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We study contention resolution (CR) on a shared channel modelled as a game with selfish players. There are n agents and the adversary chooses some k smaller than n of them as players. Each participating player in a CR game has a packet to transmit. A transmission is successful if it is performed as the only one at a round. Each player aims to minimize its packet latency. We introduce the notion of adversarial equilibrium (AE), which incorporates adversarial selection of players. We develop efficient deterministic communication algorithms that are also AE. We characterize the price of anarchy in the CR games with respect to AE. 

Agent-based crawlers are commonly used in network maintenance and information gathering. In order not to disturb the main functionality of the system, whether acting at nodes or being in transit, they need to operate online, perform a single operation fast and use small memory. They should also be preferably deterministic, as crawling agents have limited capabilities of generating a large number of truly random bits. We consider a system in which an agent receives an update, typically an insertion or deletion, of some information upon visiting a node. On request, the agent needs to output hot information, i.e., with the net occurrence above certain frequency threshold. A desired time and memory complexity of such agent should be poly-logarithmic in the number of visited nodes and inversely proportional to the frequency threshold. Ours is the first such agent with rigorous analysis and a complementary almost-matching lower bound.