Evolutional Analysis for the South China Sea Dispute Based on the Two-Stage Attitude of Philippines

Abstract

Due to different attitudes of ex-president and president of Philippines for the South China Sea dispute, the different equilibria of this conflict arose to facilitate the negotiation between China and Philippines. The evolutional conflict models resulted from decision makers’ attitude based on option prioritization under the graph model for conflict resolution are constructed and analyzed in this paper. Compared with the first stage of the South China Sea dispute, the equilibrium of the second stage conflict is different from the first one because current presidential attitude of Philippines is not negative for Chinese government. The two-stage equilibria provide the valuable information that helps decision makers to choose suitable attitude that can be better to understand and resolve the conflict.

1 Introduction

China is the first country to discover and name the Spratly Islands, and continues to exercise sovereignty over the Spratly Islands. However, after World War II, Southeast Asian countries illegally occupied the Spratly Islands, such as the Philippines, Vietnam, Malaysia and so on. Recently, due to the South China Sea arbitration case [1], the situation between the Philippines and China in the South China Sea is becoming increasingly tense, which results in the conflict between the Philippines and China. However, the South China Sea dispute between China and the Philippines undergone a great turning, due to the attitude of the current president of the Philippines towards China with positive manner. Therefore, it is important to study the evolution of conflict equilibrium caused by the change of decision makers (DMs)’ attitude. In this paper, the two-stage evolutional models within the framework of the graph model for conflict resolution (GMCR) [2] including the DMs’ attitude are presented by studying the South China Sea dispute based on the two-stage attitude of the Philippines.

GMCR was proposed by Kilgour et al. [2] to solve strategic conflict in 1987, whose greatest advantage is the need for very little conflict information compared with classical game theory. GMCR is a formal analysis method for conflict developed on the basis of the classical game theory [3] and the metagame theory [4], which has a strict mathematical structure and was applied in many fields [5,6,7]. Then, in order to depict a variety of behaviors for DMs in a conflict, a series of stability definitions were presented, including Nash stability [8, 9], General Metarationality (GMR) [4], Symmetric Metarationality (SMR) [4] and Sequential stability (SEQ) [10]. However, above definitions have not considered the attitude of DMs.

In 1993, Fang et al. [11] first suggested that the attitude of DMs should be introduced into the conflict, because the DMs’ attitude will affect the DMs’ preferences [12] and the result of conflict due to DMs’ preferences generated by the subjective judgment of DMs. In the previous studies, the preference of DMs was determined only by their own interests. When the attitude is taken into account, the preference of DMs may be changed, because the DMs’ preference is generated not only by his own interests but also by the opponent’s interests. Accordingly, in 2007, Inohara concluded the three types of attitudes [13], and defined four basic attitude stability of RNash, RGMR, RSEQ, RSMR [14, 15]. However, the correlative attitude definitions proposed by Inohara are based on logical representations, whose process for calculating attitude stability is more complex. Subsequently, Sean B transformed the logical definition of attitude stability into matrix expression [16,17,18], which provides a great convenience for us to calculate the attitude stabilities and laid the foundation for future system development.

However, above attitude definitions proposed by Inohara and Sean B are based on the preference of states, but the preference of states is difficult to obtain in the complex conflict. So Xu et al. proposed the preference of attitude based on option prioritization [19] in 2016, because the quantity of states is more than the quantity of options in a complex conflict and option prioritization is easy to get for a user. Let the numbers of states and options be m and k, respectively. Then, m and k satisfy the equation $m = 2^{k}$ that shows the preference of attitude based on option prioritization is very convenient to generate. But, the above conflicts are assumed with fixed attitudes that cannot describe the evolutional conflict due to DMs’ changed attitude. Therefore, existing attitude theory is unable to accurately analyze and predict the conflict. In this paper, the evolutional graph model within the framework of the attitude theory based on option prioritization is presented by studying the South China Sea dispute in view of the two-stage attitude of the Philippines, which helps DMs to better understand and resolve the conflict.

