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null (Ed.)Nonmonetary mechanisms for repeated allocation and decision making are gaining widespread use in many realworld settings. Our aim in this work is to study the performance and incentive properties of simple mechanisms based on artificial currencies in such settings. To this end, we make the following contributions: For a general allocation setting, we provide two blackbox approaches to convert any oneshot monetary mechanism to a dynamic nonmonetary mechanism using an artificial currency that simultaneously guarantees vanishing gains from nontruthful reporting over time and vanishing losses in performance. The two mechanisms trade off between their applicability and their computational and informational requirements. Furthermore, for settings with two agents, we show that a particular artificial currency mechanism also results in a vanishing price of anarchy.more » « less

null (Ed.)We consider an ad network’s problem of allocating the auction for each individual impression to an optimal subset of advertisers with the goal of revenue maximization. This is a variant of bipartite matching except that advertisers may strategize by choosing their bidding profiles and their total budget. Because the ad network’s allocation rule affects the bidders’ strategies, equilibrium analysis is challenging. We show that this analysis is tractable when advertisers face a linear budget cost r_j. In particular, we show that the strategy in which advertisers bid their valuations shaded by a factor of 1 + r_j is an approximate equilibrium with the error decreasing with market size. This equilibrium can be interpreted as one in which a bidder facing an opportunity cost rj is guaranteed a return on investment of at least rj per dollar spent. Furthermore, in this equilibrium, the optimal allocation for the ad network, as determined from a linear program (LP), is greedy with high probability. This is in contrast with the exogenous budgets case, in which the LP optimization is challenging at practical scales. These results are evidence that, although in general such bipartite matching problems may be challenging to solve because of their high dimensionality, the optimal solution is remarkably simple at equilibrium.more » « less

Motivated by practical concerns in applying information design to markets and service systems, we consider a persuasion problem between a sender and a receiver where the receiver may not be an expected utility maximizer. In particular, the receiver’s utility may be nonlinear in her belief; we deem such receivers as riskconscious. Such utility models arise, for example, when the receiver exhibits sensitivity to the variability and the risk in the payoff on choosing an action (e.g., waiting time for a service). In the presence of such nonlinearity, the standard approach of using revelationprinciple style arguments fails to characterize the set of signals needed in the optimal signaling scheme. Our main contribution is to provide a theoretical framework, using results from convex analysis, to overcome this technical challenge. In particular, in general persuasion settings with riskconscious agents, we prove that the sender’s problem can be reduced to a convex optimization program. Furthermore, using this characterization, we obtain a bound on the number of signals needed in the optimal signaling scheme. We apply our methods to study a specific setting, namely binary persuasion, where the receiver has two possible actions (0 and 1), and the sender always prefers the receiver taking action 1. Under a mild convexity assumption on the receiver’s utility and using a geometric approach,we show that the convex program can be further reduced to a linear program. Furthermore, this linear program yields a canonical construction of the set of signals needed in an optimal signaling mechanism. In particular, this canonical set of signals only involves signals that fully reveal the state and signals that induce uncertainty between two states.We illustrate our results in the setting of signaling wait time information in an unobservable queue with customers whose utilities depend on the variance of their waiting times.more » « less

We consider information design in spatial resource competition, motivated by ride sharing platforms sharing information with drivers about rider demand. Each of N colocated agents (drivers) decides whether to move to another location with an uncertain and possibly higher resource level (rider demand), where the utility for moving increases in the resource level and decreases in the number of other agents that move. A principal who can observe the resource level wishes to share this information in a way that ensures a welfaremaximizing number of agents move. Analyzing the principal’s information design problem using the Bayesian persuasion framework, we study both private signaling mechanisms, where the principal sends personalized signals to each agent, and public signaling mechanisms, where the principal sends the same information to all agents. We show: 1) For private signaling, computing the optimal mechanism using the standard approach leads to a linear program with 2 N variables, rendering the computation challenging. We instead describe a computationally efficient twostep approach to finding the optimal private signaling mechanism. First, we perform a change of variables to solve a linear program with O(N^2) variables that provides the marginal probabilities of recommending each agent move. Second, we describe an efficient sampling procedure over sets of agents consistent with these optimal marginal probabilities; the optimal private mechanism then asks the sampled set of agents to move and the rest to stay. 2) For public signaling, we first show the welfaremaximizing equilibrium given any common belief has a threshold structure. Using this, we show that the optimal public mechanism with respect to the senderpreferred equilibrium can be computed in polynomial time. 3) We support our analytical results with numerical computations that show the optimal private and public signaling mechanisms achieve substantially higher social welfare when compared with noinformation and fullinformation benchmarks.more » « less

We study the problem of optimal information sharing in the context of a service system. In particular, we consider an unobservable single server queue offering a service at a fixed price to a Poisson arrival of delaysensitive customers. The service provider can observe the queue, and may share information about the state of the queue with each arriving customer. The customers are Bayesian and strategic, and incorporate any information provided by the service provider into their prior beliefs about the queue length before making the decision whether to join the queue or leave without obtaining service. We pose the following question: which signaling mechanism and what price should the service provider select to maximize her revenue? We formulate this problem as an instance of Bayesian persuasion in dynamic settings. The underlying dynamics make the problem more difficult because, in contrast to static settings, the signaling mechanism adopted by the service provider affects the customers' prior beliefs about the queue (given by the steady state distribution of the queue length in equilibrium). The core contribution of this work is in characterizing the structure of the optimal signaling mechanism. We summarize our main results as follows. (1) Structural characterization: Using a revelationprinciple style argument, we find that it suffices to consider signaling mechanisms where the service provider sends a binary signal of "join" or "leave", and under which the equilibrium strategy of a customer is to follow the service provider's recommended action. (2) Optimality of threshold policies: For a given fixed price for service, we use the structural characterization to show that the optimal signaling mechanism can be obtained as a solution to a linear program with a countable number of variables and constraints. Under some mild technical conditions on the waiting costs, we establish that there exists an optimal signaling mechanism with a threshold structure, where service provider sends the "join" signal if the queue length is below a threshold, and "leave" otherwise. (In addition, at the threshold, the service provider randomizes.) For the special case of linear waiting costs, we derive an analytical expression for the optimal threshold i terms of the two branches of the LambertW function. (3) Revenue comparison: Finally, we show that with the optimal choice of the fixed price and using the corresponding optimal signaling mechanism, the service provider can achieve the same revenue as with the optimal statedependent pricing mechanism in a fullyobservable queue. This implies that in settings where statedependent pricing is not feasible, the service provider can effectively use optimal signaling (with the optimal fixed price) to achieve the same revenue.more » « less