We introduce a novel non-cooperative game to analyse opinion formation and resistance, incorporating principles from social psychology such as confirmation bias, resource constraints, and influence penalties. Our simulation features Large Language Model (LLM) agents competing to influence a population, with penalties imposed for generating messages that propagate or counter misinformation. This framework integrates resource optimisation into the agents' decision-making process. Our findings demonstrate that while higher confirmation bias strengthens opinion alignment within groups, it also exacerbates overall polarisation. Conversely, lower confirmation bias leads to fragmented opinions and limited shifts in individual beliefs. Investing heavily in a high-resource debunking strategy can initially align the population with the debunking agent, but risks rapid resource depletion and diminished long-term influence