Dynamic Thin Markets

Abstract

Extensive empirical research has shown that in many markets institutional investors have a significant impact on prices and mitigate its adverse effects through their trading strategies. This paper develops a dynamic model of such thin markets, in which the market structure is one of bilateral oligopoly. The paper demonstrates that market thinness qualitatively changes equilibrium properties of prices and dynamic trading strategies, compared to the existing theories of asset pricing. The predictions match a number of empirical facts that are hard to reconcile with the competitive or Cournot-based models. The paper further establishes that the nonstrategic general-equilibrium approach and the strategic approach to trade via Nash in demands are dual representations of a model with endogenous price impact. The proposed approach yields an analytical framework that can be used to study dynamic markets with bilateral market power.

Equilibrium in risk-sharing games

“…Even under the appreciation that other agents will not report true beliefs and the negotiation will not produce an Arrow-Debreu equilibrium, agents still want to reach a Nash equilibrium as they will improve their initial position. In fact, transactions with a limited number of participants typically equilibrate far from their competitive equivalents, as has been also highlighted in other models of thin financial markets with symmetric information structure like the ones in [14] and [25]; see also the related discussion in the introductory section.…”

“…(Note that inefficient allocation of risk in symmetricinformation thin market models may also occur when securities are exogenously given; see e.g. [25]. When securities are endogenously designed, [14] highlights that imperfect competition among issuers results in risk-sharing inefficiency, even if securities are traded among perfectly competitive investors.…”

Information and strategic behavior

“…(28). Proposition 1 states that, whether the market becomes more competitive with a new 14 The price impact of a trader, defined as a price change following an off-equilibrium quantity deviation, changes the expectations of other traders, who act according to the equilibrium map between prices and signals. If agents could observe the signal vector, a deviation would not impact beliefs, and the price impact would be as with independent private values, with the private value adjusted accordingly to condition on all signals.…”

“…Conveniently, in the double auction studied in this paper, symmetric traders reduce their 18 Concerning the implementability of the competitive rational expectations equilibrium as a demand function equilibrium, it can be shown that, for any finite number of traders, the necessary and sufficient conditions for the existence of the Linear Bayesian Equilibrium in demand schedules from Rostek and Weretka [13, Proposition 1; see the Appendix], which involve bounds on the commonality statistics, are also sufficient for the implementability of the competitive rational expectations as equilibrium in demand functions. (The results in Rostek and Weretka [13] on inference and Rostek and Weretka [14] on the duality between a (Bayesian Nash) equilibrium in demand functions and a general-equilibrium (REE) representation of equilibrium in quantity levels (a duality based on a formulation of a double auction as the model of "trading against price impact") allow for the implementability of the non-competitive and competitive rational expectations in markets with information structures with heterogeneously interdependent preferences.) Given the feature of the model that each agent has mass equal to one, since the market clearing condition is not well defined in the limit with a continuum of traders, we characterize the limit of equilibria in the sequence of finite auctions.…”

An Equilibrium Model of Institutional Demand and Asset Prices

“…Nevertheless, a natural microfoundation for our model is an imperfectly competitive asset market, in which investors internalize the price impact of trades. Equation (2) can be interpreted as an empirical implementation of the optimal demand schedules in Kyle (1989), Vayanos (1999), and Rostek and Weretka (2014).…”