2 Attitude Based on Option Prioritization Under GMCR

2.1 The Graph Model for Conflict Resolution

A graph model for conflict resolution is a 4-tuple $\left( {N,\,S,\,(A_{i} )_{i \in N} ,\,( > i,\sim i)_{i \in N} } \right)$, where N: the set of DMs $\left( {\left| N \right| \ge 2} \right)$, S: the set of all states in the conflict $\left( {\left| S \right| \ge 2} \right)$, (S, $A_{i}$): DM i’ s graph (S: the set of all vertices, $A_{i} \in S \times S$: the set of all arcs such that $(s,s) \notin A_{i}$ for all $s \in S$ and all $i \in N$), and $\left( { >_{i,} \,\sim_{i} } \right)$: DM i’s preferences on S.

Briefly, the conflict includes four elements (DMs, States, Moves, Preference). DMs denote all participants in the conflict; States indicate the strategy combination of all DMs; Moves represent DM can move between two states by changing his own strategy; Preference denotes the rank of states according to DMs’ preference. Here, the states and DMs’ moves are represented by the vertices and directed arcs in the graph model, respectively. Therefore, a graph constitutes a natural construct in which to model a conflict.

With respect to preferences, for $s,t \in S$, $s >_{i} \,t$ means that DM i prefers state s to t, while $s\sim_{i} t$ indicates that DM i is indifferent between s and t.

2.2 Attitude Based on Option Prioritization

Definition 1 (Attitudes):

Attitude is a stable psychological tendency of an individual to a particular object (person, idea, emotion, or event).

This psychological tendency contains the subjective evaluation and the behavioral tendencies of the individual. In a conflict, the DMs’ preferences are generated by the subjective evaluation of DMs, hence the DMs’ attitude should be taken into account when we calculate DMs’ preference.

Inohara divides the attitude of DMs into three kinds (Positive, Negative and indifferent) [13], in which, the positive, indifferent and negative attitude of DM i towards DM j are denoted by $e_{ij} = +$, $e_{ij} = 0$ and $e_{ij} = -$, respectively.

The following related definitions are defined based on option prioritization [18, 20,21,22], which is a method to get preference of states. In the option prioritization, the DM i’s option statements are denoted by $L_{i} (i = 1,2,3, \ldots n)$. Under the $L_{i}$, the preference of DM i can be obtained, denoted by $P_{i} (i = 1,2,3 \ldots n)$.

Definition 2 (Positive attitude option statements):

If $e_{ij} = +$, DM i will make an option statements that is beneficial to DM j, denoted by $L_{i} (e_{ij} = + ) = L_{j}$.

Here, the option statements of DM i under positive attitude towards DM j are the same as the DM j’s option statements, which is beneficial for DM j.

Definition 3 (Negative attitude option statements):

If $e_{ij} = -$, DM i will make a option statements that is harmful to DM j, denoted by $L_{i} (e_{ij} = - ) = - L_{j}$.

Under the negative attitude towards DM j, the option statements of DM i are the same as the opposite of DM j’s option statements, which is injurious for DM j.

Definition 4 (Indifferent attitude option statements):

If $e_{ij} = 0$, DM i doesn’t care his option statements in this attitude, denoted by $L_{i} (e_{ij} = 0) = I$.

Definition 5 (Attitude option statements):

$$ L_{ij} = \left\{ {\begin{array}{*{20}l} {L_{j} } \hfill & {if \, e_{ij} = + } \hfill \\ { - L_{j} } \hfill & {if \, e_{ij} = - } \hfill \\ I \hfill & {if \, e_{ij} = 0} \hfill \\ \end{array} } \right. $$

Here, $L_{ij}$ denotes DM i’s option statements at corresponding attitude.

Definition 6 (Attitude preference):

According to $L_{ij}$, the attitude preference of DM i is obtained, denoted by $T_{ij}$. For $s, \, t \in S$ and $i \in N$, $t \in T_{ij} (s)$ if and only if $t >_{i} s$ satisfies $T_{ij}$.

Definition 7 (Total attitude preference):

For $s, \, t \in S$ and $i \in N$, $t \in \, T_{i}^{ + } (s)$ if and only if $t \in T_{ij} (s)$ for all $j \in N$, then we call total attitude preference.

Here, DM i’s total attitude preference satisfies all attitude preferences. In other words, the state in the intersection of all DM i’s attitude preferences is what DM i want to reach (total attitude preference).

Definition 8 (Set of less or equally preferred states at total attitude):

For $s, \, t \in S$, and $i \in N$, $t \in T_{i}^{ - = } (s)$ if and only if $t \notin \, T_{i}^{ + } (s)$.

