Traditional economic theory demonstrates how firms can sustain high prices and profits through repeated game strategies, but abstracts away from the bounded rationality of human managers. Behavioral models suggest that bounded rationality leads to biased mental models of competitor behavior, particularly underestimating competitor sophistication. We study a firm with over 20,000 gas stations, where managers have significant discretion over strategic choices, including setting fuel prices. Managers with lower cognitive skills tend to underestimate competitor sophistication in a lab-in-the-field beauty-contest game. These cognitive skills explain divergent beliefs about optimal strategies: high-skill managers favor maintaining high prices at the market's price ceiling, while low-skill managers prefer cutting prices, overestimating the profitability of such actions. Lower-skill managers set lower prices and engage more in price wars, leading to lower profits. We find that bounded rationality may increase market efficiency by lowering prices in markets with significant power, impacting producer and consumer surplus. This also implies a bias in standard measures of market power due to the role of cognitive skills in price markups.