This paper proposes a dialogue game in which coherent conversational sequences at the speech act level are described of agents that become aware they have an irresolvable disagreement and settle the dispute by agreeing to disagree. A disagreement is irresolvable from an agent?s perspective if both agents are aware that they both ran out of options to resolve the situation. A dialogue game is formulated in which agents can offer information that may result in non-reconcilable, mutually inconsistent belief states. An agent?s cognitive state consists of mental constructs, and given on these constructs, epistemic operators are defined which are used to define dialogue rules and a cognitive rule that allow an agent to agree to disagree.