Definition 9 (Reachable list):

For $i \in N,$ $s \in S$, DM i’s reachable list from state s is the set $\left\{ {t \in S|(s,t) \in A_{i} } \right\}$, denoted by $R_{i} (s) \subset S$.

The reachable list is a record of all the states that a given DM can reach from a specified starting state in one step.

Definition 10 (Unilateral improvement list for a DM at attitude):

For $s, \, t \in S$ and $i \in N$, $t \in T_{i}^{*} (s)$ if and only if $t \in R_{i} (s)$ and $t \in \, T_{i}^{ + } (s)$.

According the definition, the state in $T_{i}^{*} (s)$ is reachable and preferable for DM i at initial state s.

2.3 Stability Concepts of Attitude

Definition 11 (Relational Nash stability—RNash):

If $T_{i}^{*} (s) = \varnothing$, then $s \in S_{i}^{RNash}$.

A state s is RNASH stable for DM i iff i has no unilateral improvement moves at attitude from state s, namely, DM i doesn’t want to move or cannot reach to the preferred states from state s.

Definition 12 (Relational general metarationality—RGMR):

If for all $h \in T_{i}^{*} (s)$, and $R_{j} (h) \cap T_{i}^{ - = } (s) \ne \varnothing$, then $s \in S_{i}^{RGMR}$.

DM i will not move to the unilateral improvement state at attitude if i finds that the opponent j could make a move regardless of the benefit to himself that sanctions i’s moves.

Definition 13 (Relational symmetric metarationality—RSMR):

If for all $h \in T_{i}^{*} (s)$, exist $y \in R_{j} (h) \cap T_{i}^{ - = } (s)$ and ${\text{z}} \in T_{i}^{ - = } (s)$ for all ${\text{z}} \in R_{i} (y)$, then $s \in S_{i}^{RSMR} .$

If DM i cannot escape the sanction on i’s unilateral improvement moves at attitude by DM j, then DM i likes to stay on initial state s. RSMR presumes one step more foresight than RGMR, because it evaluates not only the response by the opponent to DM i’s moves but also the counterresponse from DM i.

Definition 14 (Relational sequential stability—RSEQ):

If for all $h \in T_{i}^{*} (s)$, and $T_{j}^{*} (h) \cap T_{i}^{ - = } (s) \ne {\varnothing}$, then $s \in S_{i}^{RSEQ}$.

Here, DM i’s all potential unilateral improvement moves at attitude are sanctioned by DM j’s unilateral improvement moves at attitude. Hence, RSEQ is the same as RGMR except that DM i takes the benefit of his own into consideration at time in sanction.

3 The Evolutional Two-Stage Dispute Between China and the Philippines for the South China Sea

The dispute between China and the Philippines in the South China Sea mainly revolves around the ownership of the islands sovereignty and maritime demarcation issues. Dispute began in the early 1950s, the U.S. military forces in the Philippines Subic Bay turned Huangyan Island into a place for military exercise without authorization, ignored China’s sovereignty. [23] On April 30, 1997, the Philippine two representatives boarded the Huangyan Island and set the Philippine national flag on it. On April 10, 2012, the Philippine navy Palawan captured Chinese fishermen in Huangyan Island waters. [24] On March 26, 2013, the Philippines unilaterally submitted the South China Sea dispute to the International Tribunal for the Law. On July 12, 2016, Arbitration tribunal made an illegal and invalid arbitration. China repeatedly states that the Aquino III of the Republic of Philippines unilaterally filed arbitration is no jurisdiction, and China will not accept and recognize [25].

But with the change of the Philippine president, the South China Sea dispute has undergone a major turning. The new president, Rodrigo Duterte, said he was more willing to promote reconciliation with China, rather than international arbitration. Furthermore, the new president does not agree with the pro-American policy of former president completely, who will consider more to promote reconciliation with China, restoring investment, trade, tourism and other aspects with China. Because the Philippines found that USA just want to utilize him to implement the Asia-Pacific rebalancing strategy, and did not provide any substantive assistance to him [26].

3.1 Basic Modeling

Decision Makers, Options and Feasible States.

