Session 5: Dynamic Games, Contracts, and Markets

An organization is autonomous if it has the right or power of self-government. Self-government implies that autonomous organizations cannot rely on outside parties for monitoring or contract enforcement. We present a model of the optimal power allocation in such an organization. The organization commits to a governance structure that allocates managerial power to agents. Members with power (“managers”) can punish members without power (“subordinates”). This power is, however, limited by the subordinates’ right to exit the organization. There are three main results. First, the goals of autonomy, decentralization, and efficiency conflict with one another. We call this result the Organizational Trilemma. Second, there is a Paradox of Power: an agent can be made worse off by their own power. Third, optimal governance structures in autonomous organizations are centralized and populist: the powerful party shows restraint in early periods, only to abuse their power in later periods.

We develop a dynamic contracting theory of asset- and cash flow-based financing that demonstrates how firm, intermediary, and capital market characteristics shape firms’ financing constraints. A firm with imperfect access to equity financing covers financing needs through costly sources — an intermediary and retained cash. The firm’s financing capacity is endogenously determined by either the liquidation value of assets (asset-based) or the intermediary’s going-concern valuation of the firm’s cash flows (cash flow-based). We implement the optimal contract between the firm and intermediary with both unsecured and secured debt (credit lines) in an overlapping pecking order: the firm simultaneously finances cash flow shortfalls with unsecured debt and either cash reserves (if available) or secured debt (otherwise). Improved access to equity financing increases debt capacity, thus debt and equity are dynamic complements. When the firm does well, it repays its debt in full, while when in distress, repayment dynamics mirror U.S. bankruptcy procedures (Chapter 7 vs 11).

We study a bilateral trade problem where a principal faces delayed information, such as a seller who does not yet know the production cost. Postponing the contracting process incurs a costly delay, while early contracting under limited information can lead to incentive issues, with the principal potentially misrepresenting private information that will be revealed later. We show that the fully optimal mechanism, which includes a menu of two-part tariffs, effectively addresses these challenges by optimally balancing the ex-ante and ex-post information rents for both parties. Since the fully optimal mechanism might be impractical in some applications, we also study price mechanisms. We show that the optimal price mechanism often entails trade at both the ex-ante and ex-post stages. By using such a price mechanism, the principal can lower the cost of delay by transacting with high-type agents early and relax the incentive constraints by postponing contracts with lower-type agents.

Pricing decisions are crucial for managing a firm’s reputation and maximizing profits. Consumer reviews reflect both the product   and its price, with more favorable reviews being left when a product is priced lower. We study whether such review behavior can induce a firm to manipulate the review process by underpricing its product, or pricing it below current consumers’ willingness to pay. We introduce an equilibrium model with a privately informed firm repeatedly selling its product to uninformed but rational consumers who learn about the quality of the product from past reviews and current prices. We show that underpricing can arise only when the firm reputation is low and then only under a specific condition on consumers’ taste shock distribution, which we fully characterize. Rating manipulation unambiguously benefits consumers, because it operates via underpricing.

We analyze the dynamic tradeoff between the generation and the disclosure of evidence.

Agents are tempted to delay investing in a new technology in order to learn from information generated by the experiences of others. This informational free-riding is collectively harmful as it slows down innovation adoption. A welfare-maximizing designer can delay the disclosure of previously generated information in order to speed up adoption.

The optimal policy transparently discloses bad news and delays good news. This finding resonates with regulation demanding that fatal breakdowns be reported promptly. Remarkably, the designer's intervention makes all agents better off.

I study a dynamic disclosure game in which an agent controls the time window over which information flows to the decision maker, but does not control the content of that information. In equilibrium, the agent has incentives to delay the start of disclosure to continue to learn privately for some time. This delay exacerbates the information asymmetry between the agent and the decision maker as the agent is learning while the decision maker is not. This information asymmetry is then (partially) resolved during the disclosure window. The length of the disclosure window is determined by the degree of information asymmetry at the beginning of the window, with longer windows associated with greater information asymmetry.

In this paper, we study the problem of information disclosure by an expert (principal) who wishes to maximize engagement faced with an agent who wishes to collect information as quickly as possible.The principal prefers agent to stay around for longer while the agent wants to acquire an information. The principal can commit to a dynamic information revelation strategy while the agent cannot commit. Several result emerge on optimal engagement: First, If the agent and principal have the same prior, the information revelation depends on their relative patience, i.e., the way the evaluate payoff over time. When the agent is more impatient than the principal, optimal revelation takes the form of gradual information revelation. In contrast, when the principal is more impatient, optimal communication results in a period of no information revelation and then abrupt revelation. Second, when the principal and the agent agree to disagree in terms of their beliefs, we will have catering to the bias, where principal always starts with signals that are more aligned to that of agent’s prior and the information revelation will always starts with a period of gradual information revelation. We discuss how our model can be used to analyze the effect of personalized news on belief polarization, and the effect of regulatory policies on optimal information revelation.

