Bounded rational learning in differential information economies: Core and value

We apply the private core and the private value to a dynamic economy and study the evolution of private core and private value allocations as individuals acquire information (learn) through time. In particular, a realized agreement in each period generates information that changes the underlying information structure in the economy. Since the private core (value) depends on the distribution of information across individuals, when agents learn some new information a realized agreement may no longer be in the private core (value) for the new information structure that arises. We define a 'limit full information' economy and address the following issues; (i) Given a sequence xt of approximate private core (value) allocations in each period, there is a subsequence that converges to a private core (value) x* allocation for the limit full information economy. (ii) Private core (value) allocations x* in the limit full information economy, can be approximated by a sequence xet of approximate private core (value) allocations in each time period. The approximate notions we consider can be viewed as the errors that agents make due to bounded rationality.