Social connections provide various benefits, such as access to information, support, and collaboration, motivating individuals to form networks. However, in many social settings—like academic conferences or networking events—participants are initially strangers, making the networking process inherently anonymous and random. This paper incorporates anonymity into the canonical non-cooperative connections model ([Bala and Goyal, 2000]) to explore symmetric, mixed-strategy equilibria in network formation. We show that, for any trembling-hand perfect equilibrium, strategies can be interpreted as socialization effort and yield a random network, closely related to but distinct from classical Erdos-Renyi graphs. This provides a strategic microfoundation for random graphs. We fully characterize these equilibria and efficient networks for large populations as a function of connection costs.

Blackwell's celebrated theorem is a cornerstone of information economics, establishing a necessary and sufficient condition for when a distribution F of posterior means can be induced from a prior G: namely, if and only if F majorizes G. While this result provides a deep understanding of the structure of feasible belief distributions, it is non-constructive and does not explain how to design a signal that achieves a given F.

We study an information design problem with two informed senders and a receiver in which, in contrast to traditional Bayesian persuasion settings, senders do not have commitment power. In our setting, a trusted mediator/platform gathers data from the senders and recommends the receiver which action to play. We characterize the set of feasible action distributions that can be obtained in equilibrium, and provide an O(n log n) algorithm (where n is the number of states) that computes the optimal equilibrium for the senders. Additionally, we show that the optimal equilibrium for the receiver can be obtained by a simple revelation mechanism.

In a misspecified social learning setting, agents are condescending if they perceive their peers as having private information that is of lower quality than it is in reality. Applying this to a standard sequential model, we show that outcomes improve when agents are mildly condescending. In contrast, too much condescension leads to worse outcomes, as does anti-condescension.

We study a setting with a decision maker making a binary decision by aggregating information from symmetric agents. Each agent provides the decision maker a recommendation depending on her private signal about the hidden state. We assume that agents are truthful - an agent recommends guessing the more likely state based on her information. This assumption is natural if the agents are unaware of how the decision-maker will aggregate their recommendations. While the decision maker has a prior distribution over the hidden state and knows the marginal distribution of each agent's private signal, the correlation between these signals is chosen adversarially. The decision maker's goal is choosing an information aggregation rule that is robustly optimal.

We study the robustness of cheap-talk equilibria to infinitesimal private information of the receiver in a model with a binary state-space and state-independent sender-preferences.

We study a model of opinion exchange in social networks where a state of the world is realized and every agent receives a zero-mean noisy signal of the realized state. It is known from Golub and Jackson [6] that under DeGroot [3] dynamics agents reach a consensus that is close to the state of the world when the network is large. The DeGroot dynamics, however, is highly non-robust and the presence of a single "stubborn agent" that does not adhere to the updating rule can sway the public consensus to any other value. We introduce a variant of DeGroot dynamics that we call 1/m-DeGroot. 1/m-DeGroot dynamics approximates standard DeGroot dynamics to the nearest rational number with m as its denominator and like the DeGroot dynamics it is Markovian and stationary. We show that in contrast to standard DeGroot dynamics, 1/m-DeGroot dynamics is highly robust both to the presence of stubborn agents and to certain types of misspecifications.

We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We ask which distributions over empirical distributions of posteriors beliefs in the population are feasible. We provide a necessary and sufficient condition for feasibility. We apply this result in several domains. First, we study the problem of maximizing the polarization of beliefs in a population. Second, we provide a characterization of the feasible agent-symmetric product distributions of posteriors. Finally, we study an instance of a private Bayesian persuasion problem and provide a clean formula for the sender's optimal value.

We consider a model of Bayesian persuasion with one informed sender and several uninformed receivers. The sender can affect receivers' beliefs via private signals and the sender's objective depends on the combination of induced beliefs.

