We show that several decision problems originating from max-plus or tropical convexity are equivalent to zero-sum, two player game problems. In particular, we set up an equivalence between the external representation of tropical convex sets and zero-sum stochastic games, in which tropical polyhedra correspond to deterministic games with finite action spaces. Then, we show that the winning initi...

Dynamical mechanisms that can stabilize the coexistence or diversity in biology are generally of fundamental interest. In contrast to many two-strategy evolutionary games, games with three strategies and cyclic dominance like the rock-paper-scissors game (RPS) stabilize coexistence and thus preserve biodiversity in this system. In the limit of infinite populations, resembling the traditional pi...

a {em roman dominating function} on a graph $g = (v ,e)$ is a function $f : vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v) = 0$ is adjacent to at least one vertex $u$ for which $f (u) = 2$. the {em weight} of a roman dominating function is the value $w(f)=sum_{vin v}f(v)$. the roman domination number of a graph $g$, denoted by $gamma_r(g)$, equals the...

We solve large two-player zero-sum extensive-form games with perfect recall. We propose a new algorithm based on fictitious play that significantly reduces memory requirements for storing average strategies. The key feature is exploiting imperfect recall abstractions while preserving the convergence rate and guarantees of fictitious play applied directly to the perfect recall game. The algorith...

In this paper we consider a dynamic nonzero-sum game between the polluting firms and the authorities. Although the proposed game is not easily solvable for the feedback case, i.e., it is not the linear quadratic case of game and not a degenerated case, we calculate explicitly a stationary feedback equilibrium. In the proposed game the regulator has the ability to turn the optimal allocation of ...

Data-free quantization (DFQ) recovers the performance of quantized network (Q) without accessing real data, but generates fake sample via a generator (G) by learning from full-precision (P) instead. However, such generation process is totally independence Q, specialized as failing to consider adaptability generated samples, i.e., beneficial or adversarial, over resulting into non-ignorable loss...