We need to show that these strategies form a perfect Bayesian equilibrium
. Consider a deviation by a firm offering a menu different from the proposed equilibrium contract, for example, including an undercutting contract (menu).
On the other hand, a perfect Bayesian equilibrium
in which [[lambda].sub.i] = 0 if [V.sub.i] = L and = 1 if [V.sub.i] = H still does not exist in this framework.
Specifically, the separating perfect Bayesian equilibrium
would be formalized as follows.
To fully characterize the perfect Bayesian equilibrium
, we combine these strategies for the union with the union's beliefs that the true value of [pi] is uniformly distributed on [0, [[pi].sub.H]] in the first round and, in the case that [w.sub.1.sup.*] is rejected in the first round, that [pi] is uniformly distributed on [0, [[pi].sub.1] ([w.sub.1.sup.*])].
Example 1 shows a case in which a contract has more than one perfect Bayesian equilibrium
Our solution concept is a perfect Bayesian equilibrium
. Hence, MPC members' strategies will be sequentially rational given their beliefs and the beliefs will be consistent, wherever possible, with the played strategies.
We focus on perfect Bayesian equilibria that minimize the social cost of financial distress (5) while leaving the bank profit constant; i.e, we focus on equilibria (x,[alpha] m, p, M) such that there is no other perfect Bayesian equilibrium
(x', [alpha]', m', p', M) satisfying W(x', [alpha]', m' /M) > W(x, [alpha], m/ M) and [[PI].sub.i] (x', [alpha]', m' /M) = [[PI].sub.i] (x, [alpha], m/M) for every i.
(i) The strategy of the firm ([[[pi].sup.*].sub.n], [[[pi].sup.*].sub.r]) = (z, z); the strategy of the worker ([[R.sup.*].sub.1], [[R.sup.*].sub.2], [[phi].sup.*]) = (z, z, 0); and the beliefs ([[[pi].sup.*].sub.n], [[[pi].sup.*].sub.r]) (0, 1) constitute a Perfect Bayesian Equilibrium
. (ii) In the Perfect Bayesian Equilibrium
described in part (i), all workers accept the first offer they receive and earn a wage, [[w.sup.*].sub.n], equal to the value of leisure, z.
This may tempt us to conclude that the defendant should place zero probability that an out-of-equilibrium offer made subsequent to filing comes from a player with a NEV suit; however, this belief is not ruled out in a perfect Bayesian equilibrium
. Osborne and Rubinstein (1994, p.
There can exist a perfect Bayesian equilibrium
where both types of player 1 eat quiche, and player 2 challenges player 1 to a fight if and only if player 1 has beer for breakfast.
In the framework of this imperfect-information bargaining game, the concept of perfect Bayesian equilibrium
is analyzed and applied to how the class of pure-strategy equilibria depends on the probability of observing the contract between the agent and his delegate.