Axel Anderson

Opportunistic Matching in the Housing Market

We construct a model of the housing market in which agents differ in their flow values while searching. Agents enter the market relaxed (with high flow values) but move to a desperate state (low flow values) at a Poisson rate if they have not already transacted. We characterize the equilibrium steady-state matching pattern and the joint distribution of price and time to sale (for sellers). The expected price conditional on time to sale falls with time spent on the market, whereas the conditional variance of price first rises and then falls with time on the market.

Search by Committee

We consider the problem of sequential search when the decision to stop is made by a committee and show that a unique symmetric stationary equilibrium exists given a log concave distribution of rewards. We compare search by committee to the corresponding single-agent problem and show that committee members are less picky and more conservative than the single agent. We show how (i) increasing committee size holding the plurality fraction constant and (ii) increasing the plurality rule affect the equilibrium acceptance threshold and expected search duration. Finally, we show that unanimity is optimal if committee members are sufficiently patient.

Rushes in Large Timing Games

We develop a continuum player timing game that subsumes standard wars of attrition and pre‐emption games, and introduces a new rushes phenomenon. Payoffs are continuous and single‐peaked functions of the stopping time and stopping quantile. We show that if payoffs are hump‐shaped in the quantile, then a sudden “rush” of players stops in any Nash or subgame perfect equilibrium. Fear relaxes the first mover advantage in pre‐emption games, asking that the least quantile beat the average; greed relaxes the last mover advantage in wars of attrition, asking just that the last quantile payoff exceed the average. With greed, play is inefficiently late: an accelerating war of attrition starting at optimal time, followed by a rush. With fear, play is inefficiently early: a slowing pre‐emption game, ending at the optimal time, preceded by a rush. The theory predicts the length, duration, and intensity of stopping, and the size and timing of rushes, and offers insights for many common timing games.

Greed, Fear, and Rushes

We develop a simple new timing game that offers a unified theor y of sudden mass movements in economics, such as arise in matching, asset bubbles, and bank runs. We distinguish between rushes precipitated by greed and fear — i.e., the hunger for greater rewards from outlasting others, and the fear of missing out on early rewards. In our continuum player game, a payoff-relevant fundamental first “ripens”, peaks at a “harvest time”, and then “rots”. Payoffs are also scaled by a single-peaked quantile rank reward. Three local timing games arise in equilibrium: a war of attrition, a slow pre-emption game, and a pre-emptive rush. Our theory explains why matching rushes and bank runs happen inefficiently early, and asset sales rushes occur lat e. For with greed, the harvest time precedes an accelerating war of attrition ending in a rush, whereas with fear, an inefficiently early rush precedes a slowing pre-emption game ending at the harvest time. The theory yields consistent predictions for rush size, timing, gradual play timing, duration, and stopping rates. By our theory: (a) asset sales rushes reflect liquidity and relative compensat ion; (b) “unraveling” in matching markets depends on early matching stigma and market thinness; (c) illiquid bank loans yields complete bank runs before incomplete ones.

A Dynamic Generalization of Becker's Assortative Matching Result

This paper considers a dynamic matching model in which each agents future productivity depends in part on their current match, as in labor markets, schooling, intergenerational marriage markets, and other environments. The Planners endogenous rankings of human distributions are characterized. These Planner rankings are then used to develop sufficient conditions for positive assortative matching to be dynamically efficient. One lesson that emerges is that complementarity assumptions alone are insufficient for a robust sorting theory — the curvature of the static production function is also critical to determine optimal sorting patterns. In addition, the Planners ranking of distributions over human capital yield characterizations of individual attitudes toward human capital gambles in an associated market equilibrium. Finally, the implied dynamics for (1) individual wages and (2) wage distributions across age cohorts are characterized.

Geometric Asymptotic Approximation of Value Functions

This paper characterizes the behavior of value functions in dynamic stochastic discounted programming models near fixed points of the state space. When the second derivative of the flow payoff function is bounded, the value function is proportional to a linear function plus geometric term. A specific formula for the exponent of this geometric term is provided. This exponent continuously falls in the rate of patience.If the state variable is a martingale, the second derivative of the value function is unbounded. If the state variable is instead a strict local submartingale, then the same holds for the first derivative of the value function. Thus, the proposed approximation is more accurate than Taylor series approximation.The approximation result is used to characterize locally optimal policies in several fundamental economic problems.