GAME THEORETICAL ANALYSIS OF SINO-AFRICAN RELATIONS

Abstract

China for long claims it does not interfere in domestic issues of any foreign country, but somehow it influences foreign countries politics, economic policies, business environment, and so on. One undisputable example is the precondition China asks to establish diplomatic relations with a foreign country; the one-China principle, where only the Beijing government represents China. Development assistance is also used as a powerful tool by Beijing to advance Chinese interests overseas, especially developing countries in Africa searching for alternative ways to source finance. This research points out that Government tenders in Mozambique, a Least Developed Country (LCD) in Africa, in a project with grants or loans provided by the Chinese government, where both the LCD and China possess perfect or imperfect information of one another’s intention and outcomes, leaves an option for alternative behavior that could be different from their past interaction on similar tenders. This study employs Game Theoretical analysis to deduce that in the event Mozambique opens a tender with funds provided by China, both parties revealing their terms simultaneously, the best outcome for both countries would be Mozambique’s disagreement to conditionality attached to funds provided by China, and China agreeing to that decision. When China sees the terms of agreement proposed by Mozambique in a game that information has been perfectly available, behaves in a manner leading to Nash equilibrium. The observed behavior in a perfect and imperfect information scenario is also a pattern when China plays the game in a repeated manner that is consecutive with Mozambique.

Keywords: China, Mozambique, Game theory, Foreign aid

?Introduction

Some judgments emphasize that a Sino-centric worldview is a guiding principle behind China’s engagement to the outside world, whilst some are still searching for Africa’s importance to China. I concur with the former, at the same time it is easy to refute the latter, because the recent years have witnessed other evidence of what Segal (1992) has put forward “If Africa did not matter to China, at least during the liberalization period, China knew one day it would matter and now and the future to come it is this period”.

There are a number of skeptics who doubt if China’s economic engagement is pro or will eventually promote economic growth in Africa because China gives preferential financial support to infrastructure construction of facilities such as National Stadium, presidential palaces, a joint venture with the military to build national defense learning institutions that contribute less to development (Davies et all, 2008) or may not be a priority, although some projects such as electricity and information and communication technology projects may significantly work toward progress. In the extractive sector, as postulated by Tull (2006), chances of promoting economic development are also scarce; job markets do not oftentimes favor locals, as an example, ICT equipment and manuals are written in Chinese which can only be handled by Chinese people. In Angola for example, a massive transfer of personnel prevents the capacity building of locals and technology transfer (Tull, 2006), in which some of the Chinese are non-skilled workers.

One evidence can be observed on the share between locals and Chinese that worked in infrastructures constructed and rehabilitated by Chinese companies, to mention the rehabilitation of 540?km of the Benguela railway between Munhango and Luau, which employed 300 Chinese technicians and 300 Angolans (Railway Gazette International, 2010), and in 2010 while the construction of Luanda stadium, 700 Chinese were employed and only 250 Angolans did (The African Report, 2010). Chinese traders that have already settled in African states exacerbate this negative perception because they tend to dump the market with cheap goods undermining legitimate African businesses (Vines, 2007). In Mozambique, the non-mineral that covers 90 percent of exports to China is timber, which has also proven challenging in Sino-Mozambican relations, for a big portion is logged with limited plan to replenish the forest.

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Study Objectives and Methodology

The objective of this paper is to examine a simulation outcome of a game where Mozambique and China play in a scenario Mozambique launches a tender for an infrastructure project financed by the Chinese government, and depict what could be alternative behaviors the two parts had, given their strategies and outcomes. The game theory used in this study will help to illustrate how China uses its financial muscle in form of grants, and loans to advance its economic interest in Africa LDCs in general, and Mozambique in particular; at the same time, explores the best chances Mozambique would have to maximize their gains when engaging with China in the tender process.

Backward Induction is currently the most used technique to find the Nash equilibrium, which we have used in this study. We used backward reasoning in time, from where the problem ends, to define a series of optimal actions. We first considered the final decision to be made, and select options at that time. The outcome of these options then defined the course of action at the second-to-last time of decision. We employed this continuously backward thinking until we have determined the best action for every possible situation Mozambique and China have at every point in time. We use the Backward Induction method on a matrix model - one where the game is presented as cooperative, and on the tree form game, presented in the non-cooperative form.

