Equilibria and learning dynamics in mixed network coordination/anti-coordination games

Robust Coordination of Linear Threshold Dynamics on Directed Weighted Networks

“…Let every agent i in V be equipped with an independent rate-1 Poisson clock. 1 If agent i's clock ticks at some time t ≥ 0, 2 then agent i modifies her current state X i (t − ) into a new state X i (t) such that…”

“…(i) For every initial profile X(0) = x (0) , Theorem 4 (i) guarantees the existence of an H-robust I-path (x (0) , x (1) , . .…”

“…Definition 3. Given two configurations x and y in X and a nonnegative integer l, a (length-l) path from x to y is an (l + 1)-tuple of configurations (x (0) , x (1) , . .…”

“…We now apply the results of Section IV-A to prove Theorem 1. Recall that the ATV-LTD X(t) on a graph G = (V, E, W ) with external field h(t) is a continuous-time inhomegeneous Markov chain X(t), whereby agents i in V get activated at the ticking of independent rate-1 Poisson clocks and, when activated at time t ≥ 0, they modify their state according to the update rule (1).…”

“…Our goal is different in this paper, as we are mainly interested in understanding the resilience of the system against external attacks. Recently, vulnerability of network coordination games against adversarial attacks has been investigated in [40], [41], while [1], [42], [43] study games with a mix of coordinating and anti-coordinating players, and [44] proposes network coordination games as a micro-foundation for community structure in networks.…”