Economics Insights @ CBS

This paper considers non-cooperative N-person stochastic games with a countable state space and compact metric action spaces. We concentrate upon the average return per unit time criterion for which the existence of an equilibrium policy is established under a number of recurrency conditions with respect to the transition probability matrices associated with the stationary policies.

Gillies showed that the core of a game depends only on the vital coalitions. We show that the essential coalitions--which include the vital coalitions--determine the nucleolus if the core is not empty.

This paper considers undiscounted Markov Decision Problems. For the general multichain case, we obtain necessary and sufficient conditions which guarantee that the maximal total expected reward for a planning horizon of n epochs minus n times the long run average expected reward has a finite limit as n approaches infinity for each initial state and each final reward vector. In addition, we obtain a characterization of the chain and periodicity structure of the set of one-step and J-step maximal gain policies.

This paper develops optimal portfolio choice and market equilibrium when investors behave according to a generalized lexicographic safety-first rule. We show that the mutual fund separation property holds for the optimal portfolio choice of a risk-averse safety-first investor. We also derive an explicit valuation formula for the equilibrium value of assets.