We analyze the performance of heterogeneous learning agents in asset markets with stochastic payoffs. Agents aim to maximize the expected growth rate of their wealth but have different theories on how to learn to do this best. Our main focus is on comparing Bayesian learners and no-regret learners who compete in markets and identifying the conditions under which each approach is more effective. Bayesian learners with a finite prior that assigns positive probability to the correct model have posterior beliefs that converge exponentially fast, and such agents survive even in the presence of agents who invest according to the correct model. Bayesian learners with a continuum prior converge at a slower rate of O((logT)/T).

Incentive design is more likely to elicit desired outcomes when it is derived based on accurate models of agent behavior. A substantial literature in behavioral economics, however, demonstrates that individuals systematically and consistently deviate from the standard economic model---expected utility theory---for decision-making under uncertainty, %a central component of which is at the core of the equilibrium analysis necessary to facilitate mechanism design. Can these behavioral biases---as modeled by prospect theory [Kahneman and Tversky 1979]---in agents' decision-making make a difference to the optimal design of incentives in these environments? In this paper, we explore this question in the context of markets for online labor and crowdsourcing where workers make strategic choices about whether to undertake a task, but do not strategize over quality conditional on participation. We ask what kind of incentive scheme---amongst a broad class of contracts, including those observed on major crowdsourcing platforms such as fixed prices or base payments with bonuses (as on MTurk or oDesk), or open-entry contests (as on platforms like Kaggle or Topcoder)---a principal might want to employ, and how the answer to this question depends on whether workers behave according to expected utility or prospect theory preferences.

Gamification is growing increasingly prevalent as a means to incentivize user engagement of social media sites that rely on user contributions. Badges, or equivalent rewards such as top-contributor lists that are used to recognize a user's contributions on a site, clearly appear to be valued by users who actively pursue and compete for them. However, different sites use different badge designs, varying how, and for what, badges are awarded--- some sites such as StackOverflow award badges for meeting fixed levels of contribution, while others like Amazon and Y! Answers reward users for being amongst some top set of contributors on the site, corresponding to a competitive standard of performance. Given that users value badges, and that contributing to a site requires effort, how badges are designed will affect the incentives--- and therefore the participation and effort--- elicited from strategic users on a site.

The spread of a cascading failure through a network is an issue that comes up in many domains - in the contagious failures that spread among financial institutions during a financial crisis, through nodes of a power grid or communication network during a widespread outage, or through a human population during the outbreak of an epidemic disease. Here we study a natural model of threshold contagion: each node v is assigned a numerical threshold ℓ(v) drawn independently from an underlying distribution μ, and v will fail as soon as ℓ(v) of its neighbors fail. Despite the simplicity of the formulation, it has been very challenging to analyze the failure processes that arise from arbitrary threshold distributions; even qualitative questions concerning which graphs are the most resilient to cascading failures in these models have been difficult to resolve. Here we develop a set of new techniques for analyzing the failure probabilities of nodes in arbitrary graphs under this model, and we compare different graphs G according to their μ-risk, defined as the maximum failure probability of any node in G when thresholds are drawn from μ. We find that the space of threshold distributions has a surprisingly rich structure when we consider the risk that these thresholds induce on different graphs: small shifts in the distribution of the thresholds can favor graphs with a maximally clustered structure (i.e., cliques), those with a maximally branching structure (trees), or even intermediate hybrids.

There are a number of domains where agents must collectively form a network in the face of the following trade-off: each agent receives benefits from the direct links it forms to others, but these links expose it to the risk of being hit by a cascading failure that might spread over multi-step paths. Financial contagion, epidemic disease, and the exposure of covert organizations to discovery are all settings in which such issues have been articulated.

In a wide range of markets, individual buyers and sellers often trade through intermediaries, who determine prices via strategic considerations. Typically, not all buyers and seller shave access to the same intermediaries, and they trade at correspondingly different prices that reflect their relative amounts of power in the market. We model this phenomenon using a game in which buyers, sellers, and traders engage in trade on a graph that represents the access each buyer and seller has to the traders. In this model, traders set prices strategically, and then buyers and sellers react to the prices they are offered. We show that the resulting game always has a subgame perfect Nash equilibrium, and that all equilibria lead to an efficient (i.e. socially optimal) allocation of goods. We extend these results to a more general type of matching market, such as one finds in the matching ofjob applicants and employers. Finally, we consider how the profits obtained by the traders depend on the underlying graph -- roughly, a trader cancommand a positive profit if and only if it has an "essential" connection in the network structure, thus providing a graph-theoretic basis for quantifying the amount of competition among traders. Our work differs from recent studies of how price is affected by network structure through our modeling of price-setting as a strategic activity carried out by a subset of agents in the system, rather than studying prices set via competitive equilibrium or by a truthful mechanism.