The Organisation for Economic Cooperation and Development (OECD) defines Official Development Assistance (ODA) as grants and loans given to developing countries by government bodies, with a purpose of economic development and welfare, at concessional financial terms. China defines ODA?in more ambiguous terms; it also includes aid funding, which can be trade concessions or provision of commercial loans to companies that may aid in a country’s development (Davies et al, 2008). Those also include funds disbursed in kind, interest subsidies for interest-free and concessional loans, or provision of technical assistance, and a number of initiatives that do not require funds disbursement (Davies et al., 2008). The not-so-clear definition of Official Development Assistance from China leaves a grey area in terms of whether the terms are commercial or are humanitarian.

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China and Africa long engagement

The establishment of contemporary Sino-African relations dates back to the late 1950s when China entered the first official bilateral trade agreement with Algeria, Egypt, Guinea, Somalia, Morocco, and Sudan; the decade the first large-scale Afro-Asian Conference also known as the?Bandung Conference?took place in Indonesian. In the following decade, China established a diplomatic relationship with Ghana and was supporting several liberation movements for African country's independence with arms, funds, training (Taylor, 2007) against colonial power, and later gradually became the main trading partner in some former British colonies by the ’70s. China as a developing country at that period, and what still claims to be now, provided development assistance such as the construction of the Tanzania-Zambia railway. This mutual benefit found one of its highest moments when the People’s Republic of China (PRC) replaced the Taiwan-based Republic of China (ROC) as a member of the United Nation in 1971 with the help from African countries, which now china backs up African countries in the Security Council as a member.

As literally translated from mandarin “Pin Yun” - the word “Jhong Guo” i.e. China, meaning the center of the world, and during the 70s China was focused on domestic economic development and opened up to the western world, consequently their political interest in Africa diminished. This sweet harvest between china and the west was temporary; China launched a new foreign policy after has been censured and isolated by the west amid the Tiananmen Square Protest of 1989. The new policy revived its political interest in Africa and found support from its old African friends in multilateral forums once again.

At the end of the 70s, Africa only accounted for one percent of China’s trade, however, those figures exponentially changed shortly after the launching of economic and social reforms in China. Recently bilateral trade grew from US$10.6 billion in 2000 to US$160 billion in 2011 (The Guardian UK, 2012), oil being one of the major trading commodities between China and Africa, especially coming from Angola, Sudan, and Nigeria. Trade between China and Africa in 2015 has reached approximately US$300 billion in 2005 (China Daily, 2015). This frenetic search for oil pushed up one-quarter of the world's oil demand (Davies et al, 2008) and china surpassed the US, to become the largest oil importer in the world.

?During the cold war and structural adjustment - the 80s, China has lost its privilege of being a major bilateral development assistance provider; however, currently, its reputation of creating an alternative approach to economic development has a high appeal to African leaders who are failing to distinguish that China’s development model is not distant from the market economy that Segal (1992) points out, with embroiled traditional institutions and features. Indeed China lifted 800 million of its citizens out of poverty, the poverty rate fell from 88percent in 1981 to 6.5percent in 2012 (World Bank, 2016).?China’s per capita income increased fivefold between 1990 and 2000, from US$200 to US$1,000. Between 2000 and 2010, per capita income also rose by the same rate, from US$1,000 to US$5,000 (world bank, 2016), but the development success story cannot certainly be pointed as result from their policies as it was captured by Rawski (2002) “crossing the river stepping on stones spotted on the surface, not even knowing where the other side of the river bank was”; a close interpretation of Deng Xiaoping's phrase “crossing the river groping for the stones”.

?After a prolonged stagnation of western models of development in many countries (Wiarda, 1983), scholars and policymakers in the developing world are excited about the Chinese model of development, but skeptical at the same time, knowing that perhaps each individual country should follow its own path to development (Wiarda, 1983), and not just replicate what is successful elsewhere. It is even more suspicious for several developing countries that went through structural adjustments programs and liberalization of their economies, i.e. privatization, deregulation, reduction of trade barriers, to follow China and march backward on liberalizing their economies. The bottom line is that the hesitation of the Chinese model of development is somewhat lower compared to the one promulgated by western countries.

