Computational Extensive-Form Games

We define solution concepts appropriate for computationally bounded players playing a fixed finite game. To do so, we need to define what it means for a \emph{computational game}, which is a sequence of games that get larger in some appropriate sense, to represent a single finite underlying extensive-form game. Roughly speaking, we require all the games in the sequence to have essentially the same structure as the underlying game, except that two histories that are indistinguishable (i.e., in the same information set) in the underlying game may correspond to histories that are only computationally indistinguishable in the computational game. We define a computational version of both Nash equilibrium and sequential equilibrium for computational games, and show that every Nash (resp., sequential) equilibrium in the underlying game corresponds to a computational Nash (resp., sequential) equilibrium in the computational game. One advantage of our approach is that if a cryptographic protocol represents an abstract game, then we can analyze its strategic behavior in the abstract game, and thus separate the cryptographic analysis of the protocol from the strategic analysis

Adaptive Seeding in Social Networks

The algorithmic challenge of maximizing information diffusion through word-of-mouth processes in social networks has been heavily studied in the past decade. While there has been immense progress and an impressive arsenal of techniques has been developed, the algorithmic frameworks make idealized assumptions regarding access to the network that can often result in poor performance of state-of-the-art techniques. In this paper we introduce a new framework which we call Adaptive Seeding. The framework is a two-stage stochastic optimization model designed to leverage the potential that typically lies in neighboring nodes of arbitrary samples of social networks. Our main result is an algorithm which provides a constant factor approximation to the optimal adaptive policy for any influence function in the Triggering model

Locally Adaptive Optimization: Adaptive Seeding for Monotone Submodular Functions

The Adaptive Seeding problem is an algorithmic challenge motivated by influence maximization in social networks: One seeks to select among certain accessible nodes in a network, and then select, adaptively, among neighbors of those nodes as they become accessible in order to maximize a global objective function. More generally, adaptive seeding is a stochastic optimization framework where the choices in the first stage affect the realizations in the second stage, over which we aim to optimize. Our main result is a $(1-1/e)^2$-approximation for the adaptive seeding problem for any monotone submodular function. While adaptive policies are often approximated via non-adaptive policies, our algorithm is based on a novel method we call \emph{locally-adaptive} policies. These policies combine a non-adaptive global structure, with local adaptive optimizations. This method enables the $(1-1/e)^2$-approximation for general monotone submodular functions and circumvents some of the impossibilities associated with non-adaptive policies. We also introduce a fundamental problem in submodular optimization that may be of independent interest: given a ground set of elements where every element appears with some small probability, find a set of expected size at most $k$ that has the highest expected value over the realization of the elements. We show a surprising result: there are classes of monotone submodular functions (including coverage) that can be approximated almost optimally as the probability vanishes. For general monotone submodular functions we show via a reduction from \textsc{Planted-Clique} that approximations for this problem are not likely to be obtainable. This optimization problem is an important tool for adaptive seeding via non-adaptive policies, and its hardness motivates the introduction of \emph{locally-adaptive} policies we use in the main result

The Complexity of Social Coordination

Coordination is a challenging everyday task; just think of the last time you organized a party or a meeting involving several people. As a growing part of our social and professional life goes online, an opportunity for an improved coordination process arises. Recently, Gupta et al. proposed entangled queries as a declarative abstraction for data-driven coordination, where the difficulty of the coordination task is shifted from the user to the database. Unfortunately, evaluating entangled queries is very hard, and thus previous work considered only a restricted class of queries that satisfy safety (the coordination partners are fixed) and uniqueness (all queries need to be satisfied). In this paper we significantly extend the class of feasible entangled queries beyond uniqueness and safety. First, we show that we can simply drop uniqueness and still efficiently evaluate a set of safe entangled queries. Second, we show that as long as all users coordinate on the same set of attributes, we can give an efficient algorithm for coordination even if the set of queries does not satisfy safety. In an experimental evaluation we show that our algorithms are feasible for a wide spectrum of coordination scenarios.Comment: VLDB201

