Dynamic Games, Contracts, and Markets

Motivated by the problem of sustaining cooperation in large communities with limited information, we analyze sequences of repeated games where the population size N, the discount factor δ, and the monitoring structure (with channel capacity denoted by C) vary together. We show that if (1-δ) N/C → ∞ then all Nash equilibrium payoffs are consistent with approximately myopic play. A folk theorem under a novel identifiability condition provides a near converse. For example, if (1-δ) N log (N)/C → 0 then a folk theorem holds under random auditing, where each player's action is monitored with the same probability in every period. If attention is restricted to linear equilibria (a generalization of strongly symmetric equilibria), cooperation is possible only under much more severe parameter restrictions. Methodologically, we develop connections between repeated games and information theory.

Two activists with correlated private positions in a firm’s stock trade sequentially before simultaneously exerting effort that determines firm’s value. A novel linear equilibrium where trades are non-zero on average emerges, as the leading activist manipulates the price to induce the follower to acquire a larger position and thus add more value. We examine the implications of this equilibrium for outcomes, and discuss it in light of so-called “wolf-pack” activism. Finally, if the volatility of order flow is sufficiently large and hence manipulation difficult, an equilibrium arises where one or both activists trade against the initial position to coordinate.

I study how a principal should delegate to an agent with career concerns. The agent and principal are assumed to have aligned intrinsic incentives. However, the market observes the chosen action, and rewards the agent more, the higher it perceives his (private) type to be. This “reputational bias” has many similarities to the classic “material bias” studied in the communication literature, for instance, both can induce the same cheap talk equilibrium sets. However, I show that it is always optimal to impose a floor on the set of available actions in reputational delegation. This is in stark contrast to delegation to an agent with a material bias, where it is never optimal to restrict the agent’s flexibility to take low actions. I specialize to the exponential family of distributions to show that offering flexibility to high types (i.e. full separation) is optimal. This result uses a recursive approach novel to communication problems.

Motivated by online advertising auctions, we study auction design in repeated auctions played by simple Artificial Intelligence algorithms (Q-learning). We find that first-price auctions with no additional feedback lead to tacit-collusive outcomes (bids lower than values), while second-price auctions do not. We show that the difference is driven by the incentive in first-price auctions to outbid opponents by just one bid increment. This facilitates re-coordination on low bids after a phase of experimentation. We also show that providing information about lowest bid to win, as introduced by Google at the time of switch to first-price auctions, increases competitiveness of auctions.

Vertically-integrated marketplaces commonly use data on the sales of third-party products to decide which private-label products to introduce. We develop a model to evaluate the competitive implications of this practice when third-party innovation is sensitive to private-label competition. We find that a ban on data usage stimulates innovation for “experimental” product categories with significant upside demand potential, but stifles it otherwise. “Data patents”, which restrict data usage for a limited time, improve on a ban and can stimulate innovation across a wide variety of settings. Our results contribute to an ongoing policy discussion regarding data usage by dominant
online platforms.

This paper proposes a general framework in which agents are constrained to use simple time series models to forecast economic variables and characterizes the resulting bias in the agents’ forecasts. It considers agents who can only entertain state-space models with no more than d states, where d measures the agents’ cognitive abilities. Agents’ models are otherwise unrestricted a priori and disciplined endogenously by maximizing the fit to the true process. When the true process does not have a d -state representation, agents end up with misspecified models and biased forecasts. If the true process satisfies an ergodicity assumption, the bias manifests itself as persistence bias: a tendency to attend to the most persistent observables at the expense of less persistent ones. The bias causes agents’ forward-looking decisions to mimic the dynamics of backward-looking, persistent variables in the economy. It also dampens the response of agents’ actions to shocks and leads to additional co-movements between various choices. The paper then proceeds to study the implications of the theory in the context of three calibrated workhorse macro models: the new-Keynesian, real business cycle, and Diamond–Mortensen–Pissarides models. In each case, constraining agents to use simple models brings the model’s predictions more in line with the data, without adding any parameters other than the integer d.

We propose a model of sequential spatial search with learning. There is a mapping from a space of technologies (or products) to qualities that is unknown to the searcher. The searcher can learn various points on this mapping through costly experimentation. She cares both about the technology that she adopts as well as the best one available, as would a firm in an innovation race or an online shopper concerned with missing a good deal. She does not have a prior over mappings but knows only that neighboring technologies in attribute space are similar in quality. We characterize optimal search strategies when the searcher worries about worst-case mappings at every step of the way. These are mappings that trigger wild-goose chases: excessive search with relatively poor discoveries to show for it. We derive comparative statics that match patterns observed in empirical studies on spatial search. Finally, we apply the results to the problem of optimal search space design faced by online platforms.

This paper studies a sequential learning problem where individuals are ambiguous about other people’s data-generating processes. This paper finds that the occurrence of an information cascade can be interpreted as a result of ambiguity instead of details of the true data-generating process as suggested by the literature. When there is sufficient ambiguity, for all possible data generating processes, an information cascade occurs almost surely. This paper further shows that many standard results may even represent a knife-edge case with respect to ambiguity. An arbitrarily small degree of ambiguity can produce a cascade when signals are bounded and destroy complete learning when signals are unbounded.

