This Ph.D. thesis is composed of four independent research papers in the field of Market Design. It begins with a general introduction for all four papers and ends with a brief conclusion. In this thesis, I study the impact of heterogeneous market participants on allocation outcomes in different market mechanisms; in addition, how to design alternative mechanisms that can more effectively allocate scarce resources with diverse economic and social goals. Chapter 1 studies the impact of affirmative action policies in the context of school choice. It addresses the following two questions: what are the causes of possible perverse consequence of affirmative action policies, and when the designer can effectively implement affirmative actions without unsatisfactory outcomes. Using the minority reserve policy in the student optimal stable mechanism as an example, I show that two acyclicity conditions, type-specific acyclicity and strongly type-specific acyclicity, are crucial for effective affirmative action policies. However, these two cycle conditions are almost impossible to be satisfied in any finite market in practice. Given the limitation of the point-wise effectiveness in finite markets, I further illustrate that the minority reserve policy is approximately effective in the sense that the probability of a random market containing type-specific cycles converges to zero when the copies of schools grow to infinite. Chapter 2 addresses the question of how ex ante asymmetry affects bidders’ equilibrium strategies in two popular multi-unit auction rules: uniform-price auction (UPA) and discriminatory-price auction (DPA). I characterize the set of asymmetric monotone Bayes–Nash equilibria in a simple multi-unit auction game in which two units of a homogeneous object are auctioned among a set of bidders. I argue that bidders’ strategic behavior essentially comes from their diverse market positions (i.e., the winning probability and the probability of deciding the market-clearing price). That is, if a bidder has a relatively strong market position, she has less incentive to shade her bid for the second unit in a UPA, whereas in a DPA, weaker bidders tend to bid more aggressively on both of two units. Following Chapter 2, Chapter 3 further analyzes and contrasts bidders’ collusion incentives at the ex ante stage. My results indicate that the UPA is more vulnerable to collusion than the DPA in term of the expected per-member payoff and the core-stability. In the last chapter, I show that a variant of the Vickrey-Clarke-Groves auction, Ausubel’s clinching auction, is vulnerable to collusion in the sense that it always has a nonempty core. I further discuss an isomorphism relation between group strategy-proofness and non-bossiness in allocation, and the incompatibility between efficient allocation and non-bossiness in finite auction markets.
