Combinatorial scoring auctions

This paper is concerned with a combinatorial, multi-attribute procurement mechanism called combinatorial scoring auction. In the setting that we analyze, private information of the suppliers is multi-dimensional. The buyer wants to procure several items at once. Subsets of these items are characterized by a price as well as by a number of non-monetary attributes called quality (e.g. completion time). The suppliers submit offers specifying prices and quality levels for these subsets. These offers are evaluated according to a quasi-linear scoring rule. Based on the resulting scores suppliers win contracts for the delivery of certain items. Such a contract only specifies the set of items a supplier has to deliver and a score that he has to meet. The decision about the specific price-quality combination yielding this contracted score is at the discretion of the supplier who aims at optimizing his own profit. We analyze the equilibria in such auctions and show the link between combinatorial scoring auctions and combinatorial price-only auctions. We demonstrate how this link can be used to employ preexisting knowledge about the equilibrium behavior in regular price-only auctions in the strategic analysis of combinatorial scoring auctions. Our results are the multi-item extension to the results of Asker and Cantillon (2007)

On loss aversion in bimatrix games

In this paper we study three different types of loss aversion equi-libria in bimatrix games. Loss aversion equilibria are Nash equilibria of games where players are loss averse and where the reference points – points below which they consider payoffs to be losses – are endoge-nous to the equilibrium calculation. The first type is the fixed point loss aversion equilibrium, introduced in Shalev (2000) under the name of ‘myopic loss aversion equilibrium’. There, the players’ reference points depend on the beliefs about their opponents ’ strategies. The second type, the maximin loss aversion equilibrium, differs from the fixed point loss aversion equilibrium in that the reference point is now only based on the carrier of the players’ beliefs, not on the exact prob-abilities. In the third, the safety level loss aversion equilibrium, this dependence is completely dispensed with. Finally, we do a compara-tive statics analysis of all three equilibrium concepts in 2 × 2 bimatrix games. The results indicate that a player, under some conditions, benefits from his opponent falsely believing he is loss averse

Minimal belief revision leads to backward induction

We present an epistemic model for games with perfect information in which players, upon observing an unexpected move, may revise their belief about the opponents’ preferences over outcomes. For a given profile pp of preference relations over outcomes, we impose the following conditions: (1) players initially believe that opponents have preference relations as specified by pp; (2) players believe at every instance of the game that each opponent is carrying out a sequentially rational strategy; (3) if a player revises his belief about an opponent’s type, he must search for a “new” type that disagrees with the “old” type on a minimal number of statements about this opponent; (4) if a player revises his belief about an opponent’s preference relation over outcomes, he must search for a “new” preference relation that disagrees with the “old” preference relation on a minimal number of pairwise rankings. It is shown that every player whose preference relation is given by pp, and who throughout the game respects common belief in the events (1)–(4), has a unique sequentially rational strategy, namely his backward induction strategy in the game induced by pp