In this conflict, there are two DMs: China (C), Philippines (P). China has two options: 1. Settle territorial disputes through negotiation (Negotiation); 2. Resolve the dispute in the South China Sea through military power (Declaration of war). The Philippines also has two options: 3. Return the islands to China and jointly develop the rich resources in South China Sea (Return the islands); 4. Seek help from other countries or organizations, and jointly confront China, such as USA, Vietnam, Malaysia and so on (Ask for help). (Presented in the left of Table 1).

Table 1. Feasible states of the dispute between China and Philippines

Logically, there are $2^{ 4} { = 16}$ of states because the number of options is 4. But there are some states are not reasonable. For example, if China chooses option 1, option 2 cannot be selected, and the Philippines cannot choose option 3 and option 4 at same time. Lastly, we will get 9 feasible states after removing unreasonable states. (Shown in the right of Table 1).

Graph Model of Conflict.

In Fig. 1, there are China’s moves and the Philippine moves depicting the movement that DMs unilaterally control between two states, and the dot indicates 9 feasible states, the directed arc denotes DM can transfer between the two states by changing his own strategy. The reachable list of DM is naturally produced from graph model.

Fig. 1.

Graph model of the dispute between China and Philippines

Option Statements.

For China, China most likes the Philippines returns the islands, and China hopes to solve this conflict through negotiation, not war. Because if China fights with the Philippines, USA will have an excuse to intervene this dispute, and the Philippines will fight with China by seeking help from other international organizations or counties. Therefore, China’s option statements from most preferred to least is 3, 1, −2, −4. Here, 3 denotes China likes option 3, and −2 denotes China likes the opposite of option 2.

For the Philippines, the Philippines does not want China to solve this dispute through military power, because the Philippine military power is far less than China’s and USA has not given clear attitude to help the Philippines in military. But the Philippines also doesn’t like to return the Spratly Islands to China, because the Spratly Islands have a wealth of resources and the important military strategy position. Hence the Philippines’ option statements from the most preferred to least preferred is −2, −3, 4, −1.

3.2 Attitude Modeling and Analysis for the First Stage Dispute

Attitude.

For China, his position on the South China Sea issue is to uphold the sovereignty of the South China Sea islands and the surrounding waters, who hope to resolve this issue through negotiation according international law. The main purpose of China is to defend the integrity of national sovereignty, and China insists on the principle, putting aside disputes and developing together, for the rich resources in the South China Sea before solving this dispute. China just considers his own benefit and is not evil intention to the Philippines, in other words, China has a positive attitude for himself and an indifferent attitude towards the Philippines [27].

For the Philippines, he does not want to return the island, because the South China Sea has a wealth of resources, and is the only way which must be passed for the East Asian countries shipping trade. Moreover, the Philippines was a former US colony, is the alliance relationship with the United States during World War II. As China’s military power in the South China Sea gradually increase, the Philippines hopes to join forces with USA and other counties to suppress China’s power in the South China Sea. Thus, the Philippines has a positive attitude for himself and a negative attitude towards China. [28] (Presented in the Table 2)

Table 2. Attitudes of the first stage dispute between China and Philippines

Attitude Option Statements.

According to definition 5 and the attitude among DMs, the attitude option statements of DMs are obtained presented in the Table 3. For example, $L_{CC} = L_{C}$($e_{CC} = +$) denotes China’s attitude option statements under the attitude ($e_{CC} = +$) is same to China’s option statements.

Table 3. Attitude option statements of the first stage dispute between China and Philippines

Attitude Preference.

The attitude preference of DM is generated by corresponding attitude option statements presented in the Table 4. For example, $T_{CC}$ denotes China’s attitude preference under the attitude $\left( {e_{CC} = + } \right)$.

Table 4. Attitude preference of the first stage dispute between China and Philippines

Total Attitude Preference.

The total attitude preference should satisfy every attitude preference (Presented in the Table 5). For example, $T_{C}^{ + } = T_{CC} \cap T_{CP}$ denotes China’s total attitude preference satisfies attitude preferences $T_{CC}$ and $T_{CP}$.

Table 5. Total attitude preference of the first stage dispute between China and Philippines

Attitude Stability Analysis.

Based on above total attitude preference, graph model and the definition of attitude stabilities, the equilibrium of this conflict is calculated and displayed in the Table 6, in which the “√” denotes the state is stable for DM under the corresponding stability, and “Eq” means an equilibrium that is a stable state for all DMs. It is clear that S8 is an equilibrium under four kinds of attitude stabilities, that is to say S8, China wants to solve this dispute through negotiation and the Philippines chooses to join other countries and organizations to boycott China, is the possible result of the first stage dispute.

