How Much Due Diligence Before You Bid? Learning in Intractable Takeover Auctions

In takeover auctions, bidders must decide how much due diligence—costly, imperfect information about a target's value—to acquire before bidding. This paper investigates the economic question of how much diligence is worth buying and the computational question of how to solve these auctions when they grow too complex for exact methods.

To address these questions, the author models takeover contests as zero-sum and general-sum auction games. The study benchmarks nine different solvers, ranging from exact methods like Counterfactual Regret Minimization (CFR) to deep reinforcement learning methods like Proximal Policy Optimization (PPO). The author uses a reusable DealGame abstraction to simulate these auctions on commodity hardware and solves for the Bayes-Nash equilibrium to determine the economic value of diligence.

• Optimal Diligence: The study finds that the profit-maximizing level of due diligence is finite and falls monotonically as the per-signal cost increases. This holds true even in a symmetric acquisition equilibrium where both bidders are choosing their diligence levels simultaneously.
• Solver Performance: While exact solvers dominate in games small enough to enumerate, generic policy-gradient methods (PPO and PPG) are the strongest learning solvers. They are significantly more sample-efficient and stable than other deep learning baselines like Deep CFR or NFSP.
• Scaling: The computational cost of exact solvers grows steeply with the game tree size, whereas the cost for learning methods remains relatively flat. This makes learning methods the most viable option for genuinely intractable, multi-signal auctions where exact enumeration is impossible.
• Toehold Effects: Contrary to some relativized analyses, the study finds that in a symmetric equilibrium, a bidder's toehold primarily increases their value rather than significantly altering their equilibrium bidding behavior.