Over the past three decades, China has evolved a political system that can best be described as “political meritocracy” (Bell, 2015); this political system is accompanied by an economic development policy that does not include corresponding democratic reforms. The China Model is also known as the Beijing Consensus is characterized by a strong state role typical of a developmental state, heavy focus on investment, export-oriented economy, less focus on electoral democracy, emphasis on good governance, gradual and pragmatic reform, selective cultural borrowing of foreign ideas, and gradual reform rather than neo-liberal economic shock therapy as the Washington consensus postulates. Washington consensus embraces the idea of free-market capitalism, which included open trade policies, privatization, and deregulation, and believed that only through this path Third World could spur growth and cure its development problems (Williamson, 1989). Alternatively, the China model differs from traditional socialism mainly in its use of a market system in the economy, it also differs in its commitment to democracy “with Chinese characteristics” and to a new model of the party leadership (Zhang, 2011).

?China’s economic ties and development assistance to Mozambique strengthened around the mid-90s when China has presented itself as an attractive alternative to Western assistance, in the field of non-commercial infrastructure projects (Vines, 2007). China regards its investment in public sector works as goodwill projects, which not only exerts a pull on sympathies of African leaders but also enables china to gain political influence, creating opportunities to commercially or strategically more attractive business in oil and mining sectors (Davies et al, 2008). Knowing they are resource reach, African governments pursue to capitalize the China interest on natural resources, as china will back them up with its veto power in case of aggression – their benefit is mutual.

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China’s assistance and benefits??

Beijing frequently stresses that China’s development assistance is provided with few political conditionalities, and indeed China firmly sticks to the belief of national sovereignty and non-interference in the internal political affairs of its partner. Vines (2007) highlights that Chinese policy is openly non-rigid, in which political stability and internal driven development are prerequisites, along with the noninterventionist dogma that separates business from politics; nevertheless, the terms and practices on assistance sphere remain undisclosed (Vines, 2007). China’s foreign policy fits well to some African leaders’ philosophies of never leave their cabinet to the opposition on democratic elections; constantly “looking aside” on human rights issues, corruption, and other not so appropriate governance practices; raising a question of how beneficial is the noninterference policy for the greater good?

Mozambique’s trade with China does not differ from the patterns other developing countries follow when engaging with China, at least when it comes to imports from China. Basically, Mozambique imports vehicle parts, electrical appliances, iron, and steel articles, construction materials and related machinery, manufactured goods like footwear, bags, electronic products, and textiles (Ilheu, 2010). The main exports are mostly natural resources including coal, wood, oilseeds, cotton, vegetables, and seafood (Ilheu, 2010). Trade between China and Mozambique in 2014 reached US$ 3.62 billion, in which US$1.96 billion represented Chinese exports and US$1.65 billion was Mozambican exports to China (Ministry of Commerce - PRC, 2015).

China’s interest in Africa is undoubtedly focused on energy and mineral resources, also political influence, and diplomatic backup at international multilateral organizations (Tull, 2006). Countries that China mostly engage with have some particularities: Angola, Sudan, Zambia, Zimbabwe, and Nigeria, are oil and minerals rich; South Africa, Ethiopia, and Egypt lead the political environment in the continent (Alex Vines, 2007), and judging from its most important partners, China’s economic interest in Africa don’t vary from those of western states (Tull 2006).

Evidence regarding Chinese interest over the years is vast, so to mention a few: when the U.S. sponsored African Growth and Opportunity Act, Chinese textile companies established themselves in Africa, and when the agreement expired in 2005 Chinese companies relocated their production back to China (Tull, 2006). China announced US$ 60 billion development assistance to Africa in the 2015 Forum on China-Africa Cooperation, these included USD$5 billion in form of grants and free-interest loans, $35 billion for preferential loans, export credits, and concessional loans, $5 billion to the?China-Africa Development Fund,?private equity and venture capital investment arm of the?China Development Bank; $5 billion for?the?Special Loan for the Development of African SMEs, another financial vehicle implemented by the China Development Bank that operates on a commercial basis, and finally, US$10 billion to create and offer the initial capital for the?China-Africa production capacity cooperation fund.

