English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We compute equilibrium strategies in multi-stage games with continuous signaland action spaces as they are widely used in the management sciences andeconomics. Examples include sequential sales via auctions, multi-stageelimination contests, and Stackelberg competitions. In sequential auctions,analysts are required to derive not just single bids but bid functions for allpossible signals or values that a bidder might have in multiple stages. Due tothe continuity of the signal and action spaces, these bid functions come froman infinite dimensional space. While such models are fundamental to game theoryand its applications, equilibrium strategies are rarely known. The resultingsystem of non-linear differential equations is considered intractable for allbut elementary models. This has been limiting progress in game theory and is abarrier to its adoption in the field. We show that Deep Reinforcement Learningand self-play can learn equilibrium bidding strategies for various multi-stagegames without making parametric assumptions on the bid function. We findequilibrium in models that have not yet been explored analytically and newasymmetric equilibrium bid functions for established models of sequentialauctions. The verification of equilibrium is challenging in such games due tothe continuous signal and action spaces. We introduce a verification algorithmand prove that the error of this verifier decreases when considering Lipschitzcontinuous strategies with increasing levels of discretization and samplesizes.

Equilibrium Computation in Multi-Stage Auctions and Contests