Seminar Details
2023-10-31 (14h) : On mixed network coordination/anticoordination games
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Martina Vanelli (Politecnico di Torino)
Abstract :
Whilst network coordination games and network anti-coordination games have received a considerable amount of attention in the literature, network games with coexisting coordinating and anti-coordinating players are known to exhibit more complex behaviors. In fact, depending on the network structure, such games may even fail to have pure-strategy Nash equilibria. An example is represented by the well-known matching pennies (discoordination) game. We derive graph-theoretic conditions for the existence of pure-strategy Nash equilibria in mixed network coordination/anti-coordination games of arbitrary size. For the case where such conditions are met, we study the asymptotic behavior of best-response dynamics and provide sufficient conditions for finite-time convergence to the set of Nash equilibria. These results build on an extension and refinement of the notion of network cohesiveness and on the formulation of the new concept of network indecomposability. The findings are extended to directed graphs and employed to prove necessary and sufficient conditions for global stability of consensus equilibria in linear threshold dynamics, robustly with respect to a (constant or time-varying) external field.