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.

We consider a group of agents who can each take an irreversible costly action whose payoff depends on an unknown state. Agents learn about the state from private signals, as well as from past actions of their social network neighbors, which creates an incentive to postpone taking the action. We show that outcomes depend on network structure: on networks with a linear structure patient agents do not converge to the first-best action, while on regular directed tree networks they do.

We study a contract design problem between a principal and multiple agents. Each agent participates in an independent task with binary outcomes (success or failure), in which she may exert costly effort towards improving her probability of success, and the principal has a fixed budget which it can use to provide outcome-dependent rewards to the agents. Crucially, each agent's reward may depend not only on whether she succeeds or fails, but also on whether other agents succeed or fail, and we assume the principal cares only about maximizing the agents' probabilities of success, not how much of the budget it expends. A motivating example might be that of a sales manager who is endowed with a fixed budget by the firm and is tasked with incentivizing the salespeople to successfully close sales. The manager can observe whether each salesperson was able to sell the product or not, but now how much effort the salesperson exerted towards making the sale.

In the classic herding model, agents receive private signals about an underlying binary state of nature, and act sequentially to choose one of two possible actions, after observing the actions of their predecessors. We investigate what types of behaviors lead to asymptotic learning, where agents will eventually converge to the right action in probability. It is known that for rational agents and bounded signals, there will not be asymptotic learning. Does it help if the agents can be cooperative rather than act selfishly? This is simple to achieve if the agents are allowed to use randomized protocols. In this paper, we provide the first deterministic protocol under which asymptotic learning occurs. In addition, our protocol has the advantage of being much simpler than previous protocols.