An Uncertain Multi-oligopoly Model

When launching a new product to the market,in order to get the maximal profit,it is quite important for firms t.o adjust or decide its selling price of their own products.According to Beath and Katsoulacos’s research,the demand of a product is related to the selling price of the product.However,the demand of a product is also dependent on the market price:on the condition of the same selling price,the products with,high market prices are more favored(because they are more eost-effective).This paper introduces a kind of new multi-oligopoly model,in which the Nash equilibrium points are discussed.And to ensure that the benefits of all parties are optimal,the new products5 selling prices are decided and the selling prices of those products on the market are adjusted.In the case of complete information,the market price of a product is assumed to be an uncertain variable since it is lack of the historical data.Then,A game model is set up and expected value,optimistic value and uncertain measure approach are used to deal with the uncertainty in the model.Also the method for solving the model is proposed.Therefore,the optimal selling prices and the maximal profits for new products axe obtained based on the model.In the case of incomplete information,because of commercial confidentiality,the cost of new products is not known for other firms.Then the cost of new products is assumed to be uncertain variables.By improving the model under the case of complete information,we set up a new game model and use expectation value,optimistic value method to deal with the uncertainty in the model.Also the method for solving the model is proposed.Therefore,the optimal selling prices and the maximal profits of the products on market after being adjusted are obtained.Finally,numerical examples of these two cases are given.