The classic herding model examines the asymptotic behavior of agents who observe their predecessors' actions as well as a private signal from an exogenous information structure. In this paper we introduce a self-interested sender into the model, and study the sender's problem of designing this information structure. If agents cannot observe each other the model reduces to Bayesian persuasion. However, when agents observe predecessors' actions, they may learn from each other, potentially harming the sender. We identify necessary and sufficient conditions under which the sender can nevertheless obtain the same utility as when the agents are unable to observe each other.

We analyze boundedly rational updating from aggregate statistics in a model with binary actions and binary states. Agents each take an irreversible action in sequence after observing the unordered set of previous actions. Each agent first forms her prior based on the aggregate statistic, then incorporates her signal with the prior based on Bayes rule, and finally applies a decision rule that assigns a (mixed) action to each belief. If priors are formed according to a discretized DeGroot rule, then actions converge to the state (in probability), i.e., asymptotic learning, in any informative information structure if and only if the decision rule satisfies probability matching. This result generalizes to unspecified information settings where information structures differ across agents and agents know only the information structure generating their own signal. Also, the main result extends to the case of n states and n actions.

Bayes-rational agents reside on a social network. They take binary actions sequentially and irrevocably, and the right action depends on an unobservable state. Each agent receives a bounded private signal about the realized state and observes the actions taken by the neighbors who acted before. How does the network topology affect the ability of agents to aggregate the information dispersed over the population by means of the private signals?

We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. Our main result is that, for the two-agent case, a quantitative version of Aumann's Agreement Theorem provides a necessary and sufficient condition for feasibility. For any number of agents, a related "no-trade" condition likewise provides a characterization of feasibility. We use our characterization to construct joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior. We study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.

The canonical Bayesian persuasion setting studies a model where an informed agent, the Sender, can partially share his information with an uninformed agent, the Receiver. The Receiver's utility is a function of the state of nature and the Receiver's action while the Sender's is only a function of the Receiver's action. The classical results characterize the Sender's optimal information disclosure policy whenever the state space is finite. In this paper we study the same setting where the state space is an interval on the real line. We introduce the class of bi-pooling policies and the induced distribution over posteriors which we refer to as bi-pooling distributions. We show that this class of distributions characterizes the set of optimal distributions in the aforementioned setting. Every persuasion problem admits an optimal bi-pooling distribution as a solution. Conversely, for every bi-pooling distribution there exists a persuasion problem in which the given distribution is the unique optimal one. We leverage this result to study the structure of the price function (see [1]) in this setting and to identify optimal information disclosure policies. The full paper can be accessed at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3511516.

Society uses the following game to decide on the supply of a public good. Each agent can choose whether or not to contribute to the good. Contributions are collected and the good is supplied whenever total contributions exceed a threshold. We study the case where the public good is excludable, agents have a common value and each agent receives a private signal about the common value. This game models a standard crowdfunding setting as it is executed in popular crowdfunding platforms such as Kickstarter and Indiegogo. We study how well crowdfunding performs from the firm's perspective, in terms of market penetration, and how it performs from the perspective of society, in terms of efficiency.

We consider ε-equilibria notions for a constant value of ε in n-player m-action games, where m is a constant. We focus on the following question: What is the largest grid size over the mixed strategies such that ε-equilibrium is guaranteed to exist over this grid.

Bayesian experts with a common prior that are exposed to different evidence possibly make contradicting probabilistic forecasts. A policy maker who receives the forecasts must aggregate them in the best way possible. This is a challenge whenever the policy maker is not familiar with the prior nor the model and evidence available to the experts. We propose a model of non-Bayesian forecast aggregation and adapt the notion of regret as a means for evaluating the policy maker's performance. Whenever experts are Blackwell ordered taking a weighted average of the two forecasts, the weight of which is proportional to its precision (the reciprocal of the variance), is optimal. The resulting regret is equal 1/8(5√ 5-11) approx 0.0225425, which is 3 to 4 times better than naive approaches such as choosing one expert at random or taking the non-weighted average.