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We study equilibrium computation with extensive-form correlation in two-player turn-taking stochastic games. Our main results are two-fold: (1) We give an algorithm for computing a Stackelberg extensive-form correlated equilibrium (SEFCE), which runs in time polynomial in the size of the game, as well as the number of bits required to encode each input number. (2) We give an efficient algorithm for approximately computing an optimal extensive-form correlated equilibrium (EFCE) up to machine precision, i.e., the algorithm achieves approximation error 𝜀 in time polynomial in the size of the game, as well as log(1/𝜀). Our algorithm for SEFCE is the first polynomial-time algorithm for equilibrium computation with com- mitment in such a general class of stochastic games. Existing algorithms for SEFCE typically make stronger assumptions such as no chance moves, and are designed for extensive-form games in the less succinct tree form. Our algorithm for approximately optimal EFCE is, to our knowledge, the first algorithm that achieves 3 desiderata simultaneously: approximate optimality, polylogarithmic dependency on the approximation error, and compatibility with stochastic games in the more succinct graph form. Existing algorithms achieve at most 2 of these desiderata, often also relying on additional technical assumptions. 

We consider the problem of planning with participation constraints introduced in [24]. In this problem, a principal chooses actions in a Markov decision process, resulting in separate utilities for the principal and the agent. However, the agent can and will choose to end the process whenever his expected onward utility becomes negative. The principal seeks to compute and commit to a policy that maximizes her expected utility, under the constraint that the agent should always want to continue participating. We provide the first polynomial-time exact algorithm for this problem for finite-horizon settings, where previously only an additive ε-approximation algorithm was known. Our approach can also be extended to the (discounted) infinite-horizon case, for which we give an algorithm that runs in time polynomial in the size of the input and log(1/ε), and returns a policy that is optimal up to an additive error of ε. 

We pose and study the problem of planning in Markov decision processes (MDPs), subject to participation constraints as studied in mechanism design. In this problem, a planner must work with a self-interested agent on a given MDP. Each action in the MDP provides an immediate reward to the planner and a (possibly different) reward to the agent. The agent has no control in choosing the actions, but has the option to end the entire process at any time. The goal of the planner is to find a policy that maximizes her cumulative reward, taking into consideration the agent's ability to terminate. We give a fully polynomial-time approximation scheme for this problem. En route, we present polynomial-time algorithms for computing (exact) optimal policies for important special cases of this problem, including when the time horizon is constant, or when the MDP exhibits a "definitive decisions" property. We illustrate our algorithms with two different game-theoretic applications: the problem of assigning rides in ride-sharing and the problem of designing screening policies. Our results imply efficient algorithms for computing (approximately) optimal policies in both applications.