This paper investigates a new class of two-player games in continuous time, in which the players' observations of each other's actions are distorted by Brownian motions. These games are analogous to ...repeated games with imperfect monitoring in which the players take actions frequently. Using a differential equation, we find the set ε(r) of payoff pairs achievable by all public perfect equilibria of the continuous-time game, where r is the discount rate. The same differential equation allows us to find public perfect equilibria that achieve any value pair on the boundary of the set ε(r). These public perfect equilibria are based on a pair of continuation values as a state variable, which moves along the boundary of ε(r) during the course of the game. In order to give players incentives to take actions that are not static best responses, the pair of continuation values is stochastically driven by the players' observations of each other's actions along the boundary of the set ε(r).
Dynamic CEO Compensation EDMANS, ALEX; GABAIX, XAVIER; SADZIK, TOMASZ ...
The Journal of finance (New York),
October 2012, Letnik:
67, Številka:
5
Journal Article
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We study optimal compensation in a dynamic framework where the CEO consumes in multiple periods, can undo the contract by privately saving, and can temporarily inflate earnings. We obtain a simple ...closed-form contract that yields clear predictions for how the level and performance sensitivity of pay vary over time and across firms. The contract can be implemented by escrowing the CEO's pay into a "Dynamic Incentive Account" that comprises cash and the firm's equity. The account features state-dependent rebalancing to ensure its equity proportion is always sufficient to induce effort, and time-dependent vesting to deter short-termism.
We derive the optimal dynamic contract in a continuous-time principal-agent setting, and implement it with a capital structure (credit line, long-term debt, and equity) over which the agent controls ...the payout policy. While the project's volatility and liquidation cost have little impact on the firm's total debt capacity, they increase the use of credit versus debt. Leverage is nonstationary, and declines with past profitability. The firm may hold a compensating cash balance while borrowing (at a higher rate) through the credit line. Surprisingly, the usual conflicts between debt and equity (asset substitution, strategic default) need not arise.
We study a principal–agent setting in which both sides learn about future profitability from output, and the project can be abandoned/terminated if profitability is too low. With learning, shirking ...by the agent both reduces output and lowers the principal's estimate of future profitability. The agent can exploit this belief discrepancy and earn information rents, reducing his incentives to exert effort. The optimal contract controls information rents to improve incentives by distorting the termination decision. Our results capture the transition from a young, financially constrained firm to a mature firm that pays dividends. For young firms, poor performance permanently raises the termination threshold, as doing so lowers information rents. Mature firms pay smoothed dividends and have a fixed termination threshold. Dividend smoothing occurs because earnings surprises are used to adjust financial slack in line with profitability. When profitability only reflects the agent's private ability, a simple equity contract is optimal.
This paper develops a dynamic two-country neoclassical stochastic growth model with incomplete markets. Short-term credit flows can be excessive and reverse suddenly. The equilibrium outcome is ...constrained inefficient due to pecuniary externalities. First, an undercapitalized country borrows too much since each firm does not internalize that an increase in production capacity undermines their output price, worsening their terms of trade. From an ex ante perspective each firm undermines the natural "terms of trade hedge." Second, sudden stops and fire sales lead to sharp price drops of illiquid capital. Capital controls or domestic macro-prudential measures that limit short-term borrowing can improve welfare.
This paper describes a new continuous-time principal-agent model, in which the output is a diffusion process with drift determined by the agent's unobserved effort. The risk-averse agent receives ...consumption continuously. The optimal contract, based on the agent's continuation value as a state variable, is computed by a new method using a differential equation. During employment, the output path stochastically drives the agent's continuation value until it reaches a point that triggers retirement, quitting, replacement, or promotion. The paper explores how the dynamics of the agent's wages and effort, as well as the optimal mix of short-term and long-term incentives, depend on the contractual environment.
This article studies the full equilibrium dynamics of an economy with financial frictions. Due to highly nonlinear amplification effects, the economy is prone to instability and occasionally enters ...volatile crisis episodes. Endogenous risk, driven by asset illiquidity, persists in crisis even for very low levels of exogenous risk. This phenomenon, which we call the volatility paradox, resolves the Kocherlakota (2000) critique. Endogenous leverage determines the distance to crisis. Securitization and derivatives contracts that improve risk sharing may lead to higher leverage and more frequent crises.
We study the pure-strategy subgame-perfect Nash equilibria of stochastic games with perfect monitoring, geometric discounting, and public randomization. We develop novel algorithms for computing ...equilibrium payoffs, in which we combine policy iteration when incentive constraints are slack with value iteration when incentive constraints bind. We also provide software implementations of our algorithms. Preliminary simulations indicate that they are significantly more efficient than existing methods. The theoretical results that underlie the algorithms also imply bounds on the computational complexity of equilibrium payoffs when there are two players. When there are more than two players, we show by example that the number of extreme equilibrium payoffs may be countably infinite.
We study reputation dynamics in continuous-time games in which a large player (e.g., government) faces a population of small players (e.g., households) and the large player's actions are imperfectly ...observable. The major part of our analysis examines the case in which public signals about the large player's actions are distorted by a Brownian motion and the large player is either a normal type, who plays strategically, or a behavioral type, who is committed to playing a stationary strategy. We obtain a clean characterization of sequential equilibria using ordinary differential equations and identify general conditions for the sequential equilibrium to be unique and Markovian in the small players' posterior belief. We find that a rich equilibrium dynamics arises when the small players assign positive prior probability to the behavioral type. By contrast, when it is common knowledge that the large player is the normal type, every public equilibrium of the continuous-time game is payoff-equivalent to one in which a static Nash equilibrium is played after every history. Finally, we examine variations of the model with Poisson signals and multiple behavioral types.
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