Improving Salt Farmer’s Bargain Power through Demand Allocation and Profit Sharing: A Cooperative Game Approach

Oligopoly has remained a serious problematic market structure in the Indonesian salt supply chain, which exterminates the bargaining power of farmers. To eradicate the problem, a hybrid collaboration structures, i.e., vertical collaboration (farmers with cooperatives) and horizontal collaboration (farmers with farmers), are proposed, enabling to bring positive economic impacts to farmers. This novel supply chain-system model follows the cooperative game theory with Shapley's value for decision-making process. This work aimed to evaluate the implementation of the two partnership models for the supply chain of salt regarding their impacts on economic benefits for farmers assessed by Shapley's value of coalitions. The constructed model revealed that collaborative works between salt stakeholders improved farmers’ revenue, and the optimum benefit was achieved by farmers when their supply (?20%) was purchased by cooperatives, while the remaining was bought by middlemen. In this regard, the significant capacity of the cooperative should be invigorated in various sectors, including saving and loan services, market seekers, salt price making, and improvement of salt quality. Although farmers-to-farmers collaboration also bring mutual benefits, additional attempts by cooperatives, especially for small farmers, can be created to nurture a partnership between cooperatives and farmers, enabling them to generate more benefits. 

Cooperative game; Horizontal collaboration; Revenue; Shapley value; Vertical collaboration

From 2016 to 2019, salt prices ranged $0.01 to $0.06 per kilogram (Suhendi, Abdullah, Shalihati, 2020). Farmers should get at least $0.06 per kilogram to cover production costs. The government regulates prices, but it is ineffective due to the role of intermediaries. In addition, the government needs to hold the number of salt imports and supply chain systems by increasing productivity. This effort is to increase income by improving the bargaining ability of farmers. The salt supply chain can be enhanced by involving cooperatives to increase farmers' revenue (Mustofa et al., 2021).

Research on the salt supply chain have been approached using qualitative and quantitative approaches such as margin share methods (Rinardi & Rochwulaningsih, 2017), SWOT analysis (Holis, Sayyidi, and Musoffan,  2019), system dynamics (Muhandhis et al., 2021), and SCOR approach (Purnanto, Suadi, and Ustadi, 2020). Unfortunately, those methods are unable to discuss a collaborative model of the salt supply system. This drawback can be solved by other approaches, such as game theory, which enables to overview of the collaborations aiming to increase farmer’s revenue. The method can formulate and analyze competitive situations and conflicts implicating more than one player with disparate goals (Maschler, Solan, and Zamir, 2013). Determination of options for the supply chain system for agricultural products (Prasad et al., 2019) and allocation of product supply (Bonamini et al., 2019) using the game theory.  Game theory can be applied to agricultural products in various ways. For instance, it can use a single pricing strategy or a two-stage pricing strategy for products in the chain of two echelons - suppliers and retailers (Chen et al., 2018). Additionally, game theory can also be used to determine the coordination approach between farmers and traders while accounting for uncertainties like harvesting yields and demand (Behzadi et al., 2018; Gao, Yang, and Liu, 2017).

This study applies coalition game theory and transferable utility concepts using cooperative games. Coalition members are assumed to agree on the price and amount of payoff among the members (Maschler, Solan, and Zamir, 2013). The coalition in the salt supply-chain model involves a cooperative as one of the key elements in the system. In this regard, a cooperative has the functions of facilitating salt farmers to improve their revenue. Moreover, farmers, middlemen, and cooperatives have different interests. Implementing vertical (farmers with cooperative) and horizontal (farmers with farmers) collaboration systems is expected to improve the salt supply chain. Vertical collaboration is a partnership between farmers and cooperatives to reduce the role of the middlemen (Zhong et al., 2018). In addition, a horizontal collaboration between farmers and farmers is also able to increase revenue (Martins, Trienekens, and Omta, 2019). This work aimed to evaluate the implementation of horizontal and vertical collaboration models regarding their impacts on farmers' revenue based on the Shapley value obtained from the salt supply chain coalition.

1.1. Cooperative Game Theory

Shapley's value is used to determine the optimal solution in cooperative game theory. Each participant's final result in the game focuses on the acquisition in the cooperative game. The coalition is an agreement of the N player set based on the game's mathematical model and is represented by the symbol S (Brown & Shoham, 2008). A grand coalition is an agreement of all players (n players) without an empty coalition with a 2n possible alliance. The structure coalition is how the player forms a coalition where a set of S = (S1, S2, ..., Sm) of the m coalition is built. Some definitions of the Shapley value concept in cooperative game theory are as follows:

Definition 1 The transferable utility used in coalition games (N,v) consists of: (1) a set of N players;  (2) the characteristic function of the game v(S) is the total coalition available to all members of S of N players, which N is the set for each player, for i = 1, 2, ..., n.  The grand coalition is the N set and not the empty set  for all S and T where  The concept of cooperative games is a super additive  where the acquisition of coalition results must be greater or equal to non-coalition income (Brown & Shoham, 2008).

Definition 2 (Brown & Shoham, 2008): The axiomatic method is used to obtain Shapley values, including game values v with n-vector, which must meet the following requirements:  if xx is the xx carrier, then  for each permutation ; if u and v are two games: then Shapley's value with the number of players in the Each player has  2n-1 possible coalition forms. Player i revenue from a coalition is called the payoff value, so the value of the player's contribution is  i  to the S coalition.

Definition 3 (Brown & Shoham, 2008): The dummy player  for each coalition S with i.

