Impatient Agents Research Articles

Sophisticated reasoning, learning, and equilibrium in repeated games with imperfect feedback

AbstractWe analyze the infinite repetition with imperfect feedback of a simultaneous or sequential game, assuming that players are strategically sophisticated—but impatient—expected-utility maximizers. Sophisticated strategic reasoning in the repeated game is combined with belief updating to provide a foundation for a refinement of self-confirming equilibrium. In particular, we model strategic sophistication as rationality and common strong belief in rationality. Then, we combine belief updating and sophisticated reasoning to provide sufficient conditions for a kind of learning—that is, the ability, in the limit, to exactly forecast the sequence of future observations—thus showing that impatient agents end up playing a sequence of self-confirming equilibria in strongly rationalizable conjectures of the one-period game.

Matching Impatient and Heterogeneous Demand and Supply

Balancing Speed and Value in On-Demand Matching Platforms In “Matching Impatient and Heterogeneous Demand and Supply,” Aveklouris, DeValve, Stock, and Ward consider a fundamental trade-off faced by many platforms (e.g., Uber/Lyft) that match supply (e.g., drivers) and demand (e.g., riders) dynamically over time: making matches quickly capitalizes on the value of current supply and demand in the system, whereas waiting may enable better matches at the risk of losing impatient customers. They show that this trade-off can be balanced by waiting a short amount of time before making matches: long enough to gather enough agents to make valuable matches but not so long that impatient agents are likely to leave. Intuitively, this balance depends on how long agents are willing to wait, on average, but the authors show that it also depends on the full distribution of the willingness to wait (i.e., not only mean, but also variance and higher moments play a role). Thus, approaches that only take into account the mean willingness to wait may perform quite poorly. Further, the authors develop an algorithm to rank matching priorities in order to achieve an optimized trade-off between speed and value of matches.

Quality Versus Quantity in Dynamic Matching with Impatient Agents

Quality Versus Quantity in Dynamic Matching with Impatient Agents

Dynamic effects of consumption externalities

This paper examines the dynamic effects of consumption externalities in Bosi and Seegmuller (J Math Econ 46:475–492, 2010). We show that only the patient agent holds the entire capital stock at the steady state, while the impatient agent works to finance his consumption. Our main result states that consumption externalities represent the main mechanism that explains the emergence of endogenous fluctuations due to self-fulfilling expectations. Finally, consumption externalities promote the appearance of deterministic cycles of period two.

Delegated Learning and Non-Credible Communication

We consider a setting in which an impatient agent acquires payoff-relevant information about the true state of the world. The agent endogenously chooses when to stop learning, at which point an uninformed principal takes an action to maximize her own expected payoff. The agent's preferences are biased relative to the principal's, generating misalignment of expected payoffs. When communication is non-credible, the principal can only rely upon the agent's endogenous stopping rule when strategically specifying her course of action. In the no-communication equilibrium, the agent adopts a one-sided stopping rule as a function of her posterior belief that is consistent with the principal's pre-specified course of action at the time of stopping. When the principal has commitment power, relative to the full-communication equilibrium, the agent is always worse off; for intermediate values of prior beliefs, the principal is better off. The one-sided equilibrium stopping rule (and associated action) can switch discretely as a function of prior beliefs, generating dramatic regime changes for arbitrarily small changes in beliefs. When learning is initiated in the no-communication equilibrium there is a non-zero probability of indefinite delay, in which the agent never ceases learning and the principal never takes an action.

Disequilibrium Trade in a Large Market for an Indivisible Good

AbstractDisequilibrium trade can occur in a market lacking both recontracting and a computational system that maps utilities into prices. This paper studies disequilibrium trade in a large market for an indivisible good. We focus on the possible speed of adjustment when arbitrage among periods is feasible and the surplus loss. We find that incentive compatible sequential trade through a disequilibrium path is only compatible with sluggish price adjustments and sufficiently impatient agents. Thus, price adjustment does not depend on excess demand alone but on arbitrage opportunities and the willingness of agents to engage on them. We find that the upper bound on the speed of price adjustment involves a lower bound for the social surplus loss, whatever the kind of rationing. The reason is that even when the market price converges to the surplus maximizing value, as it happens when rationing is efficient, some pieces of surplus are not attainable at the current period due to arbitrage. Moreover, faster price adjustments do not imply less surplus loss, because the effect of price changes on transactions via arbitrage. Finally, under weaker-than-efficient rationing there is a one period incentive compatible trading procedure in which most of the surplus is destroyed. The procedure has the property that almost every agent in the market trades.

Roads to prosperity without environmental poverty: The role of impatience

This paper advances the hypothesis that impatience negatively depends on environmental quality and aims to explain why some countries stagnate in an ‘environmental and economic poverty trap’. For low levels of environmental quality, advancements in productivity lead impatient agents to direct income increases to consumption (rather than savings), depleting further the environment. Given that productivity increases do not help such economies to escape the trap (contrary to perceived notions), policies should focus on the implementation of behavioral changes.

