Sequential asymmetric auctions with endogenous participation

In this paper we suggest a model of sequential auctions with endogenous participation where each bidder conjectures about the number of participants at each round. Then, after learning his value, each bidder decides whether or not to participate in the auction. In the calculation of his expected value, each bidder uses his conjectures about the number of participants for each possible subgroup. In equilibrium, the conjectured probability is compatible with the probability of staying in the auction. In our model, players face participation costs, bidders may buy as many objects as they wish and they are allowed to drop out at any round. Bidders can drop out at any time, but they cannot come back to the auction. In particular we can determine the number of participants and expected prices in equilibrium. We show that for any bidding strategy, there exists such a probability of staying in the auction. For the case of stochastically independent objects, we show that in equilibrium every bidder who decides to continue submits a bid that is equal to his value at each round. When objects are stochastically identical, we are able to show that expected prices are decreasing.

Investigating the influence of achievement on self-concept using an intra-class design and a comparison of the PASS and SDQ-1 self-concept tests

Background. The formation and measurement of self-concept were the foci of this research. Aims. The study aimed to investigate the influence of achievement on academic self-concept and to compare the Perception of Ability Scale for Students (PASS, Boersma & Chapman, 1992) with the Self-Description Questionnaire-1 (SDQ-1, Marsh, 1988). Sample. The participants were 479 grade 5 (mean age 126.6 months) coeducational Australian students, located in 18 schools. Method. An intra-class research design was used to investigate the influence of frame-of-reference on self-concept development. Results. As students' academic scores rose above their class mean their self-concepts increased and as students' academic scores fell below their class mean their self-concepts decreased. Students' difference from class mean predicted their self-concept scores. This finding was consistently shown across the reading, spelling, and mathematics domains using test and teaching rating data. A comparison between the PASS and the SDQ-1 demonstrated concurrent validity across self-concept domains. Conclusion. The findings support the notions that the social environment is a significant agent that influences self-concept, and that teacher ratings and standardised tests of achievement and the PASS and the SDQ-1 are valid measures for self-concept research.