The aim of this paper is to develop a bilinear programming method for solving bimatrix games in which the payoffs are expressed with trapezoidal intuitionistic fuzzy numbers (TrIFNs), which are called TrIFN bimatrix games for short. In this method, we define the value index and ambiguity index for a TrIFN and propose a new order relation of TrIFNs based on the difference index of value index to ambiguity index, which is proven to be a total order relation. Hereby, we introduce the concepts of solutions of TrIFN bimatrix games and parametric bimatrix games. It is proven that any TrIFN bimatrix game has at least one satisfying Nash equilibrium solution, which is equivalent to the Nash equilibrium solution of corresponding parametric bimatrix game. The latter can be obtained through solving the auxiliary parametric bilinear programming model. The method proposed in this paper is demonstrated with a real example of the commerce retailers’ strategy choice problem.

Multiplayer bargaining is a game in which all possible divisions are equilibrium outcomes. This paper presents the classical subgame perfect equilibria strategies and analyses their weak robustness, namely, the use of weakly dominated strategies. The paper then develops a refined equilibrium concept, based on trembling hand perfection applied only on the replies, in order to overcome such weakness. Concluding that none of the classical equilibrium strategies survives the imposition of the extrarobustness and albeit using more complex strategies, the equilibrium outcomes do not change.

We present a series of two-person games, which lead to various DEA models. The relationship between the DEA models and the games is explicit in our setting, although the Nash equilibrium solutions do not generally exist. Besides the classic DEA models, we also establish an explicit relationship between the games and some extended DEA models, such as free disposable hull DEA models and “negative” or “inverted” DEA models.

Instant messenger (IM) is one of the most popular Internet applications all over the world. This paper examines the pricing problem of IM based on two-sided market model. IM serves as a two-sided platform, which gets both Internet users and advertisers on board. This paper concludes that IM operator adopts a heavily skewed price structure that favors IM users both under monopolistic case and under horizontal differentiated duopolistic case. When advertising revenue is large enough relatively to marginal cost for serving IM users, IM users can enjoy free service provided by IM operators. The competitive equilibrium of duopolistic case is not necessarily symmetric when advertisers choose singlehoming. Even in the symmetric equilibrium platform would rather deter all advertisers.

It is reported in the literature that the most fundamental idea to address uncertainty is to begin by condensing random variables. In this paper, we propose Cournot duopoly game where quantity-setting firms use nonlinear demand function that has no inflection points. A random cost function is introduced in this model. Each firm in the model wants to maximize its expected profit and also wants to minimize its uncertainty by minimizing the cost. To handle this multiobjective optimization problem, the expectation and worst-case approaches are used. A model of two rational firms that are in competition and produce homogenous commodities is introduced using an unknown demand function. The equilibrium points of this model are obtained and their dynamical characteristics such as stability, bifurcation, and chaos are investigated. Complete stability and bifurcation analysis are provided. The obtained theoretical results are verified by numerical simulation.

In the standard leader-follower duopoly models with otherwise symmetric firms, the market outcome and total welfare are the same whichever firm is the leader. This paper studies and compares total welfare in a sequential-move mixed duopoly when either the public firm or the private firm acts as the leader. It is found that the fact that which firm is the leader affects total welfare and that whether firms compete in quantity or price also affects the optimal choice of market leader.

Cooperative (co-op) advertising is attracting more and more attention. This paper analyzes co-op advertising behavior based on a dual-brand model with a single manufacturer and a single retailer, and some interesting conclusions are achieved. Firstly, the firm in the supply chain advertises both brands, and the difference of advertising expenditure is not very large in equilibrium. Secondly, the retailer's advertising and the manufacturer's participation ratios depend on both the retailer's and the manufacturer's marginal profits. Thirdly, the stimulating effect increases the advertising investment while the competition effect decreases it, but they have no effect on the manufacturer's participation ratio. Fourthly, co-op advertising is more sensitive to the manufacturer's marginal profits than those of the retailer. Lastly, total advertising investment and profit are greater under cooperative decision than under Stackelberg decision.

Based on pricing strategy of value standard method, we establish a three-stage game model of energy production to compare the differences of optimal regulated price and social welfare under three regulation types of feed-in tariffs. We show that the optimal price levels under three main regulation types are different. But the choice of regulation type does not impact the optimal social welfare. So policymakers with different preferences may make regulation decisions in different ways. This successfully explains why many regulation types exist in different countries. Moreover, although it is difficult to determine the optimal price by the value standard method in practice, the conclusions of this paper also provide a judgment criterion for other pricing strategies on how to choose a suboptimal regulation type.

Spatial competition plays important roles in economics, which attracts extensive research. This paper addresses spatial competitions along with horizontal product differentiations and entry deterrence. By the dynamic game theory model about one firm and a potential entrant with different cost in a linear city, this paper finds that both the higher fixed setup cost and the higher transportation cost deter entrants. To efficiently deter the entrants, the establisher is inclined to locating at the middle point of the linear city.