Robert P. Gilles

Using game theory to analyze wireless ad hoc networks

The application of mathematical analysis to the study of wireless ad hoc networks has met with limited success due to the complexity of mobility and traffic models, the dynamic topology, and the unpredictability of link quality that characterize such networks. The ability to model individual, independent decision makers whose actions potentially affect all other decision makers renders game theory particularly attractive to analyze the performance of ad hoc networks. In this article we describe how various interactions in wireless ad hoc networks can be modeled as a game. This allows the analysis of existing protocols and resource management schemes, as well as the design of equilibrium-inducing mechanisms that provide incentives for individual users to behave in socially-constructive ways. We survey the recent literature on game theoretic analysis of ad hoc networks, highlighting its applicability to power control and waveform adaptation, medium access control, routing, and node participation, among others.

Spatial Social Networks

Abstract. We introduce a spatial cost topology in the network formation model analyzed by Jackson and Wolinsky, Journal of Economic Theory (1996), 71: 44–74. This cost topology might represent geographical, social, or individual differences. It describes variable costs of establishing social network connections. Participants form links based on a cost-benefit analysis. We examine the pairwise stable networks within this spatial environment. Incentives vary enough to show a rich pattern of emerging behavior. We also investigate the subgame perfect implementation of pairwise stable and efficient networks. We construct a multistage extensive form game that describes the formation of links in our spatial environment. Finally, we identify the conditions under which the subgame perfect Nash equilibria of these network formation games are stable.

Games with permission structures: the conjunctive approach

This paper is devoted to the game theoretic analysis of decision situations, in which the players have veto power over the actions undertaken by certain other players. We give a full characterization of the dividends in these games with a permission structure. We find that the collection of these games forms a subspace of the vector space of all games with side payments on a specified player set.Two applications of these results are provided. The first one deals with the projection of additive games on a permission structure. It is shown that the Shapley value of these projected games can be interpreted as an index that measures the power of the players in the permission structure. The second application applies the derived results on games, where the organization structure can be analysed separately from the production capacities of the participating players.

Convergence of cognitive radio networks

In this paper, we examine the conditions and behavior of several common convergence dynamics from game theory and show how they influence the structure of networks of cognitive radios. We then apply these to previously proposed distributed power control algorithms and describe how they impact network complexity.

Measuring Domination in Directed Networks

Abstract Dominance relations between individuals can be represented by a directed social network . A relational power measure is a function that assigns to each position in a directed network a value representing the relational power of that position in the network. We axiomatically characterize two such power measures, the β - measure and the score-measure . We also apply these measures to weighted directed networks that can be interpreted as dominance structures which dominance relations are assigned weights representing the ‘importance’ of each relation.

Game theoretic analysis of a network of cognitive radios

Cognitive radio is an enhancement on traditional software radio design where observations of the operating environment are combined with knowledge of the radios available hardware and software capabilities to form decisions as to how to modify the radios behavior to produce a desired level of performance. This paper addresses how the insertion of cognitive radio technology into a network will impact performance and demonstrates how techniques from game theory can be used to analyze the network as a first step of shaping the decisions of the radios to achieve optimal network performance.

Effect of Selfish Node Behavior on Efficient Topology Design

The problem of topology control is to assign per-node transmission power such that the resulting topology is energy efficient and satisfies certain global properties such as connectivity. The conventional approach to achieve these objectives is based on the fundamental assumption that nodes are socially responsible. We examine the following question: if nodes behave in a selfish manner, how does it impact the overall connectivity and energy consumption in the resulting topologies? We pose the above problem as a noncooperative game and use game-theoretic analysis to address it. We study Nash equilibrium properties of the topology control game and evaluate the efficiency of the induced topology when nodes employ a greedy best response algorithm. We show that even when the nodes have complete information about the network, the steady-state topologies are suboptimal. We propose a modified algorithm based on a better response dynamic and show that this algorithm is guaranteed to converge to energy-efficient and connected topologies. Moreover, the node transmit power levels are more evenly distributed, and the network performance is comparable to that obtained from centralized algorithms.

The cooperative game theory of networks and hierarchies

Cooperative Game Theory.- The Core of a Cooperative Game.- Axiomatic Value Theory.- The Cooperative Potential.- Directed Communication Networks.- Cooperative Theories of Hierarchical Organizations.

Hierarchical organization structures and constraints on coalition formation

This paper studies the constraints in coalition formation that result from a hierarchical organization structure on the class of players in a cooperative game with transferable utilities. If one assumes that the superiors of a certain individual have to give permission to the actions undertaken by the individual, then one arrives at a limited collection of formable orautonomous coalitions. This resulting collection is a lattice of subsets on the player set.We show that if the collection of formable coalitions is limited to a lattice, the core allows for (infinite) exploitation of subordinates. For discerning lattices we are able to generalize the results of Weber (1988), namely the core is a subset of the convex hull of the collection of all attainable marginal contribution vectors plus a fixed cone. This relation is an equality if and only if the game is convex. This extends the results of Shapley (1971) and Ichiishi (1981).

Decentralization of Pareto Optima in Economies with Public Projects, Nonessential Private Goods and Convex Costs

SummaryIn the theory of economies with public goods one usually considers the case in which private goods are essential, i.e., each agent receives a fixed minimum level of utility if he consumes no private goods, irrespective of the public goods consumed. This paper develops the second welfare theorem for economies with public projects and possibly inessential private goods. As a corollary we also derive conditions under which valuation equilibria exist.