Time bounds for iterative auctions: A unified approach by discrete convex analysis

详细信息    查看全文

• 作者：Kazuo Murota^a ; ^{murota@tmu.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Akiyoshi Shioura^b ; ^{shioura.a.aa@m.titech.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Zaifu Yang^c ; ^{zaifu.yang@york.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Discrete optimization ; Submodular function ; Discrete convex function ; Walrasian equilibrium ; Iterative auction
• 刊名：Discrete Optimization
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：19
• 期：Complete
• 页码：36-62
• 全文大小：665 K

文摘

We investigate an auction model where there are many different goods, each good has multiple units and bidders have gross substitutes valuations over the goods. We analyze the number of iterations in iterative auction algorithms for the model based on the theory of discrete convex analysis. By making use of L^♮$L^{♮}$-convexity of the Lyapunov function we derive exact bounds on the number of iterations in terms of the ℓ_∞${\ell }_{\infty }$-distance between the initial price vector and the found equilibrium. Our results extend and unify the price adjustment algorithms for the multi-unit auction model and for the unit-demand auction model, offering computational complexity results for these algorithms, and reinforcing the connection between auction theory and discrete convex analysis.