Definition 4 (Brown & Shoham, 2008): Shapley's axiom and characteristic function. When players i and j are exchangeable on  some of the axiom used  are (1) symmetry: If i and j are exchangeable in  dummy: If i is a dummy player in  and (3) additivity: If there are two games v and w, then,  for every,  where 

2.2.  Model Formulation

        Vertical and horizontal collaboration model is used to solve the salt supply chain problem. The stakeholders involved in this coalition are farmers, middlemen, and cooperatives (Figure 1). Farmers, as members, are obliged to sell a certain amount of salt through cooperatives. 

Figure 1 The Salt Supply Chain Coalition Model

        The research used six players (farmers 1, 2, 3, 4, 5, and 6). The characteristic function as follows: 
The Shapley values were 

          The Shapley value was determined using a selling scenario in which salt was sold based on the farmer's minimum obligation as cooperative members and the rest is sold through middlemen. As cooperative members, farmers are required to sell salt for at least 10% of the total production through the cooperative. The scenarios for selling salt from farmers to middlemen 1, middlemen 2, middlemen 3 and cooperatives are: scenario 1 (30%, 40%, 20%, and 10%); scenario 2 (30%, 30%, 20%, and 20%); scenario 3 (25%, 25%, 25%, and 25%); Scenario 4 (40%, 20%, 10%, and 30%); Scenario 5 (10%, 30%, 20%, and 40%); and Scenario 6 (20%, 10%, 10%, and 60%).

2.3.  Construction of Shapley Value Salt Coalition Model

       The model illustrates the average contribution of six farmer coalition members {1, 2, 3, 4, 5, 6} in all possible steps. Moreover, the player revenue is used for Shapley value calculations. The salt supply chain channel will determine the amount of farmer revenue. Members of the salt supply chain are i^th farmer (i=1,2, …, n), j^th middleman (j=1, 2. …, m), and k^th cooperatives (k=1, 2, …, h), while the salt supply and salt price in the intermediary depend on t^th time (t = 1.2, ..., l). In addition, the salt demand middlemen j at the time t (Da_jt)   and cooperative k at the time t (qb_kit). The price offered by each middleman j to the farmer i at time t is different (pa_jit), the price offered by the cooperative k to all i farmers at the time t (pb_kit), and the salt price in the market at the time t (pm_t).

       Middleman revenue is obtained from the sale of salt by seeing the negotiation cost (Ca), and salt carrying capacity (G). The formula of the middleman's revenue  at time t is shown in Equation 1.

The cooperative's revenue is revenue from procuring salt from farmers i and benefits distribution  The membership fee of the cooperative is , the supply chain channel through cooperatives has market unpredictability risk (Hao et al., 2018), and the negotiation costs (Cb), and salt carrying capacity (G) are allocated to the farmers at  The formula of the cooperative revenue k at the time  defined in Equation 2. 

The formula of farmer i revenue at time t  is the middlemen j revenue and cooperatives k revenue. Farmer i must become delegates cooperatives to achieve a vertical collaboration system. Furthermore, the supply farmer i through middlemen j at time t (qa_jit), and cooperatives k at time t  (qb_kit) The cooperative and farmer I collaborates have to bear half of the percent real risks  the negotiation fee (C), the membership fee (Cm_it), and receive a benefit distribution 

   There are three types of farmer’s revenue based on a horizontal collaboration, namely:

(i)    Farmers only sell salt according to the supply produced 

       The farmer's revenue is obtained from the salt supply through middlemen j and cooperativ

cooperative k, so the farmer i revenue at time t  is explained in Equation 3.

            

(ii)     The farmers who buy salt from other farmers

 Farmers receive revenue through middlemen j, and cooperatives k, and part of the profits are shared from cooperatives. However, farmers, i have to pay for a certain amount of salt purchased from other farmers. Therefore, the formula of farmer i revenue at time t  defined in Equation 4.

(iii) Farmers whose supply exceeds the demand of middlemen and cooperatives 

Farmers' revenue is obtained from sales through middlemen, cooperatives, and coalitions with other farmers, so the farmer income model is described in Equation 5.

In this scenario, all farmers (Farmer 1, Farmer 2, Farmer 3, Farmer 4, Farmer 5, and Farmer 6) are responsible for meeting the demands of three middlemen (Middlemen 1, Middlemen 2, and Middlemen 3) and the cooperative. The supply of salt from the farmers, as well as the demand from the middlemen and the cooperative, varies for each time period. Additionally, the prices offered to the farmers by each middleman and the cooperative also differ. The salt price at the market in period t (Pm_t) $83.22/tons;  cooperative salt price k in period t (Pb_kt) $76.28/tons; salt carrying capacity (G) 9 tons; risk of selling through cooperatives  benefit distribution (cooperatives and farmers)  negotiation costs from pond to cooperatives (C) $3.12/tons; salt negotiation costs by middlemen to the market (Ca) $6.73/tons; negotiation fee from cooperative to market (Cb) $3.12/tons; percentage drop in salt price (r) 40%; cooperative membership fee  $2.08/period.

The salt supply chain system without a coalition is the initial scenario in which farmers sell through middlemen 1, 2, and 3 (30%, 20%, 20%) and cooperatives (20%). Based on the scenario, the total revenue of farmer is: farmer 1, farmer 2, farmer 3, farmer 4, farmer 5, and Farmer 6 ($18,079; $27,450; $10,346; $5,703; $47,854; $2,532).

Horizontal collaborations are used as the basis for the coalition game scenario. A coalition carried out by farmers is expected to provide a minimum revenue equal to or greater than not conducting a coalition.  The coalition of six farmers in each coalition formed the functional characteristics based on Definition 1 (Table 1). Shapley's value is the solution problem states that the concept of a coalition forms a grand coalition in each game (Brown & Shoham, 2008).

Table 1 Farmer supply as a base, for example, Characteristics of the v(S) function