Table 6. Attitude stability of the first stage dispute between China and Philippines

3.3 Attitude Modeling and Analysis for the Second Stage Dispute

With the Philippine presidential transition, the South China Sea dispute has undergone a major turning due to the changed attitude of the Philippines (Fig. 2). The Philippine attitude towards China may transform from the negative to indifferent or positive, because the new President Rodrigo Duterte advocates peaceful means to solve this dispute, he publicly declared willing to jointly develop the rich resources in the South China Sea with China, emphasized his willingness to cooperate with China in economic cooperation and his reluctance to confront China. Another important reason is that the Philippines finds USA did not provide any substantive (Military, Political) assistance to him. Accordingly, the Philippines is not willing to continue to confront China with USA, and the result of this dispute may be changed [26].

Fig. 2.

Evolution of the dispute between China and Philippines

Possible Attitude of the Philippines.

There are two kinds attitude for the Philippines in the second stage dispute, the first is that the Philippine attitude to China transforms from negative to indifferent, the second is that the Philippine attitude to China transforms from negative to positive. (Presented in the Table 7).

Table 7. Possible attitude of Philippines in the second stage of dispute

Possible Attitude Preference and Total Attitude Preference of the Philippines.

Two possible attitude preferences and total attitude preferences are presented in the Tables 8 and 9, respectively.

Table 8. Possible attitude preferences of Philippines in the second stage of dispute

Table 9. Possible total attitude preferences of Philippines in the second stage of dispute

Attitude Stability Analysis.

By calculating the attitude stability of the two different attitudes of the Philippines, the equilibrium under corresponding attitudes is generated. (Presented in the right of Table 10) When the attitude of the Philippines to China is indifferent, the equilibrium is S8. When the attitude of the Philippines to China is positive, the equilibrium is S7, S8, S9.

Table 10. The result evolution process for the South China Sea dispute

3.4 Results Evolution Analysis for the South China Sea Dispute

As shown in the Table 10, when the attitude of the Philippines towards China changes from negative to indifferent, the equilibrium of the conflict does not change, is still S8, which indicates the Philippines will continue to seek assistance from other international organizations or counties. Because when the Philippine attitude towards China becomes indifferent, out of the consideration of his own interests, such as developing the rich resources and weakening China’s control in the South China Sea, the Philippines will continue to maintain the previous strategy, so the equilibrium is still S8.

When the attitude of the Philippines towards China changes from negative to positive, the equilibrium of conflict is S7, S8 and S9. S7 indicates that the Philippines has given up seeking allies to confront China. S9 denotes the Philippines chooses to return the island, and jointly develops the rich resources in the South China Sea with China. These three equilibria are likely to be the final solution. But we find that if the equilibrium changes from S8 to S7 and then to S9, the Philippine strategy is gradually beneficial to China. The Philippines firstly gives up to seek allies to confront China, and then chooses to return the island, which reflects some inner links among those equilibria. Perhaps we can further determine the final resolution based on some other properties of DMs’ attitude, which will be researched in future.

4 Conclusion and Future Work

In this paper, the two-stage evolutional conflict including the Philippines’ different attitudes based on GMCR is presented using the two-stage evolution of the South China Sea dispute. The results show that when the attitude of the Philippines towards China changes from negative to indifferent, out of the consideration of his own interests, the Philippines will maintain the previous strategy, the equilibrium does not change. When the attitude of the Philippines towards China transforms from negative to positive, the equilibria is beneficial to China. Accordingly, China should adopt some peaceful approaches to solve this dispute, including laying disputes aside and developing together, promoting strategic mutual trust and interest integration, strengthening industry collaboration with the Philippines and so on, which contributes to the transformation of Philippine attitude towards China from negative to positive. The analysis of this evolutional dispute not only provides valuable information for DMs, but also helps them to better understand and resolve conflicts, and promotes DMs cooperating well.

But this evolutional analysis for the South China Sea dispute is based on the changed attitude of the Philippines only. In fact, there may be other important factors affecting the South China Sea dispute evolution. For example, the USA may be involved in this dispute with the US new president’s attitude, which may result in the South China Sea dispute to evolve again. Considering these factors into the evolutional analysis for the South China Sea dispute will be very valuable.