We study quitting games and define the concept of absorption paths, which is an alternative definition to strategy profiles that accommodates both discrete- time aspects and continuous-time aspects, and is parametrized by the total probability of absorption in past play rather than by time. We then define the concept of sequentially 0-perfect absorption paths, which are shown to be limits of ε-equilibrium strategy profiles as ε goes to 0. We establish that any quitting game that does not have simple equilibria (that is, an equilibrium where the game terminates in the first period or one where the game never terminates) has a sequentially 0-perfect absorption path. We finally identify a class of quitting games that possess sequentially 0- perfect absorption paths.

There are many economic problems where the observable data consists of prices and selling times– airline tickets and hotel bookings are leading examples. This paper pro- vides a dynamic pricing model to help better understand such scenarios: A seller wants to sell to a buyer a good with a fixed date of consumption. The buyer’s value for it can change over time according to a Poisson process prior to the date. The seller posts a two-part tariff where the first part extracts the buyer’s surplus modulo self-selection rents, and the second part sequentially segments the market in the spirit of second degree price discrimination through a continuously increasing price path. The buyer always pays the first part of the tariff and then solves an optimal stopping problem– which price to accept for trade. The solution of this pricing problem, solved in closed form, is shown to implement the optimal deterministic contract. In the process, a novel dynamic mecha- nism design problem is operationalized where the standard relaxed approach generically fails. Alternate implementations through refund and subscription contracts are also pre- sented. The gains from randomization are explained through the channel of information acquisition, and the optimal contract for limited informational change modeled through a fixed number of Poisson arrivals is also solved.

Dynamic contracts typically allow the principal to relax future incentive constraints by backloading the agent’s information rents or asking the agent to post a bond upfront which is liquidated over time. An implicit modeling assumption at play there is that both the principal and agent have equal access to capital, captured by equal discount rates. This paper introduces unequal discounting in a canonical dynamic screening problem where the agent has Markovian private information and limited commitment. The backloading force is tempered by an inter-temporal cost of incentive provision. The optimal contract features cycles with infinite memory. The interaction of Marokvian information and unequal discounting introduces technical challenges by rendering the standard relaxed problem approach invalid for certain parameters. An approximately optimal and simple alternative is provided, where both terms are made formalized.

Algorithms for Continuous Equilibria in Quitting Games

Uncertain Repeated Games

Optimal Dynamic Allocation with Costly Verification

Screening With Hard Information

Behavioral Epidemiology: An Economic Model To Evaluate Optimal Policy In The Midst Of A Pandemic

Scoring And Favoritism