(1) Date&Time: 16:30-18:00 (JST), February 26th
Speaker: 坂東 桂介（信州大学准教授）
Title: Stability properties of the core in a generalized assignment problem (joint with Ryo Kawasaki)
We show that the core of a generalized assignment problem satisfies two types of stability properties. First, the core is the unique stable set defined using the weak domination relation when outcomes are restricted to individually rational and pairwise feasible ones. Second, the core is the unique stable set with respect to a sequential domination relation that is defined by a sequence of weak domination relations that satisfy outsider independence. An equivalent way of stating this result is that the core satisfies the property commonly stated as the existence of a path to stability. These results add to the importance of the core in an assignment problem where agents’ preferences may not be quasilinear.
The talk will be given in Japanese.[報告言語は日本語です。] 申込期限：2月25日
(2)・Date&Time: 17:00-18:00(JST), 5 March(JST)
Speaker:Zhengxing Zou（Beijing Jiaotong University）
Title:Sharing the Surplus and Proportional Values.
We introduce a family of proportional surplus division values for TU-games. Each value first assigns to each player a compromise between his stand-alone worth and the average stand-alone worths over all players, and then allocates the remaining worth among the players in proportion to their stand-alone worths. This family contains the proportional division value and the new egalitarian proportional surplus division value as two special cases. We provide characterizations for this family of values, as well as for each single value in this family.
・Date&Time: 18：00－19：00(JST), 5 March(JST)
Speaker:Rene van den Brink（Amsterdam VU）
Title: Valuation Monotonicity, Fairness and Stability in Assignment Problems (joint work with Marina Nunez and Francisco Robles)
In two-sided assignment markets with transferable utility, we first introduce two weak monotonicity properties that are compatible with stability. We show that for a fixed population, the sellers-optimal (respectively the buyers-optimal) stable rules are the only stable rules that satisfy object-valuation antimonotonicity (respectively buyer-valuation monotonicity). Essential in these properties is that, after a change in valuations, monotonicity is required only for buyers that stay matched with the same seller. Using Owen’s derived consistency, the two optimal rules are characterized among all allocation rules for two-sided assignment markets with a variable population, without explicitly requiring stability. Whereas these two monotonicity properties suggest an asymmetric treatment of the two sides of the market, valuation fairness axioms require a more balanced effect on the payoffs of buyers and sellers when the valuation of buyers for the objects owned by the sellers change.
For assignment markets with a variable population, we introduce grand valuation fairness requiring that, if all valuations decrease in the same amount, as long as all optimal matchings still remain optimal, this leads to equal changes in the payoff of all agents. We show that the fair division rules are the only rules that satisfy this grand valuation fairness and a weak derived consistency property.
・Date&Time:19:00-19:30(JST) Discussions with graduate students
These talks will be given in English. application deadline:March 3