We consider a game of two agents competing to add items into a solution set. Each agent owns a set of weighted items and seeks to maximize the sum of their weights in the solution set. In each round each agent submits one item for inclusion in the solution. We study two natural rules to decide the winner of each round: Rule 1 picks among the two submitted items the item with larger weight, Rule...

We consider an important family of cryptographic protocols and a class of security properties which encompasses secrecy and authentication. We show that it is always sufficient to consider a bounded number of agents b (b = 2 for secrecy properties for example): if there is an attack involving n agents, then there is an attack involving at most b agents.