The above mentioned is viewed as funds mainly to finance the market entry of Chinese firms into the African economy (Davies et al, 2008). In South Africa when locals complained about cheap textile imports from china threatening the eradication of local industry, trade unions persuaded the government to recourse to WTO. China intervened claiming that any attempt from the South Africa government to restrict textile imports from China would violate the WTO free trade agreement (IRLN news 29.06.2005). Angola received a loan of US$ 2 billion, in exchange to sell 10.000 barrels per day to China, which also came with 2500 Chinese workers (Tull, 2006), raising the number of Chinese workers in oil related industry in Angola to over 20.000 (Plus News, 2012).

China often uses grants, loans, and debt relief alongside commercial investments and preferential trade access in order to gain access to strategic resources assets or to build stronger political ties. This is in line with what Davies et all (2008) state that development assistance is a tool used to secure China’s political, and economic goals. It is accurate to think that the main driver of China’s interest in Africa is to secure energy and resource assets (Vines, 2007); also non-transparent tendering process in many African countries allow governments to attribute Chinese bidding companies with national benefits in exchange to peripheral development assistance (Davies et al, 2008) in which China uses their leverage. Partly due to peripheral development assistance projects, Chinese companies are preferred bidders in securing contracts (Davies et al, 2008). Thus Beijing government maximizes the opportunity to use this assistance as a tool to support Chinese companies in expanding export markets and business scope overseas, giving the Chinese ODA a distinct advantage in open protectionist doors and bureaucratic fortress.

There are several benefits African countries have gained by cooperating with China (Mozambique not being the exception), trade is the most noticed. This study classifies two types of benefits Mozambique and China harvest from one another: one is the benefit of being a cooperation partner named the Alliance benefit which does not include financial benefits. China’s Alliance benefits comprise exercising their soft power by establishing Confucius institutes, expanding Chinese language and culture, support in International forums (one country one vote system); whilst Mozambique’s alliance benefits is made up of Scholarship to Mozambicans, Chinese Medical missions working in Mozambique, technical cooperation, support in International forums, etc.

?The other benefits we identified are related to financial benefits – these benefits are called surplus benefits, and mostly the country with economic power reaps from the LDC. China’s surplus benefits include the market for Chinese goods, natural resource exploration, labor market for Chinese employees, and infrastructure development contracts. Mozambique surplus benefits are Grants and soft loans granted by China, the market for Mozambican goods. Mozambique is a country that a large portion of its national budget is supported by the international community; the country does not have the luxury to turn down aid (yet it happened from Taiwan), so the prerogative lies on the donor country.

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Theoretical framework

?Game theory

Game theory is perceived as an abstract inquiry into the concepts used in social reasoning when dealing with situations of conflict (Rubinstein, 1991). Game theoretical modeling constitutes one type of racial choice theory with goal-directed behavior, with individuals opting for means to best gain a set of ends, and targets are coupled to outcomes through actions or choices (Gates and Humes, 1997). The distinctive feature of the game we are using is the diplomatic relations between China and Mozambique that raise interdependence amongst themselves, providing an appropriate tool to analyze behavioral outcomes from the two countries. Mozambique’s utility depends not only on its own activities but also on the actions of China - this awareness is the one that gives rise to the problem of game theory.

?The essence of a choice in game theory lays in the rationality of a player, which has arrays of preferences over a set of outcomes, and in turn, selects actions that satisfy these preferences. This rationality comes often with the assumption that players of a game possess common knowledge. It is believed everyone is aware that everybody knows it; everybody knows that everyone is aware that everybody knows something, continuing endlessly. We used game theory to understand the strategic interaction between China and Mozambique, to deepen our understanding of the two players. The employment of this model clarifies the role of beliefs, preferences, and incomplete information available, to explore how external factors are causally intertwined with the strategic results.

