A battle of informed traders and the market game foundations for rational expectations equilibrium

- We model price manipulation where bulls and bears seek to manipulate the price in opposite directions.
- A fully revealing equilibrium is constructed, which converges to the fully revealing REE under replication.
- Without short-sale restrictions there is no revealing equilibrium, but there is a non-revealing equilibrium.

Potential manipulation of prices and convergence to rational expectations equilibrium is studied in a game without noise traders. Informed players with initially long and short positions (bulls and bears) seek to manipulate consumer expectations in opposite directions. In equilibrium, period 1 prices reveal the state, so manipulation is unsuccessful. Bears and uninformed consumers sell up to their short-sale limits in period 1. Bulls buy in period 1 but receive arbitrage losses. When the number of bulls and bears approaches infinity, the equilibrium converges to the REE. Without short-sale constraints there is a non-revealing equilibrium but no revealing equilibrium.