Tarun Sabarwal

Competitive Equilibria With Incomplete Markets and Endogenous Bankruptcy

This paper constructs a model of an exchange economy in which bankruptcy arises in a manner similar to what we observe. Compared to related models, this model is a more realistic representation of some markets in which intertemporal assets are traded. Using standard and natural assumptions, it is shown that every economy represented by this model has an equilibrium. Therefore, bankruptcy can co-exist with smoothly functioning competitive markets in fairly general economies. Examples highlight some welfare effects of bankruptcy.

Strong comparative statics of equilibria

Some results in the monotone comparative statics literature tell us that if a parameter increases, some old equilibria are smaller than some new equilibria. We give a sufficient condition such that at a new parameter value every old equilibrium is smaller than every new equilibrium. We also adapt a standard algorithm to compute a minimal such newer parameter value and apply this algorithm to a game of network externalities. Our results are independent of a theory of equilibrium selection and are valid for games of strategic complementarities.

Value Maximization as an Ex-Post Consistent Firm Objective When Markets are Incomplete

In competitive economies with private firm ownership, incomplete markets, and firm shareholders changing over time, several firm objectives have been proposed. Some are useful to understand efficiency of equilibria, and others are explicitly consistent with majority shareholder control or collective choice rules, but it is not always clear if versions of each type are consistent with versions of the other type. This paper shows that ex-post, value maximizing rules, (including those proposed by Dreze, and Grossman and Hart,) are consistent with shareholder preferences in such economies; that is, along the equilibrium path, in every period and state of the world, every coalition of a firms shareholders in that period and state approves a value maximizing production plan. This result applies to cases when shareholders within a firm and across firms can form coalitions, and when stock trading can be ex-dividend or cum-dividend, and with a combination of both. This result does not resolve the problem of inefficiency of stock market equilibria, or that of ex ante disagreement among shareholders. It can help understand when firm objectives with some desirable properties are consistent with a particular version of shareholder control, and it provides a stability criterion (in terms of robustness to shareholder coalitions) for organizing productive resources in such economies.

Strategic or Nonstrategic: The Role of Financial Benefit in Bankruptcy

A partial test for strategic behavior in bankruptcy filing may be formulated by testing whether consumers manipulate their debt and filing decision jointly, or not: that is, testing for endogeneity of financial benefit and the bankruptcy filing decision. Using joint maximum likelihood estimation of an extended discrete choice model, test results are consistent with non-strategic filing: financial benefit is exogenous to the filing decision. This result is confirmed in two different datasets (PSID and SCF). This result is consistent with an ex ante low net gain from a bankruptcy filing; a type of “rational inattention” to rare events such as bankruptcy.

Rationalizability, adaptive dynamics, and the correspondence principle in games with strategic substitutes

New insights into the theory of games with strategic substitutes (GSS) are developed. These games possess extremal serially undominated strategies that provide bounds on predicted behavior and on limiting behavior of adaptive dynamics, similar to games with strategic complements (GSC). In parameterized GSS, monotone equilibrium selections are dynamically stable under natural conditions, as in parameterized GSC. Dominance solvability in GSS is not equivalent to uniqueness of Nash equilibrium, but is equivalent to uniqueness of simply rationalizable strategies. Convergence of best response dynamics in GSS is equivalent to global convergence of adaptive dynamics, is equivalent to dominance solvability, and implies uniqueness of equilibrium, all in contrast to GSC. In particular, Cournot stability is equivalent to dominance solvability in GSS. The results shed light on predicted behavior, learning, global stability, uniqueness of equilibrium, and dynamic stability of monotone comparative statics in GSS. Several examples are provided.

Comparative Statics with Never Increasing Correspondences

This paper studies models where the correspondences (or functions) under consideration are never increasing (or weakly decreasing) in endogenous variables, and weakly increasing in exogenous parameters. Such models include games of strategic substitutes, and include cases where additionally, some variables may be strategic complements. It is shown that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. For a given parameter value, a pair of distinct equilibria are never comparable. Moreover, generalizing an existing result, it is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. (In particular, in n-player games with real-valued action spaces, symmetric equilibria increase with the parameter.) Furthermore, when functions under consideration are weakly decreasing in endogenous variables, a sufficient condition is presented that guarantees existence of increasing equilibria (symmetric or asymmetric) at a new parameter value. This condition is applied to two classes of examples.