How to Cut a Cake Before the Party Ends

For decades researchers have struggled with the problem of envy-free cake cutting: how to divide a divisible good between multiple agents so that each agent likes his own allocation best. Although an envy-free cake cutting protocol was ultimately devised, it is unbounded, in the sense that the number of operations can be arbitrarily large, depending on the preferences of the agents. We ask whether bounded protocols exist when the agents' preferences are restricted. Our main result is an envy-free cake cutting protocol for agents with piecewise linear valuations, which requires a number of operations that is polynomial in natural parameters of the given instance.

[1]  Ying Wang,et al.  Cutting a Cake for Five People , 2009, AAIM.

[2]  Ariel D. Procaccia,et al.  Truth, justice, and cake cutting , 2010, Games Econ. Behav..

[3]  Jack M. Robertson,et al.  Cake-cutting algorithms - be fair if you can , 1998 .

[4]  Yann Chevaleyre,et al.  Issues in Multiagent Resource Allocation , 2006, Informatica.

[5]  Elchanan Mossel,et al.  On approximately fair allocations of indivisible goods , 2004, EC '04.

[6]  K. Pruhs,et al.  Cake cutting really is not a piece of cake , 2006, SODA 2006.

[7]  Yonatan Aumann,et al.  Throw One's Cake - and Eat It Too , 2011, SAGT.

[8]  Ariel D. Procaccia,et al.  Optimal Envy-Free Cake Cutting , 2011, AAAI.

[9]  Gerhard J. Woeginger,et al.  On the complexity of cake cutting , 2007, Discret. Optim..

[10]  Ariel D. Procaccia,et al.  Cake cutting: not just child's play , 2013, CACM.

[11]  Noam Nisan,et al.  Fair allocation without trade , 2012, AAMAS.

[12]  SU Francisedward.  RENTAL HARMONY : SPERNER ’ S LEMMA IN FAIR DIVISION , 2000 .

[13]  Ariel D. Procaccia,et al.  Towards More Expressive Cake Cutting , 2011, IJCAI.

[14]  Walter Stromquist,et al.  Envy-Free Cake Divisions Cannot be Found by Finite Protocols , 2008, Electron. J. Comb..

[15]  Costas Busch,et al.  Hardness Results for Cake Cutting , 2005, Bull. EATCS.

[16]  Xiaotie Deng,et al.  On the Complexity of Envy-Free Cake Cutting , 2009, ArXiv.

[17]  Ariel D. Procaccia,et al.  On Maxsum Fair Cake Divisions , 2012, AAAI.

[18]  Ariel D. Procaccia.  Thou Shalt Covet Thy Neighbor's Cake , 2009, IJCAI.

[19]  Ning Chen,et al.  Optimal Proportional Cake Cutting with Connected Pieces , 2012, AAAI.