Growth with many agents and wages paid ex ante

In this paper, we consider a one-sector model of economic growth with several infinitely-lived heterogeneous agents, who are endowed with diverse discount factors as well as preferences over consumption. In line with the classical Ramsey model, agents are not allowed to borrow against future income. Unlike the traditional assumption of ex post wage payment, wages are paid ex ante in our model. We first explain the difference between the assumptions of wages being paid ex ante and wages being paid ex post in the framework of a simple illustrative two-class model. Our main result shows that in contrast to the many-agent Ramsey model with ex post wage payment, the capital stock sequence converges to the steady state stock irrespective of production technology employed by the firms. Further, all impatient agents own zero capital stock, whereas the most patient agent owns the entire capital stock from some time onward. Thus, we have shown that a slight modification in the timing of wage payment in growth models can lead to significant changes in the stability properties of equilibrium dynamics.

STABILIZATION POLICY AT THE ZERO LOWER BOUND

AbstractWe construct a monetary economy with aggregate liquidity shocks and heterogeneous idiosyncratic preference shocks. In this environment, not all agents are satiated at the zero lower bound (ZLB) even when the Friedman rule is the best interest‐rate policy the central bank can implement. As a consequence, central bank stabilization policy, which takes the form of repo arrangements in response to aggregate demand shocks, temporarily relaxes the liquidity constraint of impatient agents at the ZLB. Due to a pecuniary externality, this policy may have beneficial general equilibrium effects for patient agents even if they are unconstrained in their money balances.

Pushing and overtaking others in a spatial game of exit congestion

With self-driven particle models, like the social force model, most of the physics of moving crowds can be modeled. However, it has not been fully unraveled why large crowds evacuating through narrow bottlenecks often act against their self-interest. They form jams in front of the bottleneck, that slow down the evacuation, and fatal pressures build up in the crowd. Here, we take a novel approach, and model the local decision-making in an evacuating crowd as a spatial game. The game is coupled to the social force model, so that different strategies alter the physical parameters. With our integrated treatment of behavioral and physical aspects, we are able to simulate when, why and how typical phenomena of an evacuation through a bottleneck occur. Most importantly, we attain non-monotonous speed and kinetic pressure patterns, in contrast to the monotonous patterns predicted by the pure social force model. This is a result of impatient agents in the back of the simulated crowd pushing and overtaking their way forward. Our findings give insight into the origin of crowd disasters, since the build-up of kinetic pressure has been related to the risk of falling and crowd turbulence.

Only Time Will Tell: A Theory of Deferred Compensation

This paper characterizes optimal compensation contracts in principal-agent settings where the agent's action has persistent effects. As additional informative signals arrive over time, deferred compensation has the benefit of exploiting better performance measurement which, for any information environment, is captured by the martingale property of the likelihood ratio process. With bilateral risk-neutrality and a relatively impatient agent, optimal contracts are high-powered and feature at most two payout dates regardless of the nature of information arrival. If the agent is additionally risk-averse, rewards are paid out if and only if performance is above a hurdle that is gradually increasing over time. Our precise characterization allows for clear-cut comparative statics predictions on how the timing of pay depends on the nature of information arrival as well as agent characteristics and generates implications for the optimal duration of compensation packages and the maturity structure of claims in financial contracting settings.

Synchronized matching with incomplete information

This paper considers two-sided matching in continuous time without transferable utility or costly effort signaling. Two continua of impatient agents signal their types by delaying before proposing or accepting a match. I use a mechanism design approach to study what matchings and schedules of match times are implementable when there is private information on one or both sides. When only one side has private information, a sufficient condition to implement assortative matching is for the uninformed side to value the log gain in partner quality from waiting more than the informed side, so that it pays to wait. When information is incomplete on both sides, the sufficient conditions to implement assortative matching are much more restrictive: even when coarse matching is considered, a simple sufficient condition is provided under which only simple random matching is implementable.

Optimization of the Superstable Linear Stochastic System Applied to the Model with Extremely Impatient Agents

We consider the problem of stochastic linear regulator over an infinite time horizon with superexponentially stable matrix in the equation of state dynamics. The form of the optimal control based on the criterion taking into account the information about the parameters of disturbances and the matrix stability rate was determined. The results obtained were used to analyze the model of a system with extremely impatient agents where the objective functional includes discounting by the asymptotically unbounded rate.

