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4.3.2 Bayesian Rate Efficient Power Allo... > 4.3.2 Bayesian Rate Efficient Power ... - Pg. 124

124 CHAPTER 4 Bayesian Games known from Rosen (1965) that the diagonally strict concavity (DSC) is a sufficient condition for having uniqueness. This condition is as follows. The DSC is met if there exists some vector of strictly positive parameters r = (r 1 , r 2 , . . . , r K ) such that: p = p, (p - p) r (p) - r (p ) T > 0 where, by definition: r (p) = r 1 v B v B 1 (p), . . . , r K K (p) p 1 p K (4.17) (4.16) and (·) T is the transposition operator. As proven in He et al. (2010a), the DSC is always met in the considered game, which proves that there exists a unique pure Bayesian equilibrium. Figure 4.1 represents the best responses of the players in a game where: K = 2, P max = 1, 2 = 1, min = 1, max = 3 and q( min ) = q( min ) = 0.5. i