Game theory rests on a deductive analysis of the strategies that produce solutions for the game. This solution is the equilibrium and is in fact the sought objective when studying a game. The equilibrium explicit here is the Nash equilibrium, which is a situation in which no country has an incentive to unilaterally alter its own strategy. In other words, the objective sought in a game are notions of equilibrium that model the player’s behavior in a steady-state, which in other words it means searching for patterns of behavior with the property that if every country knows every other country’s behavior, it has no reason to change its own. The Nash equilibrium is the main goal in this game we are studying; when the equilibrium is attained it has the property of being simultaneously individually rational and collectively irrational (Gates and Humes, 1997). At each individual relation between China and Mozambique, neither country can by its own actions, makes itself better off than at the Nash equilibrium.

Backward induction is currently the most used technique to find the Nash equilibrium. How does it work? It is known that Taiwan and China are in a diplomatic battle for more than 50 years in the issue of one China, and this policy pushes other countries to recognize or not Taiwan as a country. Let us say Taiwan has investment intentions in a country that has diplomatic relations with China. It seems clear that Taiwan will enter as an investor and China will subsequently comply. Taiwan can reason that if it enters, then China will comply, because doing so is better for China than fighting Taiwan with diplomatic arms through the host country, which will frustrate China, knowing that the host country favors investment and does not care from where it comes from. Given that China will respond to entry with compliance, in this way Taiwan is better off entering. This line of argument is called backward induction. Whenever each country has to move, it deduces for each of its possible actions, the actions that itself as a country and the other country will subsequently rationally take and chooses the action that yields the end it most prefers.

To sharpen the logic of game theory firstly, one should be familiar with a primitive concept named strategy, which encompasses not only the country’s plan but also its opponents’ beliefs in the events it does not follow that plan (Rubinstien, 1982). The game with imperfect information, as well as the strategic form of the extensive game, as suggested by Luce and Raiffia in 1957, cited by McCarty and Meirowitz (2007) encompasses the following:

·?Players/actors – Set of players or countries in the game

·?Actions/strategies – Player’s set of actions is its set of strategies.

·?Preferences –Payoff to the terminal history generated by that action profile (payoffs are used to evaluate the outcome of the game).

Non-zero-sum games (unlike zero-sum games where the sum of all players’ utility is always zero) have essentials of both conflict and cooperation. It is in the player’s mutual interest to reach an outcome where the summation of benefits is relatively high; nevertheless, the player’s interests diverge over individual shares in the total amount. Similarly, binding agreements are hardly enforced across nations, suggesting the appropriate game-theoretical model for international trade is the non-cooperative game. China has oftentimes incentives to conceal what they are going to do; publicly displaying the amount of aid is one of them, justified by saying it will only create jealousy and protests among aid recipient nations if they find out others, are receiving more (Davies et al, 2008).

This study makes use of a decision model called game theory, to analyze several behaviors and their outcome in the process of China's engagement with Mozambique, with no attempt to predict behavior and outcome, since the scope of the theory does not allow us to do so. In 1984, New Zealand denied access to United States ships and submarines capable of carrying nuclear arms to enter its ports. The event known as the decline of the ANZUS Treaty has been a research case, it shows the preferences and outcomes of the United States and New Zealand when the former was seeking access to enter New Zealand ports not confirming and not denying they were carrying nuclear arms (Gates and Humes, 1997).?ANZUS is the 1951 collective security agreement that binds Australia, New Zealand, and the United States. We employed the same set of analyses to view the engagement between Mozambique and China.?Give and take is part of compromise relationships, either interpersonal or interstate; and that includes material or non-material assets, to some time obtain not tangible benefits. Predicting future behavior is of great importance; likewise, it is to analyze past behavior and benefit from the patterns it took place.

The study presents two models; the first depicts China and Mozambique interaction in the tendering process, both countries possessing imperfect information on one another, and both acting simultaneously. The second model portrays a scenario whereby the two countries have complete information on one another, and they act in sequence. The first model is presented in a matrix format as the traditional prison dilemma game is modeled, whilst the second is in the extensive tree form game, where the sequencing?of the country’s possible moves is known. The tree form models reveal the choices at every decision point, information each country has about the other country's moves when it makes a decision and its payoffs for all possible game outcomes.

