We analyze an infinite horizon discrete time inventory model with deterministic but non-stationary demand for a single product at a single stage. There is a finite cycle of vectors of characteristics of the environmen...We analyze an infinite horizon discrete time inventory model with deterministic but non-stationary demand for a single product at a single stage. There is a finite cycle of vectors of characteristics of the environment (demand, fixed ordering cost, variable procurement cost, holding cost) which is repeated after a finite number of periods. Future cost is discounted. In general, minimization of the sum of discounted total cost over the cycle does not give the minimum of the sum of discounted total cost over the infinite horizon. We construct an algorithm for computing of an optimal strategy over the infinite horizon. It is based on a forward in time dynamic programming recursion.展开更多
We analyze an infinite horizon difference game between four aggregated industries-production of producer goods, production of consumption goods, federation of labor unions, and commercial banking sector. Consumers do ...We analyze an infinite horizon difference game between four aggregated industries-production of producer goods, production of consumption goods, federation of labor unions, and commercial banking sector. Consumers do not behave strategically. They make their decisions on the basis of maximization of average discounted utility. Therefore, we do not include them in the set of players in the game. The payoffof each production industry and the commercial banking sector is equal to the average discounted sum of real dividends of its owners. The payoff of the federation of labor unions is equal to the average discounted sum of real wages and real unemployment benefits. A strict strong perfect general equilibrium is the applied solution concept for the game. It requires that there does not exist a coalition of players that can weakly Pareto improve the vector of continuation payoffs of its members in some subgame by a coordinated deviation. It is a refinement of Rubinstein＇s concept of a strong perfect equilibrium. We formulate and prove the sufficient condition for its existence. It is based on the assumption that no one of the aggregated industries can have a positive output without using some minimal amount of output of each other aggregated industry as an input. By definition, in each subgame, the equilibrium payoff vector in a strict strong perfect general equilibrium is strictly Pareto efficient. Thus, if each consumer either has only income from wage and unemployment benefit or receives dividend from only one aggregated industry, and his nominal income in each period along the equilibrium path exceeds social minimum, it is not possible to weakly Pareto improve the vector of consumers＇ average discounted real incomes. This holds not only for the whole game but also for each subgame starting in the first phase of some period.展开更多
基金the grant VEGA 1/0181/12 from the Slovak Ministry of Education, Science, Research, and Sport
文摘We analyze an infinite horizon discrete time inventory model with deterministic but non-stationary demand for a single product at a single stage. There is a finite cycle of vectors of characteristics of the environment (demand, fixed ordering cost, variable procurement cost, holding cost) which is repeated after a finite number of periods. Future cost is discounted. In general, minimization of the sum of discounted total cost over the cycle does not give the minimum of the sum of discounted total cost over the infinite horizon. We construct an algorithm for computing of an optimal strategy over the infinite horizon. It is based on a forward in time dynamic programming recursion.
文摘We analyze an infinite horizon difference game between four aggregated industries-production of producer goods, production of consumption goods, federation of labor unions, and commercial banking sector. Consumers do not behave strategically. They make their decisions on the basis of maximization of average discounted utility. Therefore, we do not include them in the set of players in the game. The payoffof each production industry and the commercial banking sector is equal to the average discounted sum of real dividends of its owners. The payoff of the federation of labor unions is equal to the average discounted sum of real wages and real unemployment benefits. A strict strong perfect general equilibrium is the applied solution concept for the game. It requires that there does not exist a coalition of players that can weakly Pareto improve the vector of continuation payoffs of its members in some subgame by a coordinated deviation. It is a refinement of Rubinstein＇s concept of a strong perfect equilibrium. We formulate and prove the sufficient condition for its existence. It is based on the assumption that no one of the aggregated industries can have a positive output without using some minimal amount of output of each other aggregated industry as an input. By definition, in each subgame, the equilibrium payoff vector in a strict strong perfect general equilibrium is strictly Pareto efficient. Thus, if each consumer either has only income from wage and unemployment benefit or receives dividend from only one aggregated industry, and his nominal income in each period along the equilibrium path exceeds social minimum, it is not possible to weakly Pareto improve the vector of consumers＇ average discounted real incomes. This holds not only for the whole game but also for each subgame starting in the first phase of some period.
