Session 6: Dynamic Games, Contracts and Markets

We study time-consistent debt policies in a trade-off model of debt in which the firm can freely issue new debt and repurchase existing debt. A debt policy is time-consistent if in any state equityholders prefer to follow it rather than to deviate from it but lose credibility in sustaining debt discipline in the future. In a class of policies, the optimal time-consistent debt policy consists of an interest coverage ratio (ICR) target and two regions for the ICR: the stable and the distress regions. In the stable region, the firm actively manages liabilities to the ICR target by issuing/repurchasing debt. A sufficiently large negative shock to cash flows pushes the firm into the distress region, where it abandons the target and waits until either cash flows recover or further negative shocks trigger bankruptcy. Credit spreads are sensitive to cash flow shocks in the distress region but not in the stable region. The optimal policy captures realistic features of debt dynamics, such as active debt management in both directions, interior optimal debt maturity, and dynamics of “fallen angels.”

We study how a misspecified agent learns from endogenous data when their prior belief can assign probability 0 to a neighborhood of the true model. We show that only uniform Berk-Nash equilibria can be long-run outcomes, and that all uniformly strict Berk-Nash equilibria have an arbitrarily high probability of being the long-run outcome for some initial beliefs. When the agent believes the outcome distribution is exogenous, every uniformly strict Berk-Nash equilibrium has positive probability of being the long-run outcome for any initial belief. We generalize these results to settings where the agent observes a signal before acting.

We model censorship as a dynamic game between an agent and an evaluator. Two types of public news, good and bad news, are informative about the agent’s ability. However, the agent can hide bad news from the evaluator, at some cost, and will do so if and only if this secures her a significant increase in tenure. Thus, the evaluator faces a bandit problem with endogenous news processes. When bad news is conclusive, the agent always censors when the public belief is sufficiently high, but below a threshold, she entirely or partially stops censoring. The possibility of censorship hurts the evaluator and the good agent, and it may also hurt the bad agent. However, when bad news is inconclusive, we show that the good agent censors bad news more aggressively than the bad agent does. This improves the quality of public information and may benefit all players.

We study a dynamic relationship in which a principal chooses the timing of reorganizations but delegates implementation to an agent. The implementation process requires front-loaded effort and time to yield results. There is no asymmetric information, but the agent’s effort is not verifiable. The principal, moreover, cannot commit to a reorganization policy in advance. The equilibrium is unique and inefficient. Furthermore, compared to the first-best, the organization waits too little for new reorganizations to yield results, but retains the status quo longer when successful reorganizations lead to profitable new business. We discuss how these results might shed light on two seemingly contradictory perceptions commonly held about the frequency of reorganizations.

The paper investigates factors that undermine meritocracy and policies that may restore it. To this purpose, it analyzes the Markovian dynamics, the entrenchment and the welfare properties of an organization whose members’ cooptation decisions are driven by two motives: quality and homophily. It investigates policy interventions (affirmative action, quality assessment exercises, overruling of majority decisions) and analyzes when these have unintended consequences. The paper also generates a rich set of testable implications.

An agent has access to multiple information sources, each of which provides information about a different attribute of an unknown state. Information is acquired continuously – where the agent chooses both which sources to sample from, and also how to allocate attention across them – until an endogenously chosen time, at which point a decision is taken. We provide an exact characterization of the optimal information acquisition strategy for settings where the attributes are not too strongly correlated. We then apply this characterization to derive new results regarding: (1) endogenous information acquisition for binary choice, and (2) strategic information provision by competing news sources.

Consider a repeated interaction where it is unknown which of various possible stage games will be played each period. This framework captures the logic of intertemporal incentives even though numeric payoffs to any strategy profile are indeterminate. A natural solution concept is ex post perfect equilibrium (XPE): strategies must form a subgame-perfect equilibrium for any realization of the stage game process. When (i) there is one long-run player and others are short-run, and (ii) public randomization is available, we can adapt the standard recursive approach to determine the maximum sustainable gap between reward and punishment. This leads to an explicit characterization of what outcomes. are supportable in equilibrium, and an optimal penal code that supports any such outcome. Any non-XPE-supportable outcome fails to be an SPE outcome for some specific stage game process. In contrast to standard repeated games, restrictions (i) and (ii) are crucial.

In this paper we define notions of trembling hand and sequential equilibrium and show that both types of equilibria exist in a large class of  stochastic games that may feature incomplete and imperfect information. These equilibria do not necessitate the use of a public correlating device. Under further regularity assumptions each stochastic game has a sequence of approximating finite games whose equilibria approximate equilibria of the limit game.

I study a dynamic model of consumer privacy and platform data collection. In each period, consumers choose their level of platform activity. Greater activity generates more precise information about the consumer, thereby increasing platform profits. Although consumers value privacy, a platform is able to collect much information by gradually lowering the level of privacy protection. In the long-run, consumers become “addicted” to the platform, whereby they lose privacy and receive low payoffs, but continue to choose high activity levels. Competition is unhelpful because consumers have a higher incentive to use a platform to which they have lower privacy.