An $α$-regret analysis of Adversarial Bilateral Trade
This work addresses mechanism design for strategic agents in adversarial settings, providing theoretical bounds on efficiency approximation, but it is incremental as it builds on prior regret analysis in trade mechanisms.
The paper tackles the problem of sequential bilateral trade with adversarial valuations, aiming to maximize efficiency under incentive compatibility, individual rationality, and budget balance constraints, and shows that sublinear 2-regret is achievable with full feedback or two prices, but not with a single price and partial feedback.
We study sequential bilateral trade where sellers and buyers valuations are completely arbitrary (i.e., determined by an adversary). Sellers and buyers are strategic agents with private valuations for the good and the goal is to design a mechanism that maximizes efficiency (or gain from trade) while being incentive compatible, individually rational and budget balanced. In this paper we consider gain from trade which is harder to approximate than social welfare. We consider a variety of feedback scenarios and distinguish the cases where the mechanism posts one price and when it can post different prices for buyer and seller. We show several surprising results about the separation between the different scenarios. In particular we show that (a) it is impossible to achieve sublinear $α$-regret for any $α<2$, (b) but with full feedback sublinear $2$-regret is achievable (c) with a single price and partial feedback one cannot get sublinear $α$ regret for any constant $α$ (d) nevertheless, posting two prices even with one-bit feedback achieves sublinear $2$-regret, and (e) there is a provable separation in the $2$-regret bounds between full and partial feedback.