On Equilibrium Dynamics With Many Agents and Wages Paid Ex Ante

In this paper, we consider a one-sector model of economic growth with several infinitely-lived heterogeneous agents, who are endowed with diverse discount factors as well as preferences over consumption. In line with the classical Ramsey model, agents are not allowed to borrow against future income. Unlike the traditional assumption of ex post wage payment, wages are paid ex ante in our model. We first explain the difference between the assumptions of wages being paid ex ante and wages being paid ex post in the framework of a simple illustrative two-class model. Our main result shows that in contrast to the many-agent Ramsey model with ex post wage payment, the capital stock sequence converges to the steady state stock irrespective of production technology employed by the firms. Further, all impatient agents own zero capital stock, whereas the most patient agent owns the entire capital stock from some time onward. Thus, we have shown that a slight modification in the timing of wage payment in growth models can lead to significant changes in the stability properties of equilibrium dynamics.

Fiscal policy with banks and financial frictions

We assess the role of banks to the transmission of optimal and exogenous changes in fiscal policy to the economy. We built-up a dynamic stochastic general equilibrium model with patient and impatient agents, banks and a government to find that banks and their associated capital-adequacy constraint mitigate the negative spill-over effects to the economy from higher taxes. Specifically, we confirm that labour income tax is the most distortionary fiscal instrument. The optimal choice of a housing tax is the most favorable funding source to a temporary increase in public spending. The combination of housing and labour taxes is the most preferred tax bundle to be optimally chosen under negative output shocks. Moreover, a permanent increase in housing tax is beneficial if it is welfare enhancing and the existence of banks benefits mainly impatient households under permanently higher consumption taxes. Finally, these results remain robust to various robustness checks.

Heterogeneity, impatience, and dynamic private provision of a discrete public good

AbstractWe analyze dynamic private provision of a discrete public good by heterogeneous agents, who differ in terms of their levels of impatience, in a differential game framework. In contrast to the strategic complementarity result for homogeneous individuals, we show that an asymmetric completion Markov perfect equilibrium exists, where the individual contributions and the strategic behaviors depend crucially on an impatience differential: the difference in rates of time preference across groups of individuals. When this differential is insignificant, contributions of both types of individuals are strategic complements. On the other hand, when this impatience differential exceeds a threshold, the contributions of impatient individuals become strategic substitutes, whereas the contributions of patient individuals remain strategic complements. We show that group size has an interesting role to play in the strategic behavior: increasing the number of patient individuals aggravates the incentives to free‐ride by the impatient agents. We also derive a condition under which all the socially beneficial projects get completed in the equilibrium.

Incentive Compatible Price Adjustments in Large Markets

Abstract: Disequilibrium trade can occur in a market lacking both recontracting options and a computational system that maps utilities into prices. This paper studies disequilibrium trade in a large market for an indivisible good. We focus on two issues: the speed of adjustment when arbitrage among periods is feasible, and the surplus loss depending on the kind of rationing. We find that incentive compatible sequential trade through a disequilibrium path is only compatible with sluggish price adjustments and sufficiently impatient agents. Thus, price adjustment does not depend on excess demand alone. The upper bound on the speed of price adjustment involves a lower bound for the social surplus loss, whatever the kind of rationing. The reason is that even when market price converges to the surplus maximizing value, as it happens when rationing is efficient, some pieces of surplus are not attainable at the current period due to arbitrage. However, faster price adjustments do not imply less surplus loss, because of the effect of price changes on transactions via arbitrage. Under weaker-than-efficient rationing

Collateral and growth cycles with heterogeneous agents

We investigate the effects of collateral and monetary policy on economic growth within a Ramsey equilibrium model where agents have different discount factors. Introducing liquidity constraints in segmented markets where (poor) impatient agents without collateral have limited access to credit, we study their implications in terms of welfare and business cycles (based on deterministic cycles through bifurcations and self-fulfilling prophecies). We find that an accommodative monetary policy may be growth-enhancing and welfare-improving (through the inequality reduction) while making unpleasant fluctuations more likely. Conversely, a regulation reinforcing the role of collateral and tempering the financial market imperfections may stimulate the economic growth while pursuing the goal of stabilization.

Bargaining in endogenous trading networks

We study a model in which heterogeneous agents first form a trading network where linking costs are positive but infinitesimally small. Then, a seller and a buyer are randomly selected among the agents to bargain through a chain of intermediaries. We determine both the trading path and the allocation of the surplus among the seller, the buyer and the intermediaries at equilibrium. We show that, under the initiator bargaining protocol, a trading network is pairwise stable if it is a core–periphery network where the core consists of all impatient agents who are linked to each other and the periphery consists of all patient agents who have a single link towards an impatient agent. Once agents do not know the impatience of other agents, each bilateral bargaining session may involve delay. Then, core–periphery networks may not be pairwise stable because agents may prefer to add links for reducing the length of trading paths and so avoiding costly delays in reaching a global agreement.

Impatience versus Incentives

This paper studies the dynamics of long-term contracts in repeated principal–agent relationships with an impatient agent. Despite the absence of exogenous uncertainty, Pareto-optimal dynamic contracts generically oscillate between favoring the principal and favoring the agent.