Quasi-Patient Bidders in Auction Markets

• Quasi-patient bidders are auction participants who balance between myopic impatience and full patience by adapting bid timings and incurring repeated costs.
• They deploy strategies like interval and block bidding in settings such as LUBA, countering classical equilibrium predictions and enhancing seller revenue.
• Their behavior challenges standard models, prompting mechanism redesign that optimizes revenue, participation, and algorithmic pricing in dynamic markets.

Quasi-patient bidders are participants in auction or market mechanisms whose behavior displays neither complete impatience (acting myopically with no regard for future opportunities) nor infinite patience (willingness to delay or reallocate decisions indefinitely to optimize outcomes). Instead, quasi-patient bidders are characterized by a willingness to incur repeated costs or delays, adapt strategies based on evolving information, or accept partial/intermittent participation, thus occupying a spectrum between the extremes traditionally analyzed in auction theory. This nuanced behavioral model has significant economic, algorithmic, and strategic implications, as documented in empirical and theoretical research across online auctions, blockchain fee mechanisms, and resource allocation markets.

1. Behavioral Characterization in Empirical and Theoretical Models

Quasi-patient bidders emerge in environments where the standard assumptions of full rationality or myopic impatience do not fit observed behavior. In the context of Lowest Unique Bid Auctions (LUBA), empirical data show that, contrary to Nash equilibrium predictions where bidders would employ monotone, tightly coordinated strategies and dissipate profits, many participants act in a "lottery-like" fashion: they place scattered, uncoordinated bids without fully exploiting the structure of the game. Among these participants, a subset exhibits quasi-patient behavior—they repeatedly pay bidding costs and do not instantaneously correct after observing real-time feedback about the uniqueness and ranking of their bids. Such bidders may patiently persist, waiting for the right informational conditions to act or adjust their strategies incrementally over time rather than seeking immediate profit or instant exit (1007.4264).

Quasi-patient dynamics are not restricted to LUBA. In pay-per-bid auctions with costly participation, equilibrium behavior under re-entry allows bidders to randomize their bids indefinitely, exhibiting patience akin to repeated lottery play. The stationary symmetric subgame perfect equilibrium found in such settings is independent of individual wealth or accumulated costs, further reflecting the quasi-patient archetype: decisions in each round are made as if unaffected by previous spending (1108.2018).

2. Strategic Implications and Winning Strategies

Quasi-patient behavior translates to distinct strategic approaches, often contrasting with both fully rational and myopically impatient bidding. In online auctions with real-time information feedback, quasi-patient bidders may adopt interval or block bidding strategies. For example, in LUBA, a successful quasi-patient bidder first identifies an available low unique bid and then "kills" lower potential unique bids by incrementally bidding on contiguous blocks below their candidate, thereby protecting or rescuing their position based on evolving information (1007.4264). These moves require not just willingness to pay (despite expected short-term losses) but a strategic waiting for opportune moments, aligning with a notion of "investment in patience."

In resource allocation games with costly participation, quasi-patient bidders—especially risk-loving ones—are incentivized to "play the long game," persisting through rounds with a constant probability. When re-entry is permitted, the risk of the auction collapsing due to a break in bidder patience is alleviated, and the participation remains robust over many rounds (1108.2018). By contrast, forbidding re-entry can trap the auction in a drawn-out contest between a few highly persistent (quasi-patient) bidders, rendering the auction's profitability and duration dependent on the extreme patience of these individuals.

In market environments influenced by heavy-tailed value distributions, quasi-patient bidders benefit from broad participation and repeated engagement over multiple auctions. While the per-auction surplus may decline with additional bidders, the overall expected surplus and the probability of capturing rare, outsized rewards grow, favoring those who persist across rounds or markets rather than seeking only immediate wins (Bax, 2020).

3. Economic and Algorithmic Consequences

The presence of quasi-patient bidders produces significant deviations from equilibrium predictions in both economic outcomes and algorithmic allocation. In LUBA and pay-per-bid formats, sellers profit above theoretical equilibrium levels precisely because non-strategic and quasi-patient (as well as risk-seeking) bidders persistently engage, resulting in overbidding and excess cumulative payments (1007.4264, 1108.2018). This persistent play by quasi-patient bidders effectively subsidizes more strategic competitors and the seller, creating auction-like environments where bounded rationality or patience generates robust revenue streams.

In algorithmic contexts, such as learning bidder valuations from partial observations, quasi-patient behavior poses both challenges and opportunities. Bidders who participate only intermittently or delay their bid reveal less information about their strategic type. However, modern inference techniques—such as those employing reserve price probing and Kaplan–Meier–style estimators—enable accurate estimation of bidder value distributions even from censored or sparse data. This robustness to sparse and delayed participation means that auctioneers can still infer accurate market information and design near-optimal auctions despite having quasi-patient (i.e., low-frequency or delayed) bidders (Blum et al., 2014).

