Local Dominance

We define a local notion of dominance that speaks to the true choice problems among actions in a game tree. When we do not restrict players' ability to do contingent reasoning, a reduced strategy is weakly dominant if and only if it prescribes a locally dominant action at every decision node, therefore any dynamic decomposition of a direct mechanism that preserves strategy-proofness is robust to the lack of global planning. Under a form of wishful thinking, we also show that strategy-proofness is robust to the lack of forward planning. Moreover, we identify simple forms of contingent reasoning and foresight, driven by the local viewpoint. We construct a dynamic game that implements the Top Trading Cycles allocation in locally dominant actions under these simple forms of reasoning

Preferences with changing ambiguity aversion

Published in Economic Theory https://doi.org/10.1007/s00199-018-1156-2</p

Fair Division with Uncertain Needs

Published in Social Choice and Welfare https://doi.org/10.1007/s00355-018-1109-5</p

Three essays on fair division and decision making under uncertainty

The first chapter is based on a paper with Jin Li in fair division. It was recently discovered that on the domain of Leontief preferences, Hurwicz (1972)'s classic impossibility result does not hold; that is, one can find efficient, strategy-proof and individually rational rules to divide resources among agents. Here we consider the problem of dividing l divisible goods among n agents with the generalized Leontief preferences. We propose and characterize the class of generalized egalitarian rules which satisfy efficiency, group strategy-proofness, anonymity, resource monotonicity, population monotonicity, envy-freeness and consistency. On the Leontief domain, our rules generalize the egalitarian-equivalent rules with reference bundles. We also extend our rules to agent-specific and endowment-specific egalitarian rules. The former is a larger class of rules satisfying all the previous properties except anonymity and envy-freeness. The latter is a class of efficient, group strategy-proof, anonymous and individually rational rules when the resources are assumed to be privately owned. The second and third chapters are based on two working papers of mine in decision making under uncertainty. In the second chapter, I study the wealth effect under uncertainty --- how the wealth level impacts a decision maker's degree of uncertainty aversion. I axiomatize a class of preferences displaying decreasing absolute uncertainty aversion, which allows a decision maker to be more willing to take uncertainty-bearing behavior when he becomes wealthier. Three equivalent preference representations are obtained. The first is a variation on the constraint criterion of Hansen and Sargent (2001). The other two respectively generalize Gilboa and Schmeidler (1989)'s maxmin criterion and Maccheroni, Marinacci and Rustichini (2006)'s variational representation. This class, when restricted to preferences exhibiting constant absolute uncertainty aversion, is exactly Maccheroni, Marinacci and Rustichini (2006)'s ariational preferences. Thus, the results further enable us to establish relationships among the representations for several important classes within variational preferences. The three representations provide different decision rules to rationalize the same class of preferences. The three decision rules correspond to three ways which are proposed in the literature to identify a decision maker's perception about uncertainty and his attitude toward uncertainty. However, I give examples to show that these identifications conflict with each other. It means that there is much freedom in eliciting two unobservable and subjective factors, one's perception about and attitude toward uncertainty, from only his choice behavior. This exactly motivates the work in Chapter 3. In the third chapter, I introduce confidence orders in addition to preference orders. Axioms are imposed on both orders to reveal a decision maker's perception about uncertainty and to characterize the following decision rule. A decision maker evaluates an act based on his aspiration and his confidence in this aspiration. Each act corresponds to a trade-off line between the two criteria: The more he aspires, the less his confidence in achieving the aspiration level. The decision maker ranks an act by the optimal combination of aspiration and confidence on its trade-off line according to an aggregating preference of his over the two-criterion plane. The aggregating preference indicates his uncertainty attitude, while his perception about uncertainty is summarized by a generalized second-order belief over the prior space, and this belief is revealed by his confidence order

Sharing Sequential Values in a Network

Published in Journal of Economic Theory https://doi.org/10.1016/j.jet.2018.08.004</p

An Emergency Disposal Decision-making Method with Human--Machine Collaboration

Rapid developments in artificial intelligence technology have led to unmanned systems replacing human beings in many fields requiring high-precision predictions and decisions. In modern operational environments, all job plans are affected by emergency events such as equipment failures and resource shortages, making a quick resolution critical. The use of unmanned systems to assist decision-making can improve resolution efficiency, but their decision-making is not interpretable and may make the wrong decisions. Current unmanned systems require human supervision and control. Based on this, we propose a collaborative human--machine method for resolving unplanned events using two phases: task filtering and task scheduling. In the task filtering phase, we propose a human--machine collaborative decision-making algorithm for dynamic tasks. The GACRNN model is used to predict the state of the job nodes, locate the key nodes, and generate a machine-predicted resolution task list. A human decision-maker supervises the list in real time and modifies and confirms the machine-predicted list through the human--machine interface. In the task scheduling phase, we propose a scheduling algorithm that integrates human experience constraints. The steps to resolve an event are inserted into the normal job sequence to schedule the resolution. We propose several human--machine collaboration methods in each phase to generate steps to resolve an unplanned event while minimizing the impact on the original job plan.Comment: 15 pages, 16 figure

Precautionary Saving with Changing Income Ambiguity

We study a two-period saving model where the agent's future income might be ambiguous. Our agent has a version of the smooth ambiguity decision criterion (Klibanoff, Marinacci and Mukerji (2005)), where the agent's perception about ambiguity is described by a second-order belief over first-order risks. We model increasing ambiguity as a spreading-out of the second-order belief. We show that under a "Risk Comonotonicity" condition, our agent saves more when ambiguity in future income increases. We argue that the condition is indispensable for our result