Game Theory for Signal Processing in Networks

Giacomo Bacci (1) , Samson Lasaulce (2) , Walid Saad (3) , Luca Sanguinetti (4, 5)

1 MBI - Mediterranean Broadband Infrastructure [Pisa]
2 L2S - Laboratoire des signaux et systèmes
3 ECE - Department of Electrical and Computer Engineering [Blacksburg]
4 LANEAS - Large Networks and Systems Group
5 Dipartimento di Ingegneria dell'Informazione [Pisa]

Game theory is a branch of mathematics aimed at modeling and studying the interactions between several decision-makers (called players) who can have conflicting or common interests. A “game” is essentially a situation in which the benefit or cost reaped by each player gets from an interactive situation does not only depend on its own decisions but also on that taken by the other players. Therefore, in a game, the actions and objectives of the players are tightly coupled. Until very recently, game theory has been used quite marginally in signal processing, noticeable examples being some applications in robust detection and estimation [1], [2] as well as watermarking [3] (in which the watermarking problem is seen as a game between the data embedder and the attacker). However, the real catalyzer of the application of game theory to signal processing has been the blooming of all issues related to networking in general, and distributed networks, in particular. The primary goal of this survey is to provide an all-inclusive, holistic reference on the use of game theory in signal processing application domains. However, we note that, the extensive form, which is used to investigate simple, dynamic situations, will not be discussed in this survey (e.g., see [24] and references therein for more details). The main reason is that, in general, the extensive form is often mathematically less convenient, especially for typical signal processing problems, as advocated by the current state of the signal processing literature, that shows that the dominant model is the strategic form. Defining the corresponding model and providing important results related to the strategic form is the purpose of Section III, which shows how some solution concepts that are inherent to the strategic form can be related to algorithmic aspects. Section IV discusses the coalition form. Whereas issues related to the strategic form concentrate on the strategic choices of the individual and what strategies it chooses to reach its objective, the coalition form is typically concerned about options available to subsets of players (cooperative groups or coalitions), what cooperative coalitions can form, and how the coalition utility is divided among its members. In practice, for a given signal processing problem, the structure of the problem at hand and the practical constraints associated with it will say if the strategic or coalition form is the most suited one. For example, it may occur that both forms are acceptable in terms of information assumptions while complexity issues will lead to selecting the strategic form instead of the coalition one.

Domaines: Mathématiques [math]; Sciences de l'ingénieur [physics]; Statistiques [stat]

Giacomo Bacci, Samson Lasaulce, Walid Saad, Luca Sanguinetti. Game Theory for Signal Processing in Networks. IEEE Signal Processing Magazine, 2016, 33 (1), pp.94 - 119. ⟨10.1109/msp.2015.2451994⟩. ⟨hal-01242517⟩