Acyclic Games and Iterative Voting

We consider iterative voting models and position them within the general framework of acyclic games and game forms. More specifically, we classify convergence results based on the underlying assumptions on the agent scheduler (the order of players) and the action scheduler (which better-reply is played). Our main technical result is providing a complete picture of conditions for acyclicity in several variations of Plurality voting. In particular, we show that (a) under the traditional lexicographic tie-breaking, the game converges for any order of players under a weak restriction on voters' actions; and (b) Plurality with randomized tie-breaking is not guaranteed to converge under arbitrary agent schedulers, but from any initial state there is \emph{some} path of better-replies to a Nash equilibrium. We thus show a first separation between restricted-acyclicity and weak-acyclicity of game forms, thereby settling an open question from [Kukushkin, IJGT 2011]. In addition, we refute another conjecture regarding strongly-acyclic voting rules.Comment: some of the results appeared in preliminary versions of this paper: Convergence to Equilibrium of Plurality Voting, Meir et al., AAAI 2010; Strong and Weak Acyclicity in Iterative Voting, Meir, COMSOC 201

Essays on Network Formation and Attention

This dissertation tackles two important developing topics in economics: network formation and the allocation of attention. First, it examine the idea that the timing of entry into the network is a crucial determinant of a node’s final centrality. We propose a model of strategic network growth which makes novel predictions about the forward-looking behaviors of players. In particular, the model predicts that agents entering the network at specific times will become central “vie for dominance”. In a laboratory experiment, we find that players do exhibit “vying for dominance” behavior, but do not always do so at the predicted critical times. A model of heterogeneous risk aversion best fits the observed deviations from initial predictions. Timing determines whether players have the opportunity to become attempt to become dominant, but individual characteristics determine whether players exploit that opportunity. This dissertation also examines models of rational inattention, in which decision-makers rationally evaluate the trade-off between the costs and the benefits of information acquisition. We provide results on recovering the implicit attention cost function by looking at the relationship between incentives and performance. We conduct laboratory experiments consisting of simple perceptual tasks with fine-grained variation in the level of potential rewards. We find that most subjects exhibit monotonicity in performance with respect to potential rewards, and there is mixed evidence on continuity and convexity of costs. We also perform a model selection exercise and find that subjects’ behavior is generally most consistent with a small but diverse subset of cost functions commonly assumed in the literature

Calibrated Fairness in Bandits

We study fairness within the stochastic, \emph{multi-armed bandit} (MAB) decision making framework. We adapt the fairness framework of "treating similar individuals similarly" to this setting. Here, an `individual' corresponds to an arm and two arms are `similar' if they have a similar quality distribution. First, we adopt a {\em smoothness constraint} that if two arms have a similar quality distribution then the probability of selecting each arm should be similar. In addition, we define the {\em fairness regret}, which corresponds to the degree to which an algorithm is not calibrated, where perfect calibration requires that the probability of selecting an arm is equal to the probability with which the arm has the best quality realization. We show that a variation on Thompson sampling satisfies smooth fairness for total variation distance, and give an $\tilde{O}((kT)^{2/3})$ bound on fairness regret. This complements prior work, which protects an on-average better arm from being less favored. We also explain how to extend our algorithm to the dueling bandit setting.Comment: To be presented at the FAT-ML'17 worksho

Effective medical surplus recovery

We analyze not-for-profit Medical Surplus Recovery Organizations (MSROs) that manage the recovery of surplus (unused or donated) medical products to fulfill the needs of underserved healthcare facilities in the developing world. Our work is inspired by an award-winning North American non-governmental organization (NGO) that matches the uncertain supply of medical surplus with the receiving parties’ needs. In particular, this NGO adopts a recipient-driven resource allocation model, which grants recipients access to an inventory database, and each recipient selects products of limited availability to fill a container based on its preferences. We first develop a game theoretic model to investigate the effectiveness of this approach. This analysis suggests that the recipient-driven model may induce competition among recipients and lead to a loss in value provision through premature orders. Further, contrary to the common wisdom from traditional supply chains, full inventory visibility in our setting may accelerate premature orders and lead to loss of effectiveness. Accordingly, we identify operational mechanisms to help MSROs deal with this problem. These are: (i) appropriately selecting container capacities while limiting the inventory availability visible to recipients and increasing the acquisition volumes of supplies, (ii) eliminating recipient competition through exclusive single-recipient access to MSRO inventory, and (iii) focusing on learning recipient needs as opposed to providing them with supply information, and switching to a provider-driven resource allocation model. We use real data from the NGO by which the study was inspired and show that the proposed improvements can substantially increase the value provided to recipients