Smoothed Efficient Algorithms and Reductions for Network Coordination Games

Worst-case hardness results for most equilibrium computation problems have raised the need for beyond-worst-case analysis. To this end, we study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a PLS-complete problem in the worst case. This is a potential game where the sequential-better-response algorithm is known to converge to a pure NE, albeit in exponential time. First, we prove polynomial (resp. quasi-polynomial) smoothed complexity when the underlying game graph is a complete (resp. arbitrary) graph, and every player has constantly many strategies. We note that the complete graph case is reminiscent of perturbing all parameters, a common assumption in most known smoothed analysis results. Second, we define a notion of smoothness-preserving reduction among search problems, and obtain reductions from $2$-strategy network coordination games to local-max-cut, and from $k$-strategy games (with arbitrary $k$) to local-max-cut up to two flips. The former together with the recent result of [BCC18] gives an alternate $O(n^8)$-time smoothed algorithm for the $2$-strategy case. This notion of reduction allows for the extension of smoothed efficient algorithms from one problem to another. For the first set of results, we develop techniques to bound the probability that an (adversarial) better-response sequence makes slow improvements on the potential. Our approach combines and generalizes the local-max-cut approaches of [ER14,ABPW17] to handle the multi-strategy case: it requires a careful definition of the matrix which captures the increase in potential, a tighter union bound on adversarial sequences, and balancing it with good enough rank bounds. We believe that the approach and notions developed herein could be of interest in addressing the smoothed complexity of other potential and/or congestion games

When three’s a crowd: how relational structure and social history shape organizational codes in triads

When members of an organization share communication codes, coordination across subunits is easier. But if groups interact separately, they will each develop a specialized code. This paper asks: Can organizations shape how people interact in order to create shared communication codes? What kinds of design interventions in communication structures and systems are useful? In laboratory experiments on triads composed of dyads that solve distributed coordination problems, we examine the effect of three factors: transparency of communication (versus privacy), role differentiation, and the subjects’ social history. We find that these factors impact the harmonization of dyadic codes into triadic codes, shaping the likelihood that groups develop group-level codes, converge on a single group-level code, and compress the group-level code into a single word. Groups with transparent communication develop more effective codes, while acyclic triads composed of strangers are more likely to use multiple dyadic codes, which are less efficient than group-level codes. Groups of strangers put into acyclic configurations appear to have more difficulty establishing “ground rules”—that is, the “behavioral common ground” necessary to navigate acyclic structures. These coordination problems are transient—groups of different structures end up with the same average communication performance if given sufficient time. However, lasting differences in the code that is generated remain

The influence of topology and information diffusion on networked game dynamics

This thesis studies the influence of topology and information diffusion on the strategic interactions of agents in a population. It shows that there exists a reciprocal relationship between the topology, information diffusion and the strategic interactions of a population of players. In order to evaluate the influence of topology and information flow on networked game dynamics, strategic games are simulated on populations of players where the players are distributed in a non-homogeneous spatial arrangement. The initial component of this research consists of a study of evolution of the coordination of strategic players, where the topology or the structure of the population is shown to be critical in defining the coordination among the players. Next, the effect of network topology on the evolutionary stability of strategies is studied in detail. Based on the results obtained, it is shown that network topology plays a key role in determining the evolutionary stability of a particular strategy in a population of players. Then, the effect of network topology on the optimum placement of strategies is studied. Using genetic optimisation, it is shown that the placement of strategies in a spatially distributed population of players is crucial in maximising the collective payoff of the population. Exploring further the effect of network topology and information diffusion on networked games, the non-optimal or bounded rationality of players is modelled using topological and directed information flow of the network. Based on the topologically distributed bounded rationality model, it is shown that the scale-free and small-world networks emerge in randomly connected populations of sub-optimal players. Thus, the topological and information theoretic interpretations of bounded rationality suggest the topology, information diffusion and the strategic interactions of socio-economical structures are cyclically interdependent

Discrete Choices under Social Influence: Generic Properties

We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP). Positive additive externalities yield a family of inverse demand curves that include the classical downward sloping ones but also new ones with non constant convexity. When j, the ratio of the social influence strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. Even if the IWP distribution is mono-modal, there is a critical value of j above which the inverse demand is non monotonic, decreasing for small and high adoption rates, but increasing within some intermediate range. Depending on the price there are thus either one or two equilibria. Beyond this first result, we exhibit the generic properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend only on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite). The main results are summarized as phase diagrams in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited.Comment: 42 pages, 15 figure

Spectrum Sensing and Multiple Access Schemes for Cognitive Radio Networks

Increasing demands on the radio spectrum have driven wireless engineers to rethink approaches by which devices should access this natural, and arguably scarce, re- source. Cognitive Radio (CR) has arisen as a new wireless communication paradigm aimed at solving the spectrum underutilization problem. In this thesis, we explore a novel variety of techniques aimed at spectrum sensing which serves as a fundamental mechanism to find unused portions of the electromagnetic spectrum. We present several spectrum sensing methods based on multiple antennas and evaluate their receiving operating characteristics. We study a cyclostationary feature detection technique by means of multiple cyclic frequencies. We make use of a spec- trum sensing method called sequential analysis that allows us to significantly decrease the time needed for detecting the presence of a licensed user. We extend this scheme allowing each CR user to perform the sequential analysis algorithm and send their local decision to a fusion centre. This enables for an average faster and more accurate detection. We present an original technique for accounting for spatial and temporal cor- relation influence in spectrum sensing. This reflects on the impact of the scattering environment on detection methods using multiple antennas. The approach is based on the scattering geometry and resulting correlation properties of the received signal at each CR device. Finally, the problem of spectrum sharing for CR networks is addressed in or- der to take advantage of the detected unused frequency bands. We proposed a new multiple access scheme based on the Game Theory. We examine the scenario where a random number of CR users (considered as players) compete to access the radio spec- trum. We calculate the optimal probability of transmission which maximizes the CR throughput along with the minimum harm caused to the licensed users’ performance