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The honesty of communication in competitive situations has long been debated. We investigated the coexistence of a diverse set of strategies in a simple model of aggressive communication by means of individual-based computer simulations. The game is an extended Hawk–Dove game in which there are two types of individual, weak and strong, and in which individual can communicate by means of cost-free signals before deciding whether to attack. The available strategies can be classified into three categories: honest, cheaters and those that ignore the signalling system. We found a diverse set of equilibria, most of them consisting of a mixture of honest and cheating individuals. We found that when starting populations consist of all strategies (1) the honest equilibrium can evolve, (2) communication is almost always present when signals are informative, and (3) strategies that ignore signalling are generally rare. Honest individuals need not be the majority in these populations yet communication will be present and stable in the long run. In contrast, the pure honest equilibrium is unlikely to evolve when the starting populations consist of strategies that ignore signals. Strategies that ignore signals are more frequent in these types of run however, signalling strategies are still present in the most frequently evolved equilibria. Even in this simple system two different kinds of use of signals can evolve: the first when signals refer to resource-holding potential and a second where signals are used to create a payoff-irrelevant asymmetry. In general, regardless of the starting conditions, a low resource value favours weak individuals, both honest and cheaters, and cowards, medium values favour strong individuals that use and listen to signals, and a high resource value favours strong individuals that ignore the signalling system and attack under all conditions. Although it is possible to find parameter combinations with a negative value of information, the value of information is positive in the overwhelming majority of equilibria. Thus one can conclude that for the majority of parameter combinations an equilibrium evolved that might not be honest, not even on average, but communication is present and signals are worth listening to. [Copyright &y& Elsevier]