Equilibrium Analysis in Markets with Asymmetric Utility Functions

Traditional auction theory assumes symmetric utility functions and equilibrium bidding strategies based on common and symmetric prior distributions. Although extensive literature addresses asymmetries in prior distributions, the assumption of symmetric utility functions persists. A long history of experimental research on auctions suggests that this assumption is hard to justify and that utility functions are not symmetric across bidders, probably driven by different behavioral motives such as risk-aversion, which leads to asymmetric bidding strategies. This observation is important for markets with human bidders and agentic markets with autonomous agents. Unfortunately, equilibrium analysis with asymmetric utility functions is technically challenging, and we are not aware of equilibrium predictions. We leverage recent advances in equilibrium learning to compute equilibrium in asymmetric auction models. First, we analyze asymmetries in isolated markets. Interestingly, we can show that in contrast to the canonical symmetric model, unilateral deviation from the symmetric risk-neutral equilibrium strategy leads to higher profit for the deviating bidder compared to the bidder who follows the symmetric equilibrium strategy. Second, we analyze agentic markets, where firms compete repeatedly and can parameterize agents to bid more or less aggressively. This leads to an interesting meta-game in which it is a Nash equilibrium for both users to select a risk-seeking agent in the first-price auction and a risk-averse agent in the all-pay auction.