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The models

To model China’s engagement with Africa as a cooperative game would sound appropriate since the actors, can before acting, costless make arrangements that are binding and enforceable; however, evidence in Mozambique shows these beforehand enforced agreements, end up with a huge price tag to Mozambique, especially when jeopardizes development initiatives already on their halfway (Pehnelt, 2007).

Chinese deals with an African country leave the other player in a position as it is confronting the game for the first time; the country has no idea what actions China will take. As an example, China provides a loan to Mozambique and promises some sort of softness of the burden of the debt through partial or total forgiveness. These strategies leave China with enormous space of maneuver to advance its interest; since every single time Mozambique has got a tender process, also has in the back of the mind the promise that the debt with China could be softened, but does not know in which period or at which amount. Mozambique tries its best to maximize the least benefit it has, and the recommendation given is that it should associate with its actions, the worst outcome it will receive, as China’s actions vary, then choose the action for which this worst outcome is best, i.e. maxminimization.

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Model 1

This game has an underlying assumption that China does not take into account how its actions at this point in time might affect its future interactions with Mozambique, as well as other African states. The model we depict in figure 1 is of imperfect information because China as a player in this game does not know the moves of the previous player, that is, Mozambique. The same is also applied to Mozambique in relation to China; their strategies are revealed simultaneously.

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Mozambique Agree (A)?China Agree (A)? Outcome is B, b - c?

Mozambique Agree (A)?China Punishes (P) Outcome is b – p, - c – d

Mozambique Disagree (D) China Agree (A) Outcome is 0, b

Mozambique Disagree (D) China Punishes (P) Outcome is -p, -d?

The scenario above reflects the:?Matrix game involving China and Mozambique with imperfect information.

The payoffs are ordered in the following way:

For Mozambique: B > b – c > - d > - c – d

For China: b > b – p > 0 > – p

When China is dealing with Mozambique, we notice that each of them have two strategies. Mozambique can either agree (A) the terms proposed by China, or disagree (D). China options are to agree (A) or punish (P) Mozambique.

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Mozambique payoff

Mozambique's unequivocal unsurpassed outcome occurs when it enjoys the benefits of being cooperative to China without any costs; that is continue receiving Chinese support in form of grants, interest-free loans, concessional loans, however not being obliged to award Chinese companies with major infrastructure projects, concede mining licenses, etc. To this payoff, we will attribute the later B.

The second best preferential outcome to Mozambique is when it consents to the Chinese terms. Mozambique still receives benefits from Chinese aid through the alliance, while allowing China to reap the surplus benefits. This payoff is denoted by b-c.

The next worse payoff is observed when Mozambique disagree with the strings attached to the Chinese assistance, and the Chinese punish Mozambique by tightening the concessional loans, canceling grants, cancels scholarship to Mozambican students, envoys of Chinese doctors to Mozambique, etc. This payoff is represented by –b.

The least desirable scenario to Mozambique is the case where Mozambique complies with all demands from China but China still punishes Mozambique. The payoff for this scenario is - c - d. Nevertheless, this is the inability of Game theoretical form sometimes to exclude nonsensical strategy combinations.

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China payoff

The most preferred outcome for china comes from the agreement between both countries. China receives a payoff of b.

China considers its second-best preferred outcome when Mozambique gives China surplus benefits, but China still punishes Mozambique, canceling its Development assistance, etc. The payoff to china, in this case, is b-p.

The next most desired outcome arises when Mozambique disagrees, turning down the two types of benefits, and China agrees to the rebellion; giving a payoff of 0.

The least desired outcome to China arises when it chooses to punish Mozambique for its choice of disagreeing with China. China loses the benefits would have from the strings attached to aid i.e. the surplus benefits, as well as incur the costs of punishing Mozambique i.e. losing alliance benefits, which would be: no political back up in international forums, promotion of Chinese bad reputation among other African states, etc. For this scenario, the payoff is represented by –p.?