We consider the fixed points of nonlinear operators that naturally arise in games and general equilibrium models with endogenous networks, dynamic stochastic games, in models of opinion dynamics with stubborn agents, and financial networks. We study limit cases that correspond to high coordination motives, infinite patience, vanishing stubbornness and small exposure to the real sector in the applications above. Under monotonicity and continuity assumptions, we provide explicit expressions for the limit fixed points. We show that, under differentiability, the limit fixed point is linear in the initial conditions and characterized by the Jacobian of the operator at any constant vector with an explicit and linear rate of convergence. Without differentiability, but under additional concavity properties, the multiplicity of Jacobians is resolved by a representation of the limit fixed point as a maxmin functional evaluated at the initial conditions. In our applications, we use these results to characterize the limit equilibrium actions, prices, and endogenous networks, show the existence and give the formula of the asymptotic value in a class of zero-sum stochastic games with a continuum of actions, compute a nonlinear version of the eigenvector centrality of agents in networks, and the characterize the equilibrium loss evaluations in financial networks.

For common knowledge to arise in dynamic settings, knowledge that it has arisen must be attained simultaneously by all players. Consequently, common knowledge cannot arise in many realistic settings with timing frictions. This counterintuitive observation of Halpern and Moses (1990) was discussed by Arrow et al. (1987) and Aumann (1989), was called a paradox by Morris (2014), and has evaded satisfactory resolution for four decades. We resolve this paradox by proposing a new definition for common knowledge, which coincides with the traditional one in static settings but is more permissive in dynamic settings. Under our definition, common knowledge can arise without simultaneity, particularly in canonical examples of the Haplern–Moses paradox. We demonstrate its usefulness by deriving for it an agreement theorem `a la Aumann (1976), showing it arises in the setting of Geanakoplos and Polemarchakis (1982) with timing frictions added, and applying it to characterize equilibrium behavior in a dynamic coordination game.

Consider a population of agents who repeatedly compete for awards, as in the case of researchers annually applying for grants. Noise in the selection process may encourage entry of low quality proposals, forcing the principal to commit large resources to reviewing applications and further increasing award misallocation. A temporary exclusion policy prohibits an agent from applying in the current period if they were rejected in the previous, encouraging self-selection. We compare the steady-state equilibria of the games with and without exclusion. Whenever the benefit from winning is large, exclusion leads to fewer low-quality applications and higher welfare for agents.

A worker interacts with a sequence of clients under a manager’s supervision. I highlight a novel role of this manager’s mediation in addressing the worker’s moral hazard, namely to intertemporally reduce suspensions of the worker’s service that are surplus-depleting but crucially serve as punishments to motivate her costly effort. I show that, to best address moral hazard, the manager at times secretly asks a high-performing worker to scale down her effort against a current client and implements dynamic correlation by telling the worker that current underperformance will not be punished. These occasions are frequent in the short run and eventually disappear.

We model search in unfamiliar territories, where agents know what can be found but not where to find it. A searcher faces a set of choice arranged by an observable attribute. Each period, she either selects a choice and pays a cost to learn about its quality, or she concludes search to take her best discovery to date. She knows that similar choices have similar qualities and uses this to guide her search. We identify robustly optimal search policies with a simple structure. Search is ordered, perfect recall is never invoked, stopping follows a threshold rule, and the policy at each history depends only on a simple index.

We introduce a tractable methodology for analyzing dynamic decision problems and games involving irreversible decisions under uncertainty. By leveraging regularity properties, our approach offers an intuitive method for solving these problems using equivalent certain values, and derives properties and comparative statics of the solution. We show that irreversibility is analogous to information loss, leading agents to act as if they had worse information than with reversible actions. We use our methodology to analyze design features of previously intractable long auctions, establish revenue equivalence, and show that increasing bidding opportunities or allowing bid retraction can harm bidders and benefit the auctioneer.

Collective action is a dynamic process where individuals in a group assess over time the benefits and costs of participating toward the success of a collective goal. Early participation improves the expectation of success and thus stimulates the subsequent participation of other individuals who might otherwise be unwilling to engage. On the other hand, a slow start can depress expectations and lead to failure for the group. Individuals have an incentive to procrastinate, not only in the hope of free riding, but also in order to observe the flow of participation by others, which allows them to better gauge whether their own participation will be useful or simply wasted. How do these phenomena affect the probability of success for a group? As the size of the group increases, will a “power of large numbers” prevail producing successful outcomes, or will a “curse of large numbers” lead to failure? In this paper, we address these questions by studying a dynamic collective action problem in which n individuals can achieve a collective goal if a share αn of them takes a costly action (e.g., participate in a protest, join a picket line, or sign an environmental agreement). Individuals have privately known participation costs and decide over time if and when to participate. We characterize the equilibria of this game and show that under general conditions the eventual success of collective action is necessarily probabilistic. The process starts for sure, and hence there is always a positive probability of success; however, the process “gets stuck” with positive probability, in the sense that participation stops short of the goal. Equilibrium outcomes have a simple characterization in large populations: welfare converges to either full efficiency or zero depending on whether αn converges to zero faster or slower than the cube root of 1/n as n → ∞. Whether success is achievable or not, delays are always irrelevant: in the limit, either success is achieved either instantly or never.