TY - CHAP

T1 - Multicast Network Design Game on a Ring

AU - Mamageishvili, Akaki

AU - Mihalák, Matús

PY - 2015

Y1 - 2015

N2 - In this paper we study quality measures of different solution concepts for the multicast network design game on a ring topology. We recall from the literature a lower bound of \frac{4}{3}\frac{4}{3} and prove a matching upper bound for the price of stability, which is the ratio of the social costs of a best nash equilibrium and of a general optimum. Therefore, we answer an open question posed by fanelli et al. In [12]. We prove an upper bound of 2 for the ratio of the costs of a potential optimizer and of an optimum, provide a construction of a lower bound, and give a computer-assisted argument that it reaches 2 for any precision. We then turn our attention to players arriving one by one and playing myopically their best response. We provide matching lower and upper bounds of 2 for the myopic sequential price of anarchy (achieved for a worst-case order of the arrival of the players). We then initiate the study of myopic sequential price of stability and for the multicast game on the ring we construct a lower bound of \frac{4}{3}\frac{4}{3}, and provide an upper bound of \frac{26}{19}\frac{26}{19}. To the end, we conjecture and argue that the right answer is \frac{4}{3}\frac{4}{3}.

AB - In this paper we study quality measures of different solution concepts for the multicast network design game on a ring topology. We recall from the literature a lower bound of \frac{4}{3}\frac{4}{3} and prove a matching upper bound for the price of stability, which is the ratio of the social costs of a best nash equilibrium and of a general optimum. Therefore, we answer an open question posed by fanelli et al. In [12]. We prove an upper bound of 2 for the ratio of the costs of a potential optimizer and of an optimum, provide a construction of a lower bound, and give a computer-assisted argument that it reaches 2 for any precision. We then turn our attention to players arriving one by one and playing myopically their best response. We provide matching lower and upper bounds of 2 for the myopic sequential price of anarchy (achieved for a worst-case order of the arrival of the players). We then initiate the study of myopic sequential price of stability and for the multicast game on the ring we construct a lower bound of \frac{4}{3}\frac{4}{3}, and provide an upper bound of \frac{26}{19}\frac{26}{19}. To the end, we conjecture and argue that the right answer is \frac{4}{3}\frac{4}{3}.

U2 - 10.1007/978-3-319-26626-8_32

DO - 10.1007/978-3-319-26626-8_32

M3 - Chapter

T3 - Lecture Notes in Computer Science

SP - 439

EP - 451

BT - Proc. 9th International Conference on Combinatorial Optimization and Applications (COCOA)

PB - Springer

ER -