Both Mozambique and China have dominant strategies because both of them have a strategy that yields the country its highest payoff given the strategy choice of the other country. Mozambique’s dominant strategy results in the outcome where they restrict surplus benefits, and China not retaliating against this action. This outcome gives the Nash equilibrium of the game. Neither country has an incentive to unilaterally change its strategy from (Mozambique Disagrees, China?Agrees). Neither would do better off by unilaterally changing to agree (A) in the case of Mozambique and punish (P) in the case of china.

This model has its own limitations because the Nash equilibrium overlooks the sequential structure of an extensive game; it takes into consideration strategies as choices made once and for all before the interaction begins. As a result, the steady-state to which Nash equilibrium corresponds may not be robust, for that purpose we analyze bellow extensive form game involving China and Mozambique, both with perfect information.

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Model 2

Our game theoretical framework would be simplistic if we have stopped the analysis on model one, hence we will present the three ways this game can be viewed:

Firstly, if China chooses to punish Mozambique for its deviation, would lead us to believe China was reacting to actions following Mozambique’s action. There are no clues of expectations that China would punish Mozambique if Mozambique did not diverge. Actors in this new scenario are not acting simultaneously, rather they are acting sequentially.

The second factor may rise with the misspecification of payoffs; if China unambiguously took into account the calculations of other African countries in its decision, the payoffs of this game would differ. China may believe that punishing Mozambique's deviation would deter other nations from acting similarly. Therefore the cost of punishing this rebellion may not be as was thought in the previous model.

The third aspect is that it could be taken into account the actions of other countries or repeated play between China and Mozambique.

The diagram below allows us to observe the perfect information diagram representation of the extensive game in a tree form.

Mozambique Agree (A) China Agree (A) Outcome is b – c, b

Mozambique Agrees (A) China Punishes (P) ?Outcome is - c – d, b – p

Mozambique Disagree (D) China Agree (A) Outcome is B, 0

Mozambique Disagree (D) China Punishes (P) Outcome is - d, - p

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The above scenario shows the extensive form game involving China and Mozambique with perfect information

The payoffs of the game are as follows:

Mozambique: B > b – c > - d > - c – d

China: b > b – p > 0 > - p

The second model depicted in figure 2 is one of perfect information; the payoffs are similar to the ones in model one. ?

Let us reason backward: Mozambique decides on its preferences taking into account what China would do with its succeeding move, and Mozambique will have studied the payoff China would have in each of its sub-games and rationally chose whether to agree or punish. If China had to choose between agreeing and punish after Mozambique chose to agree, it would choose to agree, resulting in a payoff of b-c for Mozambique. If Mozambique deviates, China will still respond with an agreed choice leading to a payoff of b to Mozambique. Mozambique would choose to rebel given the expected reaction of China since b is greater than b-p.

Payoffs of Nash equilibrium are already identified; however, the equilibrium of the game is yet to be found. China’s strategy consists of two options, expressing its action after Mozambique has chosen either disagree or agree. Any of the strategies above surrender these equilibriums outcomes:

?·?{Mozambique Disagrees, China Agrees with the disagreement – Mozambique Agrees, China Agrees}.

·?{Mozambique Disagree, China Punishes – Mozambique Agrees, China Agrees}.

·?{Mozambique Agrees, China Agrees – Mozambique Disagrees, China Punishes}.

The first equilibrium is observed when Mozambique chooses to disagree, and China agrees with the choice made by Mozambique; even if Mozambique had chosen otherwise China would also stick to agree.

The second equilibrium stipulates that Mozambique would disagree and China would punish Mozambique for doing so, and China would agree with Mozambique if Mozambique had chosen to agree.?

In the third equilibrium, China has committed to sanctioning Mozambique for disagreeing. But we know that when Mozambique deviates China will be better off agreeing. China has no incentive to unilaterally change its strategy if Mozambique chooses to disagree, not even Mozambique would be made better off if opting for such, unilaterally. This strategic combination is Nash equilibrium, nevertheless, it does not sound reasonable.

