Information at equilibrium
enrico minelli2001, Economic Theory
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Abstract
In a game with rational expectations, individuals simultaneously refine their information with the information revealed by the strategies of other individuals. At a Nash equilibrium of a game with rational expectations, the information of individuals is essentially symmetric: the same profile of strategies is also an equilibrium of a game with symmetric information; and strategies are common knowledge. If each player has a veto act, which yields a minimum payoff that no other profile of strategies attains, then the veto profile is the only Nash equilibrium, and it is is an equilibrium with rational expectations and essentially symmetric information; which accounts for the impossibility of speculation.
Key takeaways
- At a Nash equilibrium of a game with rational expectations, individuals extract information from the simultaneous acts of other individuals.
- At a Nash equilibrium of a game with private information, the information of individuals is essentially symmetric, with respect to a partition, P 0 , if the profile of acts is a Nash equilibrium of the game with symmetric information P 0 .
- For every individual, the act f i * is a solution to the optimization problem with respect to the partition P i ∨ j∈{−i} P f j * , and thus f * is a Nash equilibrium for the game with rational expectations.
- is a Nash equilibrium profile of strategies for the game with rational expectations, the information partition of an individual at equilibrium P i = P i ∨ j∈{−i} P f j * , which is at least as fine as the partition ∨ j∈{−i} P f j * .
- If the veto strategies of all individuals are measurable with respect to some partition, P * , at least as coarse as their private information, P i ⊆ P * , the veto game has a Nash equilibrium, e, at which information is essentially symmetric and which, as a consequence is a rational expectations equilibrium.
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In a game with rational expectations individuals refine their information with the information revealed by the strategies of other individuals: their elementary acts of other individuals at each state of the world. At a Nash of a game with rational expectations, the information of individuals is essentially symmetric: the same profile is also an equilibrium of a game with symmetric information; and their acts are common knowledge. If each player has a veto act, which yields a minimum payoff that no other profile of strategies attains, then the veto profile is the only Nash equilibrium, and it is an equilibrium with rational expectations and essentially symmetric information; which accounts for the impossibility of speculation.
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