We develop a tractable framework that jointly determines trading connections and risk allocations banks. In an environment with ex-ante homogenous and risk averse banks, a concentrated structure arises when banks are endowed with limited liability or options of investing technologies. The equilibrium network is payoff unique, trading of between the benefit of risk-sharing vs. risk-concentration. A continuous change in asset riskiness or policy parameters can trigger a structural shift, resulting in discontinuous changes in aggregate risks and transaction prices. We use this framework to evaluate the effect of different interventions on the market structure.

We study how long-lived, rational, exponentially discounting agents learn in a social network. In every period, each agent observes the past actions of his neighbors, receives a private signal, and chooses an action with the objective of matching the state. Since agents behave strategically, and since their actions depend on higher order beliefs, it is difficult to characterize equilibrium behavior. Nevertheless, we show that regardless of the size and shape of the network, and the patience of the agents, the equilibrium speed of learning is bounded from above by a constant that only depends on the private signal distribution.

This paper builds a dynamic general equilibrium model of the market for attention. In the model, digital platforms compete for consumer attention by investing in the quality of their services which they provide for free. They sell the attention, in the form of advertisements, to firms in the product market who use consumer data to target. We characterize search frictions in the product market, ad revenues, platforms’ quality levels, and welfare in the unique stationary equilibrium. Banning data tracking, capping ad frequency, and enforcing platform interoperability may often lead to better platforms at the expense of worse product consumption. Platform investment and ad frequency may be too high or low depending on parameters. The sources of inefficiency concern appropriability, business stealing, and market power.

We study the combined use of monetary and informational incentives in a dynamic moral hazard setting. We identify a key necessary condition for incentive compatibility and use it to pin down cost-minimizing payment schedules. As an illustration we apply it to a simple principal-agent problem and to optimal dynamic contests.

The strategic importance of commitment in bargaining is widely acknowledged. Yet disentangling its role from key features of canonical models, such as proposal power and reputational concerns, is difficult. This paper introduces a model of bargaining with strategic commitment at its core. Following Schelling (1956), commitment ability stems from the costly nature of concession and is endogenously determined by players’ demands. Agreement is immediate for familiar bargainers, modelled via renegotiation-proofness. The unique prediction at the high concession cost limit provides a strategic foundation for the Kalai bargaining solution. Equilibria with delay feature a form of gradualism in demands.

We consider a firm that seeks to fill a single vacancy by searching over a sequence of ex-ante identical workers who are ex-post differentiated in their productivity. Before hiring, the firm may acquire information about a worker’s productivity by paying a certification intermediary to test the worker. The intermediary faces a trade-off in the design of its certification policy: providing a more informative test increases the price the intermediary can charge for certification but reduces the average number of workers the firm tests before hiring. We show that the intermediary’s profit-maximizing contract (i) induces efficient hiring standards, (ii) extracts the full-surplus, and (iii) strings along the firm, i.e., keeps the firm searching for longer than the firm would like. We also consider the case in which workers pay for certification and show that (iv) the intermediary may be able to create a demand for certification, even when the certificate conveys little to no information, and (v) the workers benefit when disclosure of test results is mandatory

This paper studies a dynamic principal-agent model in which the principal designs both monitoring structure and compensation scheme. The model predicts simple effort choice and coarse evaluation. In the optimal contract, the agent exerts effort until termination or tenure, and Poisson processes emerge as the optimal monitoring structure. In the trial period, the principal monitors with inconclusive Poisson bad news, arrival of which leads to termination. The non-stationary Poisson monitoring becomes more informative and less frequent over time. After the trial period, the principal switches to a stationary Poisson monitoring structure with two-sided experiments. Bad news leads to termination and good news leads to tenure.

We employ novel methods to investigate optimal project management in a setting plagued by unavoidable setbacks. The contractor can cover up delays from shirking either by making false claims of setbacks or by postponing the reports of real ones. The sponsor induces work and honest reporting via a soft deadline and a reward for completion. Latestage setbacks trigger randomization between cancellation and extension. Thus the project may run far beyond its initial schedule, generating arbitrarily large overruns, and yet be canceled. Absent commitment to randomize, the sponsor grants the contractor more time to complete the project.

This paper studies the implications of optimal insurance provision for long-run welfare and inequality in economies with persistent private information. We consider a model in which a principal insures an agent whose privately observed endowment follows an ergodic, finite Markov chain. The optimal contract always induces immiseration: the agent’s consumption and utility decrease without bound. Under positive serial correlation, the optimal contract also features backloaded high-powered incentives: the sensitivity of the agent’s utility with respect to his report increases without bound. These results significantly extend — and elucidate the limits of — the hallmark immiseration results for economies with iid private information. Our analysis utilizes recursive techniques for contracting with persistent states, accounts for the possibility of binding global incentive constraints, extends to other canonical insurance settings (e.g., Mirrleesian economies), and has additional implications for the short-run dynamics of optimal contracts.