4. Mechanism and Market Design under Quasi-Patient Participation

Markets and mechanisms must often be re-engineered to accommodate or exploit quasi-patient bidder behavior. In repeated resource allocation with costly participation, optimal auction parameterization—setting a high value-to-cost ratio (v–s)/c—encourages ongoing bidder engagement and maximizes revenue, particularly in the presence of risk-loving and patient participants (1108.2018). Permitting re-entry “smooths” auction dynamics, sustaining competition and seller revenue by keeping more (possibly quasi-patient) bidders in contention.

In blockchain and cryptocurrency settings, models of quasi-patient users—such as those with a fraction $\delta$ of pending transactions persisting in the mempool across rounds—predict dynamically oscillating admission prices and non-trivial outcomes. High levels of patience (large $\delta$) result in price oscillations and a transition phase between the impatient (monopolist-price-dominated) and fully patient (minimal admission price) regimes. The threshold behavior in these models means that market designers must account for the patience spectrum to guarantee robust transaction inclusion and miner revenue (Penna et al., 27 May 2024).

Uniform-price multi-unit auctions with value-maximizing, return-on-investment-constrained ("safe") bidders present another application. Here, strategies can be constructed so that for any valuation curve and ROI constraint, bidders select from a finite, computable set of normalized bids that guarantee feasibility in every round—irrespective of opponents’ behavior (Golrezaei et al., 6 Jun 2024). Algorithms capable of learning these safe strategies online ensure sublinear regret against hindsight-optimal policies, and empirical results show that these robust, quasi-patient bidding strategies lose very little in aggregate value compared to unconstrained optimal strategies.

5. Effects of Patience, Risk Attitudes, and Asymmetries

Quasi-patient bidding is shaped not just by information structure or auction rules, but by intrinsic bidder characteristics such as risk aversion and cost asymmetry. In first-price procurements with asymmetric bidders, empirical analysis reveals that bidders with low risk aversion and low costs (frequent participants) are more likely to employ patient, strategic bidding, tolerating extended periods of non-winning and calibrating bids for long-term gain. Highly risk-averse asymmetric bidders adopt higher, more myopic bids to minimize uncertainty and ensure a win, effectively displaying less patience (Aryal et al., 2021). Enhancing competition (e.g., by adding more frequent, risk-tolerant bidders) can substantially reduce procurement costs.

In auto-bidding ad auctions, the strategic adoption of tCPA (target cost-per-acquisition) formats over classic marginal CPA is motivated specifically by concerns over platform commitment: quasi-patient bidders, aware of potential rule changes or reserve manipulation, choose formats that secure better long-run outcomes, even at the expense of short-term optimality (Mehta et al., 2023). These choices reflect both risk attitudes and a willingness to wait or adapt for more favorable conditions.

6. Broader Applications, Algorithmic Learning, and Future Directions

The concept of quasi-patient bidding extends to collective and non-individual participants such as bidder groups or DAOs. In two-level auction models where resource pooling and in-group cost sharing are required, quasi-patient bidders are those willing to persist in, and accept, group-based decision making. These mechanisms, however, face a trade-off in welfare efficiency due to the loss of internal information and limitations imposed by group aggregation; the best approximation achievable is typically within a harmonic factor of the optimum (Bahrani et al., 2023).

Learning from quasi-patient behavior—either through online learning algorithms that track sparse bidder activity or via inference from partial, delayed data—enables mechanism designers to reconstruct accurate bidder models and optimize over dynamic, complex participation patterns. In uniform-price auctions, efficient algorithms exist to learn optimal safe strategies, and in auction markets with partial price observability, the use of interventions like reserve price probing allows the extraction of actionable bidder distribution information, even if participation is intermittent or delayed (Blum et al., 2014, Golrezaei et al., 6 Jun 2024).

Several open problems remain, including the design of blockchain fee mechanisms that are welfare-optimal in the presence of quasi-patient (or partially patient) bidders, determining minimal resource augmentation requirements for near-optimal welfare, and extending the analysis to richer or multi-dimensional value settings (Babaioff et al., 27 Feb 2025).

7. Summary Table: Key Features of Quasi-Patient Bidders

Auction/Market Type	Behavioral Feature	Strategic/Design Implication
Lowest Unique Bid, LUBA	Repeated/block bidding	Enhanced seller profits; success via interval kills (1007.4264)
Pay-per-bid, Repeated Auctions	Randomization over rounds; independence from wealth	Stationary equilibrium; revenue boosts for risk-loving, patient bidders (1108.2018)
Online Markets, Blockchains	Fraction of demand persists per round ($\delta$)	Price oscillations, monotonicity thresholds, transition phases (Penna et al., 27 May 2024)
Uniform Price, ROI-constrained	Safe strategies derived from valuation curves	Sublinear regret, explicit richness ratio bounds (Golrezaei et al., 6 Jun 2024)
First-price Procurement (Asymmetry)	Risk/cost profiles shape patience	Cost minimization by enhancing patient, low-risk, frequent participants (Aryal et al., 2021)
DAO/Two-level Mechanisms	Patience in group pooling, willingness to share	Welfare limited by harmonic factor, careful cost-sharing needed (Bahrani et al., 2023)

Quasi-patient bidders thus represent a crucial behavioral and design axis in contemporary mechanism design, requiring, motivating, and rewarding strategies and market structures that accommodate and exploit intermediate forms of patience, participation, and adaptation.