Variation margins, fires sales, and information-constrained optimality

In order to share risk, protection buyers trade derivatives with protection sellers. Protection sellers’ actions affect the riskiness of their assets, which can create counterparty risk. Because these actions are unobservable, moral hazard limits risk sharing. To mitigate this problem, privately optimal derivative contracts involve variation margins. When margins are called, protection sellers must liquidate some assets, depressing asset prices. This tightens the incentive constraints of other protection sellers and reduces their ability to provide insurance. Despite this fire-sale externality, equilibrium is information-constrained efficient. Investors, who benefit from buying assets at fire-sale prices, optimally supply insurance against the risk of fire sales.

Algorithms for Stochastic Games With Perfect Monitoring

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.

Asset Bubbles and Credit Constraints

We provide a theory of rational stock price bubbles in production economies with infinitely-lived agents. Firms meet stochastic investment opportunities and face endogenous credit constraints. They are not fully committed to repaying debt. Credit constraints are derived from incentive constraints in optimal contracts which ensure default never occurs in equilibrium. Stock price bubbles can emerge through a positive feedback loop mechanism and cannot be ruled out by transversality conditions. These bubbles command a liquidity premium and raise investment by raising the debt limit. Their collapse leads to a recession and a stock market crash. (JEL D25, E22, E32, E44, G12, G14)

Robustly Optimal Auctions with Unknown Resale Opportunities

The standard revenue-maximizing auction discriminates against a priori stronger bidders so as to reduce their information rents. We show that such discrimination is no longer optimal when the auction’s winner may resell to another bidder, and the auctioneer has non-Bayesian uncertainty about such resale opportunities. We identify a “worst-case” resale scenario, in which bidders’ values become publicly known after the auction and losing bidders compete Bertrand-style to buy the object from the winner. With this form of resale, misallocation no longer reduces the information rents of the high-value bidder, as he could still secure the same rents by buying the object in resale. Under regularity assumptions, we show that revenue is maximized by a version of the Vickrey auction with bidder-specific reserve prices, first proposed by Ausubel and Cramton (2004). The proof of optimality involves constructing Lagrange multipliers on a double continuum of binding non-local incentive constraints.

Community Structure and Market Outcomes: A Repeated Games-in-Networks Approach

Consider a large market with asymmetric information, in which sellers have the option to “cheat” their buyers, and buyers decide whether to repurchase from different sellers. We model active trade relationships as links in a buyer-seller network and study repeated games in such networks. Endowing sellers with incomplete knowledge of the network, we derive conditions that determine whether a network is consistent with cooperation between every buyer and seller that are connected. Three network features reduce the minimal discount factor sufficient for cooperation: moderate and balanced competition, sparseness, and segregation. Incentive constraints are binding and rule out efficient networks. (JEL C73, D82, D85, Z13)