Monotonicity in the stock competition game with consumer search

Analysis of a Single Manufacturer Multi-Retailer Inventory Competition Using Supermodular Multi-Objective Games

“…We will then determine the Pareto equilibrium of GPm1 using Definition 2.2. Based on the form of S in (21), if one of the players plays a strategy 𝑞 1 ∈ [1,3), then the other must choose the same strategy. The player cannot increase his strategy as long as the other retains his choice.…”

“…Therefore, a set [1,3] is a Pareto equilibrium. By contrast; based on the form of joint strategy S set in (21), the strategy which is contained in [3,25] can be chosen by each player without depending on the choices of the other player. It means that each player doesn't have to choose the same strategy as other players.…”

“…This Pareto equilibrium is the optimal solution for each player regarding their multi-objective. If one of the players chooses a strategy in [1,3), then all of the points in [1,3) are the Nash equilibrium for another player based on the definition of S in (21). Furthermore, we will determine the weighted Nash equilibrium when the players choose a strategy in the interval [3,25].…”

“…One of the earlier relevant literatures on the application of supermodular games is the application of these games to the Cournot oligopoly problem [18]. Other results can be found in several papers, such as supermodular games for tax competition [19], NTU supermodular games [20], supermodular games for stock competition proposed [21], the relation between supermodular games and potential games explained [22], newsboy problem using supermodular games [3], and multiplayer supply chain models using supermodular games [5]. However, those results are still limited to the single objective case.…”

“…In this paper, the formulation of the non-cooperative game has been extended to the noncooperative supermodular multi-objective cases for non-zerosum cases (which can be linear or non-linear). The inventory games problem provided in this paper is also different from the other reference about the application of game theory in inventory [2,3,5,[18][19][20][21][22]. The inventory model used in those references is in a single objective form.…”