Communication, correlation and cheap-talk in games with public information

This paper studies extensive form games with perfect information and simultaneous moves, henceforth called games with public information. On this class, we prove that all communication equilibrium payoffs can be obtained without mediator by cheap-talk procedures. The result encompasses repeated games and stochastic games

Communication, correlation and cheap-talk in games with public information

This paper studies extensive form games with perfect information and simultaneous moves, henceforth called games with public information. On this class, we prove that all communication equilibrium payoffs can be obtained without mediator by cheap-talk procedures. The result encompasses repeated games and stochastic games

Perfect correlated equilibria in stopping games

In many situations, such as trade in stock exchanges, agents have many instances to act even though the duration of interactions take a relatively short time. The agents in such situations can often coordinate their actions in advance, but coordination during the game consumes too much time. An equilibrium in such situations has to be sequential in order to handle mistakes made by players. In this paper, we present a new solution concept for infinite-horizon dynamic games, which is appropriate for such situations: a sequential constant-expectation normal-form correlated approximate equilibrium. Under additional assumptions, we show that every such game admits this kind of equilibrium

Sequential correlated equilibrium in stopping games

In many situations, such as trade in stock exchanges, agents have many instances to act even though the duration of interactions take a relatively short time. The agents in such situations can often coordinate their actions in advance, but coordination during the game consumes too much time. An equilibrium in such situations has to be sequential in order to handle mistakes made by players. In this paper, we present a new solution concept for infinite-horizon dynamic games, which is appropriate for such situations: a sequential constant-expectation normal-form correlated approximate equilibrium. Under additional assumptions, we show that every such game admits this kind of equilibrium

Integer Programming Approaches to Stochastic Games Arising in Paired Kidney Exchange and Industrial Organization

We investigate three different problems in this dissertation. The first two problems are related to games arising in paired kidney exchange, and the third is rooted in a computational branch of the industrial organization literature. We provide more details on these problems in the following. End-stage renal disease (ESRD), the final stage of chronic kidney disease, is the ninth-leading cause of death in the United States, where it afflicts more than a half million patients, and costs more than forty billion dollars indirect expenses annually. Transplantation is the preferred treatment for ESRD; unfortunately, there is a severe shortage of transplantable kidneys. Kidney exchange is a growing approach to alleviate the shortage of kidneys for transplantation, and the United States is considering creating a national kidney exchange program since such a program provides more and better transplants. A major challenge to establish a national kidney exchange program is the lack of incentives for transplant centers to participate in such a program. To overcome this issue, the kidney transplant community has recently proposed a payment strategy framework that incentivizes transplant centers to participate in a national program. Absent from this debate is a careful investigation of how to design these incentives. We develop a principal-agent model to analyze these incentives and find an equilibrium payment strategy. We develop a mixed-integer bilinear bilevel program to compute an equilibrium payment strategy. We show that this bilevel program can be solved as a mixed-integer linear program. We calibrate our model and provide several data-driven insights about advantages of a national kidney exchange program. We shed light on several controversial policy questions about an equilibrium payment strategy. In particular, we demonstrate that there exists a ``win-win'' payment strategy that could result in saving thousands of lives and billions of dollars annually. Consensus stopping games are a class of stochastic games that arises in the context of kidney exchange. Specifically, the problem of finding a socially optimal pure stationary equilibrium of a consensus stopping game is adapted to value a given kidney exchange. However, computational difficulties have limited its applicability. We show that a consensus stopping game may have many pure stationary equilibria, which in turn raises the question of equilibrium selection. Given an objective criterion, we study the problem of finding a best pure stationary equilibrium for the game, which we show to be NP-hard. We characterize the pure stationary equilibria, show that they form an independence system, and develop several families of valid inequalities. We then solve the equilibrium selection problem as a mixed-integer linear program (MILP) by a branch-and-cut approach. Our computational results demonstrate the advantages of our approach over a commercial solver. Industrial organization is an area of economics that studies firms and markets. Currently, a class of stochastic games are adopted to model behaviors of firms in a market. However, inherent challenges in computability of stationary equilibria have restricted its applicability. To overcome this challenge, we develop several characterizations of stationary equilibria for the class of stochastic games