A Non-blocking Online Cake-Cutting Protocol

This paper proposes an online cake-cutting protocol without a long wait. Cake-cutting protocols are used to fairly divide a heterogeneous divisible good among some number of people. Though many protocols have been proposed, most of them assume that all people must simultaneously execute one protocol. Walsh proposed an online cake-cutting protocol, in which each player can join to the protocol at any time and leave when his portion of the cake is assigned. However, each player must wait until another player arrives, thus each player's waiting time is unbounded when no other player arrives. A deadlock might occur if the number of actually arriving players is unknown. This paper proposes a new online cake-cutting protocol without above blocking of players by introducing a discount factor to the utilities. Each player must wait for a fixed constant time if no other player arrives. The protocol is truthful, immediately envy-free, and meta-envy-free for risk-adverse players.