We consider decentralized matching in a two-sided market of employers and employees (universities and students) with application costs and limited budgets. Students choose whether they should take the risk of applying to more prestigious school (with some probability of rejection) or make a safe choice. We show that application costs set by universities may be treated as a screening instrument in order to attract only strong students or to avoid the competition. Also, we find conditions for equilibria when costs are negligible, costs are a substantial part of the budget, costs imply exploding offers, in addition to other equilibria.
We consider multi-period decentralized matching in a two-sided market of employers and employees. Because of dynamics, asymmetry, and private information, we always observe delays and coordination failures with nonzero probability even in a simple case of two agents from each side. For this, we obtain conditions for different strategies to be in equilibrium. We show that problems of miscoordination and delay may be solved by signaling or by incentivizing immediate response that turn a dynamic problem into a static one and make the matching stable. In the general case, we obtain sufficient conditions for assortative matching to be and not to be in equilibrium.
The concept of iterated regret minimization (IRM) provides solutions that are more reasonable than ones offered by Nash equilibrium (NE) for many games of interest, such as the Traveler's Dilemma, the Centipede Game, and many others. For them, we analyzed new data — the IRM approach prescribes the most profitable strategy better than NE. Also, we apply the IRM to the games with continuous strategy sets, such as Colonel Blotto game and Bertrand-Edgeworth duopoly, and obtain reasonable pricing and allocating policies.
Work in Progress
We consider decentralized matching in a two-sided market of employers and employees, where each side has two types of agents, high and low. With limited capacity of employers and if both employees' types are weak enough, we observe an interesting result: in order to avoid competition with high-type employees, low-type employees send applications to high-type employers.
We analyze the dynamic application process where the probability of success is determined by the type of an applicant. In the case the type is private and may be revealed to jury only with some random noise, we prove that agents maximize their profits by aiming higher in the first rounds. However, this strategy may change if an applicant herself misinterprets her type with a positive (overconfidence) or a negative (underconfidence) bias.