Piotr Wiecek

Stationary anonymous sequential games with undiscounted rewards

Stationary anonymous sequential games with undiscounted rewards are a special class of games that combine features from both population games (infinitely many players) with stochastic games. We extend the theory for these games to the cases of total expected reward as well as to the expected average reward. We show that in the anonymous sequential game equilibria correspond to the limits of those of related finite population games as the number of players grows to infinity. We provide examples to illustrate our results.

The association problem with misleading partial channel state information

It has been known that the throughput of the 802.11 WLAN is much smaller than the nominal bit rate offered when attempting to connect to an access point. A user may discover the quality of service offered by an access point only after taking the decision of which of the access points to connect to. In fact, the actual throughput of a user is a function of not only his channel state but also of that of the other connected users. This could likely lead to congestion and overload conditions in the Access Point (AP) in question (which offers the best signal strength) and all users would lose. The information available to users attempting to connect to an AP is thus misleading. In this paper, we develop a Nash-Bayesian game framework where users compete to maximize their throughput by picking the best locally serving radio access network (RAN) with respect to their own measurement, their demand and a partial statistical channel state information (CSI) of other users. We derive analytically the utilities perceived by users to obtain the equilibria. In particular, it is shown that equilibria strongly depend on the channel quality indicator.

An Automated Dynamic Offset for Network Selection in Heterogeneous Networks

Complementing traditional cellular networks with the option of integrated small cells and WiFi access points can be used to further boost the overall traffic capacity and service level. Small cells along with WiFi access points are projected to carry over 60 percent of all the global data traffic by 2015. With the integration of small cells on the radio access network levels, there is a focus on providing operators with more control over small cell selection while reducing the feedback burden. Altogether, these issues motivate the need for innovative distributed and autonomous association policies that operate on each user under the network operators control, utilizing only partial information, yet achieving near-optimal solutions for the network. In this paper, we propose a load-aware network selection approach applied to automated dynamic offset in heterogeneous networks (HetNets). In particular, we investigate the properties of a hierarchical (Stackelberg) Bayesian game framework, in which the macro cell dynamically chooses the offset about the state of the channel in order to guide users to perform intelligent network selection decisions between macro cell and small cell networks. We derive analytically the utility related to the channel quality perceived by users to obtain the equilibria, and compare it to the fully centralized (optimal), the full channel state information and the non-cooperative (autonomous) models. Building upon these results, we effectively address the problem of how to intelligently configure a dynamic offset which optimizes networks global utility while users maximize their individual utilities. One of the technical contributions of the paper lies in obtaining explicit characterizations of the dynamic offset at the equilibrium and the related performances in terms of the price of anarchy. Interestingly, it turns out that the complexity of the algorithm for finding the dynamic offset of the Stackelberg model is O(n4) (where n is the number of users). It is shown that the proposed hierarchical mechanism keeps the price of anarchy almost equal to 1 even for a low number of users, and remains bounded above by the non-cooperative model.

Dynamic Hawk and Dove Games within Flocks of Birds

The Hawk and Dove game is a well known model from biology for competition over resources between two types of behaviors: aggressive (Hawk) and peaceful (Doves). The game allows to predict whether one of the behaviors will dominate the other or whether we may expect coexistence of both at a long run; in the latter case it allows to predict what fraction of the population will be aggressive and what peaceful. This game is quite relevant to networking, and has been used in the past to predict the outcome of competition between congestion [2] control protocols (both in wireline and in wireless) as well as between power control protocols for wireless communications. In this paper we study new aspects of the game within the framework of flocks of birds, and obtain results that can be useful for network engineering applications as well.

A game theoretic approach for the association problem in two-tier HetNets

This paper addresses a Bayesian game theoretic framework for determining the association rules that decide to which cell a given mobile user should associate in LTE two-tier Heterogeneous Networks (HetNets). Users are assumed to compete to maximize their throughput by picking the best locally serving cell with respect to their own measurement, their demand and a partial statistical channel state information (CSI) of other users. In particular, we investigate the properties of a hierarchical game, in which the macro-cell BS is a player on its own. We derive analytically the utilities related to the channel quality perceived by users to obtain the equilibria. We show by means of a Stackelberg formulation, how the operator, by dynamically choosing the offset about the state of the channel, can optimize its global utility while end-users maximize their individual utilities. The proposed hierarchical decision approach for wireless networks can reach a good trade-off between the global network performance at the equilibrium and the requested amount of signaling. Typically, it is shown that when the network goal is orthogonal to users goal, this can lead the users to a misleading association problem. Numerical results validate the expectation from the theoretical analysis and illustrate the advantages of the proposed approach.

Automated dynamic offset applied to cell association

In this paper, we develop a hierarchical Bayesian game framework for automated dynamic offset selection. Users compete to maximize their throughput by picking the best locally serving radio access network (RAN) with respect to their own measurement, their demand and a partial statistical channel state information (CSI) of other users. In particular, we investigate the properties of a Stackelberg game, in which the base station is a player on its own. We derive analytically the utilities related to the channel quality perceived by users to obtain the equilibria. We study the Price of Anarchy (PoA) of such system, where the PoA is the ratio of the social welfare attained when a network planner chooses policies to maximize social welfare versus the social welfare attained in Nash/Stackeleberg equilibrium when users choose their policies strategically. We show by means of a Stackelberg formulation, how the operator, by sending appropriate information about the state of the channel, can configure a dynamic offset that optimizes its global utility while users maximize their individual utilities. The proposed hierarchical decision approach for wireless networks can reach a good trade-off between the global network performance at the equilibrium and the requested amount of signaling. Typically, it is shown that when the network goal is orthogonal to users goal, this can lead the users to a misleading association problem.

An Anonymous Sequential Game Approach for Battery State Dependent Power Control

The sensitivity of mobile terminals to energy and power limitations keeps posing challenges to wireless technology. The ratio between the useful signals power and that of noise and interferences has a crucial impact on the achievable throughputs and on outage aspects, little has been done concerning another central challenge that limited energy poses: that of limitation on battery life. In this paper we study power control in a way that combines the two aforementioned aspects. We propose a modeling approach which extends the Anonymous Sequential Game framework introduced in 1988 by Jovanovic and Rosenthal. The approach is designed for systems that have a very large number of interacting decision makers, so large that they can be modeled as a continuum of players. We introduce an appropriate equilibrium concept for this game (which extends the Wardrop equilibrium by including random individual states with controlled transitions), characterize the structure of the equilibrium policies and provide two efficient equilibrium computation procedures.

Pure equilibria in a simple dynamic model of strategic market game

We present a discrete model of two-person constant-sum dynamic strategic market game. We show that for every value of discount factor the game with discounted rewards possesses a pure stationary strategy equilibrium. Optimal strategies have some useful properties, such as Lipschitz property and symmetry. We also show value of the game to be nondecreasing both in state and discount factor. Further, for some values of discount factor, exact form of optimal strategies is found. For β less than

On the Two-User Multi-Carrier Joint Channel Selection and Power Control Game

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