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...d in a finite amount of bits. Moreover, several authors have pointed out that better global performance (e.g. spectral efficiency) is achieved when the set of PA vectors is substantially reduced [5], =-=[6]-=-, [7], [8]. Indeed, this effect has been reported as a Braess kind paradox [9]. In this paper, our contribution is twofold: first, we present a fully decentralized learning algorithm able to keep the ...

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...imental effect. This phenomenon is known as a Braesstype paradox [21], and it has already been observed in other different contexts (such as routing in [22], [23] and wireless communications in [24], =-=[25]-=-). Roughly speaking, the Braess-type paradox occurs because the average number of GNEs increases when K becomes larger. For example, when ∆|dB = 1, the numerical results indicate that the average numb...

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....2 3.4 3.6 3.8 4 av er ag e sy st em sp ec tr al ef fi ci en cy (b p s/ H z) number of iterations BRD RL RM best NE Fig. 11: Average system spectral efficiency as a function of the number of iterations at a fixed SINR of 10 dB. D. Illustration and comparison analysis Table II summarizes the different features of the three classes of distributed algorithms, which have been discussed throughout this section. Here, we consider a special instance of game GBS in which only two transmitters and two receivers are operating and two bands are assumed, and each transmitter has to select one single band [69]. Fig. 10 depicts the performance in terms of sum-utility (i.e., the transmission sum-rate) as a function of the SINR for both BRD and RM algorithms. As shown in Fig. 10, the RM learning algorithm is more efficient in terms of sum-rate than the BRD algorithm. In fact, here the performance of the CCE, which is obtained by implementing the RM learning algorithm, is very close to the performance of the best pure NE of the game. On the other hand, the BRD is observed to converge to a pure NE, which does not coincide with the best NE. Although this is not what is observed generically, there may exi...

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...c or block fading IC, can be shown to hold with probability zero in parallel MAC [9]. In particular, the sufficient condition for the uniqueness of the NE provided in [14] is not necessary in general =-=[20]-=-. The (more explicit) sufficient conditions for uniqueness given by [19] are generally not verified in parallel MAC. More precisely, from [19] it is implied that there exists a unique pure NE with hig...

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... instance, when K = {1, 2} and H and J are unitary, the number of NE can be 1 or 2 in pure strategies [13]. When, J = K = {1, 2} and H is unitary, the number of NE can be 1, 2 or 3 in pure strategies =-=[17]-=-. 5. LEARNING LOGIT EQUILIBRIA In this section, we design behavioral strategy profiles σ = (σ1, . . . , σK) ∈ Σ such that given the information gathered by player k at each stage n, i.e., given the se...

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...c or block fading IC, can be shown to hold with probability zero in parallel MAC [9]. In particular, the sufficient condition for the uniqueness of the NE provided in [14] is not necessary in general =-=[20]-=-. The (more explicit) sufficient conditions for uniqueness given by [19] are generally not verified in parallel MAC. More precisely, from [19] it is implied that there exists a unique pure NE with hig...