We study a retailer's strategic decision with regard to outsourcing the production of such types of store brands (SBs) to national brand (NB) manufacturers. The wholesale price of NB is assumed to be set by the manufacturer, while that of the SB is assumed to be set by the retailer. When a retailer outsources SB production to an NB manufacturer, the NB manufacturer might suffer from cannibalization due to offering both the SB and the NB, implying that a strategic interaction between the retailer and manufacturer is an important issue. Based on this motivation, we mainly focus on the strategy of a dominant retailer in such a situation and investigate it with a game-theoretic approach. We show that the optimal strategy for the SB retailer sensitively depends on the degree of differentiation between the SB and the NB. In particular, if both products are less differentiated, the retailer benefits from offering only the SB, and, in this case, the retailer should offer its wholesale price, after the manufacturer sets the NB wholesale price. Furthermore, it is shown that the optimal strategies of the retailer are socially efficient, if and only if the SB and the NB are sufficiently differentiated.

We study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik’s (1971) assignment game. We consider the Core, three other notions of group stability, and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related to the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated with the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.

We consider a two-period model in which a continuum of agents trade in a context of costly information acquisition and systematic heterogeneous expectations biases. Because of systematic biases agents are supposed not to learn from others' decisions. In a previous work under somehow strong technical assumptions a market equilibrium was proved to exist and the supply and demand functions were proved to be strictly monotonic with respect to the price. Here we extend these results under very weak technical assumptions. We also prove that the equilibrium price maximizes the trading volume and further additional properties (such as the antimonotonicity of the trading volume with respect to the marginal information price).

This paper investigates the impact of corporate social responsibility (CSR) on hospital duopoly with price and quality competition. A CSR hospital is defined in this paper that cares about not only the profit but also the patient benefit. We start our analysis by establishing a two-stage Hotelling model with and without CSR. Results indicate that privatization mechanism may not be the best way of improving medical quality. Competition between hospitals with zero-CSR would lower the equilibrium qualities compared to the first-best level. So the coexistence of a public (more accurately, partial public) and a private hospital might be more efficient than a private-private hospital duopoly. During the competition with CSR in price and quality, social welfare level acts in accordance with an inverted U-shaped trajectory as CSR degree increases. The main reason lies in tha fact that optimal degree of CSR is determined by the trade-off between the benefit of quality improvement and the cost of quality investment. Numerical simulation shows that the optimal degree of CSR is less than a third.

We study a local interaction model where agents play a finite n-person game following a perturbed best-response process with inertia. We consider the concept of minimal p-best response set to analyze distributions of actions on the long run. We distinguish between two assumptions made by agents about the matching rule. We show that only actions contained in the minimal p-best response set can be selected provided that p is sufficiently small. We demonstrate that these predictions are sensitive to the assumptions about the matching rule.

Evolutionary graph theory is a nice measure to implement evolutionary dynamics on spatial structures of populations. To calculate the fixation probability is usually regarded as a Markov chain process, which is affected by the number of the individuals, the fitness of the mutant, the game strategy, and the structure of the population. However the position of the new mutant is important to its fixation probability. Here the position of the new mutant is laid emphasis on. The method is put forward to calculate the fixation probability of an evolutionary graph (EG) of single level. Then for a class of bilevel EGs, their fixation probabilities are calculated and some propositions are discussed. The conclusion is obtained showing that the bilevel EG is more stable than the corresponding one-rooted EG.

The main goal is to reveal the 1-concavity property for a subclass of cost games called data cost games. The motivation for the study of the 1-concavity property is the appealing theoretical results for both the core and the nucleolus, in particular their geometrical characterization as well as their additivity property. The characteristic cost function of the original data cost game assigns to every coalition the additive cost of reproducing the data the coalition does not own. The underlying data and cost sharing situation is composed of three components, namely, the player set, the collection of data sets for individuals, and the additive cost function on the whole data set. The proof of 1-concavity is direct, but robust to a suitable generalization of the characteristic cost function. As an adjunct, the 1-concavity property is shown for the subclass of so-called “bicycle” cost games, inclusive of the data cost games in which the individual data sets are nested in a decreasing order.

Since advertisement is an important strategy of firms to improve market share, this paper highlights duopoly advertisement under the Hotelling model. A model of advertisement under spatial duopoly is established, and corresponding effects of brand values and transportation costs are all captured. This study presents the proportion of sales revenue spending on advertisement. The condition for free-rider in advertisement investment is discussed. Under firms with the identical brand values, if firms' advertisement points to corresponding consumers, price and advertisement investment are all reduced. Therefore, advertisement is discussed under spatial competition in this work.

