interesting classes of games that do allow for an exact solution to be computed efficiently? Third, are there alternative solution concepts that are computationally tractable, and how does the value of solutions selected by these concepts compare to those selected by established solution concepts? The work reported in this thesis is part of the effort to answer the latter two questions. We study the complexity of well-known solution concepts, like Nash equilibrium and iterated dominance, in various classes of games that are both natural and practically relevant: ranking games, where outcomes are rankings of the players; anonymous games, where players do not distinguish between the other players in the game; and graphical games, where the well-being of any particular player depends only on the actions of a small group other players. In ranking games, we further compare the payoffs obtainable in Nash equilibrium outcomes with those of alternative solution concepts that are easy to compute. We finally study, in general games, solution concepts that try to remedy some of the shortcomings associated with Nash equilibrium, like the need for randomization to achieve a stable outcome

On strictly competitive multi-player games

We embark on an initial study of a new class of strategic (normal-form) games, so-called ranking games, in which the payoff to each agent solely depends on his position in a ranking of the agents induced by their actions. This definition is motivated by the observation that in many strategic situations such as parlor games, competitive economic scenarios, and some social choice settings, players are merely interested in performing optimal relative to their opponents rather than in absolute measures. A simple but important subclass of ranking games are single-winner games where in any outcome one agent wins and all others lose. We investigate the computational complexity of a variety of common game-theoretic solution concepts in ranking games and deliver hardness results for iterated weak dominance and mixed Nash equilibria when there are more than two players and pure Nash equilibria when the number of players is unbounded. This dashes hope that multi-player ranking games can be solved efficiently, despite the structural restrictions of these games