Preference Signaling in Matching Markets
Open Access
- Author:
- Kushnir, Alexey
- Graduate Program:
- Economics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 25, 2010
- Committee Members:
- Vijay Krishna, Dissertation Advisor/Co-Advisor
Vijay Krishna, Committee Chair/Co-Chair
Marek Pycia, Committee Member
Kalyan Chatterjee, Committee Member
Tymofiy Mylovanov, Committee Member
Gary Bolton, Committee Member - Keywords:
- Matching
signaling
market design
job market - Abstract:
- This dissertation examines a natural signaling mechanism in a two-sided matching market between firms and workers. We consider a basic game of incomplete information. Each agent knows her own preferences over matches, but uncertain about other agent preferences. Each worker can send a limited number of private costless signals to firms indicating her interest in positions there; workers send signals simultaneously. Then, each firm makes an offer to a fixed number of workers; firms make offers simultaneously. Finally, workers can choose a fixed number of offers from those available to them. We study the impact of the signaling mechanism for different environments that vary in market size, agent preference distribution, the number of signals, firm and worker positions, and periods of interaction. Chapter 1 discusses the motivation for our analysis. It describes the necessity for a signaling mechanism in practice and instances of real markets that already use some form of signaling mechanisms. Chapter 2 analyzes the basic model where each firm can hire at most one worker, each worker can be matched with at most one firm, and each worker can send at most one signal. We analyze the environment where agent preferences are quite dispersed. Specifically, workers have idiosyncratic (and uniformly distributed) preferences over firms. Firms have also idiosyncratic (and uniformly distributed) preferences over workers. We prove the existence of symmetric equilibrium in pure strategies as well as that multiple symmetric equilibria, with varying responsiveness to signals, may exist. These equilibria can be welfare ranked: workers prefer equilibria where firms respond more to signals, while firms prefer the equilibria where they respond less. Finally, we show that, on average, introducing a signaling mechanism increases both the expected number of matches as well as the expected welfare of workers for this environment. The welfare of firms, on the other hand, changes ambiguously. Chapter 3 presents extensions to our main model. First, we show that the welfare results of the basic model carry over to a setting in which workers have correlated preferences. Second, the effects of a signaling mechanism persists if we consider another extension where each firm can hire several workers, each worker can be matched to several firms, and workers can send several signals. Finally, we analyze a simpler environment where agents only care about getting a match, but not the quality of the match, defining the value of a signaling mechanism as the expected increase in the number of matches from the introduction of a signaling mechanism. For such an environment, the value of a signaling mechanism is maximal for markets markets where the number of firms and workers are of roughly the same magnitude. Furthermore, additional periods of interaction between firms and workers decrease the impact of signaling. Finally, the optimal number of signals—the number of signals that maximizes the expected increase in the number of matches—increases when workers can be matched to more firms. Chapter 4 analyzes a version of our basic model where agent preferences are tightly distributed. Workers have almost aligned preferences over firms: each worker has “typical” commonly known preferences with probability close to one and “atypical” idiosyncratic preferences with the complementary probability close to zero. Firms have some commonly known preferences over workers that may vary across firms. Though signals transmit previously unavailable information, they also facilitate information asymmetry in this environment. Prior to the signaling, all firms have identical beliefs about worker preferences. However, after the signals are received they may have diverse beliefs. This disparity in beliefs leads to coordination failure. As a result, the introduction of a signaling mechanism may decrease the total number of matches and the welfare of agents. Finally, Chapter 5 summarizes our findings of previous chapters and analyzes the roles of preference signaling in matching markets. Signals play two important roles in match formation: they transmit information and they facilitate information asymmetry. When there is only a small amount of information about agent preferences available, as in Chapter 2 and 3, information transmission plays a more important role in match formation. However, when there is almost complete information about agent preferences, as in Chapter 4, the introduction of signaling may lead to coordination failure.