We propose an equilibrium pricing model in a dynamic multiperiod stochastic framework with uncertain income. There are one tradable risky asset (stock/commodity), one nontradable underlying (temperature), and also a contingent claim (weather derivative) written on the tradable risky asset and the nontradable underlying in the market. The price of the contingent claim is priced in equilibrium by optimal strategies of representative agent and market clearing condition. The risk preferences are of exponential type with a stochastic coefficient of risk aversion. Both subgame perfect strategy and naive strategy are considered and the corresponding equilibrium prices are derived. From the numerical result we examine how the equilibrium prices vary in response to changes in model parameters and highlight the importance of our equilibrium pricing principle.

Data envelopment analysis (DEA) is a nonparametric approach for measuring the relative efficiencies of peer decision-making units (DMUs). For systems with two-stage structures, where all the outputs from the first stage are the only inputs to the second stage, the centralized model, which is based on the concept of cooperative game theory, has been widely used to examine the efficiencies of such systems. We define the cross efficiencies of systems with two-stage structures. Since the centralized model may lead to multiple and unacceptable cross efficiencies and rankings of DMUs due to its high flexibility in choosing optimal weights on input and output factors, we develop a game model to obtain a unique cross efficiency measure, which is constructed from the perspective of noncooperative game. An iterative algorithm is then proposed to obtain the game cross efficiencies for the overall systems and subsystems. We use the proposed game model to evaluate the performance of top 30 US commercial banks. The results show that the game model can lead to a unique reasonable cross efficiency for each DMU.

Classical extensions of fuzzy game models are based on various integrals, such as Butnariu game and Tsurumi game. A new class of symmetric extension of fuzzy game with fuzzy coalition variables is put forward with Concave integral, where players’ expected values are on a partial set of coalitions. Some representations and properties of some limited models are compared in this paper. The explicit formula of characteristic function determined by coalition variables is given. Moreover, a calculation approach of imputations is discussed in detail. The new game could be regarded as a general form of cooperative game. Furthermore, the fuzzy game introduced by Tsurumi is a special case of the proposed game when game is convex.

We first analyze quality and price decisions in a supply chain with two Stackelberg games: Manufacturer’s Stackelberg (MS) and Supplier’s Stackelberg (SS). Then, we investigate how equilibrium solutions are influenced by proposed quality improvement policies: coordination and manufacturer’s involvement. Also, we derive the conditions under which the policies can be implemented in both MS and SS strategies. Numerical experiments illustrate the problems and several related issues are discussed. The results suggest that proposed quality improvement policies can realize Pareto improvement for the supply chain performance.

Based on the community structure characteristics, theory, and methods of frequent subgraph mining, network motifs findings are firstly introduced into social network analysis; the tendentiousness evaluation function and the importance evaluation function are proposed for effectiveness assessment. Compared with the traditional way based on nodes centrality degree, the new approach can be used to analyze the properties of social network more fully and judge the roles of the nodes effectively. In application analysis, our approach is shown to be effective.

Taking government preference into consideration, we consider a three-stage game model to compare the differences of innovation subsidy and product subsidy. The findings reveal that stronger preference to consumers’ welfare leads to higher subsidy rates, which benefit not only consumers but also firms. To choose between the two subsidies, the optimal choice varies with the changing preference of policymakers. According to the results of numerical simulation, product subsidy is better than innovation subsidy in most cases, while the government’s expenditure of the former one is larger than the latter one. Moreover, subsidizing firms symmetrically and asymmetrically has different effects on the consequences.

A generalized form of a cooperative game with fuzzy coalition variables is proposed. The character function of the new game is described by the Concave integral, which allows players to assign their preferred expected values only to some coalitions. It is shown that the new game will degenerate into the Tsurumi fuzzy game when it is convex. The Shapley values of the proposed game have been investigated in detail and their simple calculation formula is given by a linear aggregation of the Shapley values on subdecompositions crisp coalitions.

This paper investigates simultaneous learning about both nature and others’ actions in repeated games and identifies a set of sufficient conditions for which Harsanyi’s doctrine holds. Players have a utility function over infinite histories that are continuous for the sup-norm topology. Nature’s drawing after any history may depend on any past actions. Provided that (1) every player maximizes her expected payoff against her own beliefs, (2) every player updates her beliefs in a Bayesian manner, (3) prior beliefs about both nature and other players’ strategies have a grain of truth, and (4) beliefs about nature are independent of actions chosen during the game, we construct a Nash equilibrium, that is, realization-equivalent to the actual plays, where Harsanyi’s doctrine holds. Those assumptions are shown to be tight.