A Refinement of Sequential Equilibrium

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.We propose a refinement of sequential equilibrium for extensive form games by generalizing a restriction proposed for signaling games in Cho and Kreps (1987).2 The restriction is that beliefs must not assign positive weight to the possibilities that can be excluded through reasonable introspection based on the data available as common knowledge.A new technique is developed in order to prove the existence of forward induction equilibrium, which consists of two steps. First, we establish the generic existence of forward induction equilibrium by exploiting the results of Kohlberg and Mertens (1986). Then, we show that the forward induction equilibrium correspondence is upper hemi-continuous in the outcome space with respect to the changes of parameters of the game.

Repeated Bargaining with Persistent Private Information

“…On the other hand the low-valuation buyer's equilibrium payoff is zero in example P1, whereas rejection of p 1 would yield an expected payoff of (1-L ) if the seller believed that rejection signaled the low valuation. Forward induction then implies that the seller should indeed interpret an unexpected rejection as a signal that the buyer's valuation was low, since the low-valuation buyer might gain by rejection, while the high-valuation Cho (1987) defines forward induction equilibrium as a refinement of sequential equilibrium in general (finite) games; this generalizes the Cho-Kreps (1987) Intuitive Criterion, which is formally defined only for signaling games. The consistency condition is strengthened to include "introspective" consistency, meaning that after a deviation by an informed player, the belief system puts no weight on types of that player which would receive less than the equilibrium payoff, if everyone behaves optimally, unless all types would lose.…”

“…13 buyer necessarily loses. This means that the equilibrium in example P1 is not a forward-induction equilibrium, in the sense of Cho (1987). 10 The same argument rules out all pooling equilibria with…”

Strategic Delay in Bargaining with Two-Sided Uncertainty

“…Nonetheless, (µ2) and (π2) do satisfy the spirit of the Cho-Kreps intuitive criterion, since beliefs are revised (as they must be) following a credible signal of strength. (The qualifier "in the spirit of " is used here, since the refinements by Cho and Kreps (1987) and Cho (1987) are not formally defined for models with two-sided signalling and a continuum of actions.) In addition, the beliefs (µ2) have a desirable property: if a trader mistakenly reveals that she is weaker than she truly is by making an offer too early, it is the trader's best response to correct the mistake by delaying her next offer so as to reveal the truth.…”

A Conversational War of Attrition

“…When we consider the jurors'ex-ante problem of searching (`; m) in the joint type space, the search exhibits diminishing marginal returns. Both the probability of terminating the conversation 3 and the expected value of the true information is decreasing in the number of rounds. As the bene…t of investment into information aggregation is realized only when the information is utilized and the verdict is taken, the total return on investment ex-post is actually the marginal return to the investment ex-ante.…”