As algorithms increasingly mediate competitive decision-making, their influence extends beyond individual outcomes to shaping strategic market dynamics. In two preregistered experiments, we examined how algorithmic advice affects human behavior in classic economic games with unique, non-collusive, and analytically traceable equilibria. In Experiment 1 (N = 107), participants played a Bertrand price competition with individualized or collective algorithmic recommendations. Initially, collusively upward-biased advice increased prices, particularly when individualized, but prices gradually converged toward equilibrium over the course of the experiment. However, participants avoided setting prices above the algorithm's recommendation throughout the experiment, suggesting that advice served as a soft upper bound for acceptable prices. In Experiment 2 (N = 129), participants played a Cournot quantity competition with equilibrium-aligned or strategically biased algorithmic recommendations. Here, individualized equilibrium advice supported stable convergence, whereas collusively downward-biased advice led to sustained underproduction and supracompetitive profits - hallmarks of tacit collusion. In both experiments, participants responded more strongly and consistently to individualized advice than collective advice, potentially due to greater perceived ownership of the former. These findings demonstrate that algorithmic advice can function as a strategic signal, shaping coordination even without explicit communication. The results echo real-world concerns about algorithmic collusion and underscore the need for careful design and oversight of algorithmic decision-support systems in competitive environments.