Analysis of the Blockchain Protocol in Asynchronous Networks

Nakamoto\u27s famous blockchain protocol enables achieving consensus in a so-called \emph{permissionless setting}---anyone can join (or leave) the protocol execution, and the protocol instructions do not depend on the identities of the players. His ingenious protocol prevents ``sybil attacks\u27\u27 (where an adversary spawns any number of new players) by relying on computational puzzles (a.k.a. ``moderately hard functions\u27\u27) introduced by Dwork and Naor (Crypto\u2792). The analysis of the blockchain consensus protocol (a.k.a. Nakamoto consensus) has been a notoriously difficult task. Prior works that analyze it either make the simplifying assumption that network channels are fully synchronous (i.e. messages are instantly delivered without delays) (Garay et al, Eurocrypt\u2715) or only consider specific attacks (Nakamoto\u2708; Sampolinsky and Zohar, FinancialCrypt\u2715); additionally, as far as we know, none of them deal with players joining or leaving the protocol. In this work we prove that the blockchain consensus mechanism satisfies a strong forms of *consistency* and *liveness* in an asynchronous network with adversarial delays that are a-priori bounded, within a formal model allowing for adaptive corruption and spawning of new players, assuming that the computational puzzle is modeled as a random oracle. (We complement this result by showing a simple attack against the blockchain protocol in a fully asynchronous setting, showing that the “puzzle-hardness” needs to be appropriately set as a function of the maximum network delay; this attack applies even for static corruption.) As an independent contribution, we define an abstract notion of a blockchain protocol and identify appropriate security properties of such protocols; we prove that Nakamoto\u27s blockchain protocol satisfies them and that these properties are sufficient for typical applications; we hope that this abstraction may simplify further applications of blockchains

Approximability of Adaptive Seeding under Knapsack Constraints

Adapting Seeding is a key algorithmic challenge of influence maximization in social networks. One seeks to select among certain available nodes in a network, and then, adaptively, among neighbors of those nodes as they become available, in order to maximize influence in the overall network. Despite recent strong approximation results [25, 1], very little is known about the problem when nodes can take on different activation costs. Surprisingly, designing adaptive seeding algorithms that can appropriately incentivize users with heterogeneous activation costs introduces fundamental challenges that do not exist in the simplified version of the problem. In this paper we study the approximability of adaptive seeding algorithms that incentivize nodes with heterogeneous activation costs. We first show a tight inapproximability result which applies even for a very restricted version of the problem. We then complement this inapprox-imability with a constant-factor approximation for general submodular functions, showing that the difficulties caused by the stochastic nature of the problem can be overcome. In addition, we show stronger approximation results for additive influence functions and cases where the nodes’ activation costs constitute a small fraction of the budget

I'M Only Human: Game Theory With Computationally Bounded Agents

Rationality in games and decisions is traditionally understood as requiring that agents act optimally. However, as pointed out by Simon [64] acting optimally might be hard. We study how the analysis of games and behaviors changes when agents are assumed to be rational but computationally bounded, and thus cannot always act optimally. We first argue that some observed "irrational" human behaviors can be explained by viewing people as computationally bounded agents. We show that adding computation costs into interactive settings have some unintuitive consequences that might lead to behaviors that seem irrational at first. We then consider a dynamic decision problem, and show that some observed human behavior can be actually explained by modeling people as computationally bounded agents that are doing as well as they can, given their limitations. We then develop appropriate models of computationally bounded agents modeled as polynomial-time TM. We study the implications of these models and use these models to analyze different aspect of economic systems. We first develop a model appropriate for a repeated game setting and show that problems that are considered intractable, such as computing a NE in repeated games, actually become tractable in this model. We then develop a model of computational games, which are finite extensive-form games played by computationally bounded players and show an application of this model to the analyzing of cryptographic protocols from a game theoretic perspective

The Truth Behind the Myth of the Folk Theorem

We study the problem of computing an ɛ-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model—modeling the players as polynomial-time Turing machines that maintain state (rather than stateless polynomial-time Turing machines)—and make some standard cryptographic hardness assumptions (the existence of public-key encryption), the problem can actually be solved in polynomial time.