Working Papers:
1. Informed speculation with k-level reasoning (Job market paper). [Link]
Abstract: This paper studies the effect of strategic reasoning on financial markets by revisiting the microstructure model of Kyle (1989) with the level-k reasoning framework. A level-k speculator performs k rounds of iterative reasoning to infer information from asset price. In contrast to symmetric Bayesian Nash equilibrium, the level-k framework explains the coexistence of momentum and contrarian trading strategies. Regarding market implications, this paper discusses how the distribution of reasoning levels affects macrovariables and sheds new light on empirical puzzles such as: (1) overreaction of asset prices, (2) extra price volatility, and (3) excessive trading volume.
1. Informed speculation with k-level reasoning (Job market paper). [Link]
Abstract: This paper studies the effect of strategic reasoning on financial markets by revisiting the microstructure model of Kyle (1989) with the level-k reasoning framework. A level-k speculator performs k rounds of iterative reasoning to infer information from asset price. In contrast to symmetric Bayesian Nash equilibrium, the level-k framework explains the coexistence of momentum and contrarian trading strategies. Regarding market implications, this paper discusses how the distribution of reasoning levels affects macrovariables and sheds new light on empirical puzzles such as: (1) overreaction of asset prices, (2) extra price volatility, and (3) excessive trading volume.
2. On the sophistication of financial investors and the information revealed by prices, with Andres, Carvajal. [Link]
Abstract: Does sufficient sophistication on the reasoning of financial traders lead to rational expectations equilibrium? We provide an answer by studying a simple exchange economy with complete markets and asymmetric information. Traders are classified as fundamentalists, who know the true probability distributions of random shocks, or speculators, who try to infer the true probabilities from asset prices. Starting with the naive beliefs that asset prices transmit no information, the speculators learn the mapping from asset prices to probabilities through level-k reasoning. We characterize the necessary conditions on convergence to rational expectations equilibrium for some specific utility functions (CRRA and CARA) and discuss the general case. Our result are that: (1) convergence to rational expectations requires that speculators have less market impact than fundamentalists; (2) convergence, when it takes place, occurs in an oscillating manner; and (3) asset prices can be more volatile than at rational expectations equilibrium when speculators display low sophistication.
Abstract: Does sufficient sophistication on the reasoning of financial traders lead to rational expectations equilibrium? We provide an answer by studying a simple exchange economy with complete markets and asymmetric information. Traders are classified as fundamentalists, who know the true probability distributions of random shocks, or speculators, who try to infer the true probabilities from asset prices. Starting with the naive beliefs that asset prices transmit no information, the speculators learn the mapping from asset prices to probabilities through level-k reasoning. We characterize the necessary conditions on convergence to rational expectations equilibrium for some specific utility functions (CRRA and CARA) and discuss the general case. Our result are that: (1) convergence to rational expectations requires that speculators have less market impact than fundamentalists; (2) convergence, when it takes place, occurs in an oscillating manner; and (3) asset prices can be more volatile than at rational expectations equilibrium when speculators display low sophistication.
3. A discussion on the symmetric Bayesian Nash equilibrium in Kyle(1989). [Link]
Abstract: This paper revisits the symmetric Bayesian Nash equilibrium in informed speculation with imperfect competition and argues that the original solution is not a Nash equilibrium. The mistake arises from imposing symmetry incorrectly. This paper then proposes the appropriate solution and provides numerical simulations to show the difference.
Abstract: This paper revisits the symmetric Bayesian Nash equilibrium in informed speculation with imperfect competition and argues that the original solution is not a Nash equilibrium. The mistake arises from imposing symmetry incorrectly. This paper then proposes the appropriate solution and provides numerical simulations to show the difference.
4. Extensive form level-k thinking, with Burkhard Schipper. [Draft available soon]
Abstract: We consider the extension of level-k model to extensive-form games. Player's may learn about levels of opponent's during the play of the game because some information sets may be inconsistent with certain levels. In particular, for any information set reached, a level-k player attaches the maximum level-l thinking for l< k to her opponents consistent with the information set. We compare extensive-form level-k thinking with other solution concepts such as level-k thinking in the associated normal-form, backward induction, extensive-form rationalizability, and iterated admissibility. We also design experiments which are in the spirit of Arad and Rubinstein (2012) to elicit players extensive form levels.
Abstract: We consider the extension of level-k model to extensive-form games. Player's may learn about levels of opponent's during the play of the game because some information sets may be inconsistent with certain levels. In particular, for any information set reached, a level-k player attaches the maximum level-l thinking for l< k to her opponents consistent with the information set. We compare extensive-form level-k thinking with other solution concepts such as level-k thinking in the associated normal-form, backward induction, extensive-form rationalizability, and iterated admissibility. We also design experiments which are in the spirit of Arad and Rubinstein (2012) to elicit players extensive form levels.