THE WAIT-AND-SEE OPTION IN ASCENDING PRICE AUCTIONS

Cake-cutting protocols aim at dividing a ``cake'' (i.e., a divisible resource) and assigning the resulting portions to several players in a way that each of the players feels to have received a ``fair'' amount of the cake. An important notion of fairness is envy-freeness: No player wishes to switch the portion of the cake received with another player's portion. Despite intense efforts in the past, it is still an open question whether there is a \emph{finite bounded} envy-free cake-cutting protocol for an arbitrary number of players, and even for four players. We introduce the notion of degree of guaranteed envy-freeness (DGEF) as a measure of how good a cake-cutting protocol can approximate the ideal of envy-freeness while keeping the protocol finite bounded (trading being disregarded). We propose a new finite bounded proportional protocol for any number n \geq 3 of players, and show that this protocol has a DGEF of 1 + \lceil (n^2)/2 \rceil. This is the currently best DGEF among known finite bounded cake-cutting protocols for an arbitrary number of players. We will make the case that improving the DGEF even further is a tough challenge, and determine, for comparison, the DGEF of selected known finite bounded cake-cutting protocols.Comment: 37 pages, 4 figure

A winner determination algorithm for multi-unit combinatorial auctions with reserve prices

Combinatorial auction mechanisms have been used in many applications such as resource and task allocation, planning and time scheduling in multi-agent systems, in which the items to be allocated are complementary or substitutable. The winner determination in combinatorial auction itself is a NP-complete problem, and has attracted many attentions of researchers world wide. Some outstanding achievements have been made including CPLEX and CABOB algorithms on this topic. To our knowledge, the research into multi-unit combinatorial auctions with reserve prices considered is more or less ignored. To this end, we present a new algorithm for multi-unit combinatorial auctions with reserve prices, which is based on Sandholm\u27s work. An efficient heuristic function is developed for the new algorithm. Experiments have been conducted. The experimental results show that auctioneer agent can find the optimal solution efficiently for a reasonable problem scale with our algorithm. <br /

Fraction auctions: the tradeoff between effciency and running time

This paper studies the sales of a single indivisible object where bidders have continuous valuations. In Grigorieva et al. [13] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders. We discuss the running time and the efficiency in the ex-post equilibrium of the auction. We show that by changing the parameter c of the auction we can trade off efficiency against running time.operations research and management science;

The family of c-bisection auctions: efficiency and running time

In this paper we analyze the performance of a recently proposed sequential auction, called the c-bisection auction, that can be used for a sale of a single indivisible object. We discuss the running time and the e±ciency in the ex-post equilibrium of the auction. We show that by changing the parameter c of the auction we can trade o® e±ciency against running time. Moreover, we show that the auction that gives the desired level of e±ciency in expectation takes the same number of rounds for any number of players.computer science applications;

Knightian Auctions

We study single-good auctions in a setting where each player knows his own valuation only within a constant multiplicative factor \delta{} in (0,1), and the mechanism designer knows \delta. The classical notions of implementation in dominant strategies and implementation in undominated strategies are naturally extended to this setting, but their power is vastly different. On the negative side, we prove that no dominant-strategy mechanism can guarantee social welfare that is significantly better than that achievable by assigning the good to a random player. On the positive side, we provide tight upper and lower bounds for the fraction of the maximum social welfare achievable in undominated strategies, whether deterministically or probabilistically

Fraction auctions : the tradeoff between efficiency and running time

This paper studies the sales of a single indivisible object where bidders have continuous valuations. In grigorieva et al. [14] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show the existence of an ex-post equilibrium, called bluff equilibrium, in which bidders behave truthfully except for particular constellations of observed bids at which it is optimal to pretend a slightly higher valuation. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders, when bidders choose to play the bluff equilibrium. We discuss the running time and the efficiency in the bluff equilibrium. We show that by changing the parameter c of the auction we can trade off efficiency against running time