Sub-game perfect equilibrium is the refinement technique of the Nash equilibrium that will distinguish the multitude between the three equilibriums above. According to Gates and Humes (1997) subgame is defined as a subset of a complete tree that begins with an information set of all players and ends with associated payoffs. A sub-game perfect equilibrium of a game is Nash equilibrium for all sub-games (Gates and Humes, 1997).

The sub-game that results when Mozambique disagrees leaves China with a dominant strategy; which is to agree to this disagreement. This outcome would lead to a payoff of b-c to Mozambique. Mozambique's rebellious behavior would on the other hand lead china to punish; that would yield a payoff of -d. Mozambique in that case would choose to agree since it knows China would respond with agree. The Nash equilibrium that represents this behavior is the third equilibrium, confirming that this is not a sub-game perfect equilibrium.?

{Mozambique Disagree, China Punishes – Mozambique Agrees, China Agrees} is not a sub-game of perfect equilibrium. If the sub-game was reached resulting from Mozambique consent, China is made worse off by punishing than agreeing.

Finally, the first equilibrium {Mozambique Disagree, China Agrees – Mozambique Agree, China Agrees} is the only subgame perfect equilibrium; given that “agree” must be the equilibrium strategy for each sub-game of the same game for China. In both sub-games, China receives a better payoff from playing agree than from punishing. This strategy combination leads us to conclude where the sub-game perfect equilibrium rests, representing equilibrium for each sub-game of the game since neither country would unilaterally alter its own strategies.

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Repeated game

We have the prerogative to model this game as a repeated game, since China plays with Mozambique repeatedly when the new tender is launched, or China plays all African states that have diplomatic relations with it, sequentially in similar games. When the number of states facing China is finite, surprisingly China will maximize the payoff by agreeing, because it gets a higher payoff by agreeing than punishing a rebellion. Acting likewise prevents China from being seen as tough at the beginning of the repeated game, which is then used to persuade remaining partners to opt to agree instead of punishing.

If China is facing all other African states sequentially, allowing the same payoff to holding in the final period as in the 1st, it is witnessed the last country dealing with China maximizes its payoffs by disagreeing; China’s subsequent resolution is to play willingly. China has no incentive to punish the last country knowing that it is the last stage of the game; it no longer needs to worry about its reputation. The last African country having this expectation will decide to deviate in view of the fact that punishment is unlikely. China would also not sanction the deviation of the second from the last country, since it knows that its move will have no effect on the future actions of the last country; so the second country from last deviates too. Working backward along the tree illustrates that the same decisions hold for all periods of play. The assumption that prevails is that what is rational in the last period is rational for all the periods.?

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Conclusion

Engagement between China and Mozambique reveals an increasing tendency to commercial one rather than assistance driven, future relations between the two may be shaped more and more by shifts in comparative advantages and changes in global supply chains. I believe the Mozambique government is not na?ve to take china’s rhetoric of south-south solidarity or extended the hand of the largest developing country as it is given. Perhaps by now, they have learned the reality that China is not less self-serving than any other nation that uses development assistance as a tool to pursue its commercial and other interests.

China as a player in this game knows that African countries are resisting the strategy of locking in supplies through long-term contracts with China. Along this period of engagement, China has well-read about politics in Africa, and the dogma of noninterference has turned to a slogan that has not yet found its formal replacement. In several African countries, deviations are common practices, as examples, we observed that In 2006 “Total” won operation rights for an oil block in Angola, outbidding China (Vines, 2007); in 2007 Sinopec was stopped from investing US$ 3.5 billion in an oil refinery by the state-owned petrol company Sonangol (Vines, 2007); a Sonangol official stated, “we cannot construct a refinery just to make products for China.” In Nigeria, rebel groups at the Niger delta have stated that Chinese petrol companies stand in their line of fire and not much could be done by the Lagos government to ensure total security of Chinese investments.

This study reveals public tenders that already took place and were conducted in a behavior pattern that raises curiosity; why not otherwise? Mozambique indeed had room to improve its bargaining power during interstate relations when receiving development assistance from China and asked in return to “grant favors. Mozambique in all its power and options tries to maximize the smallest value it has - we recommend that it should associate with its actions, the most awful outcome it will receive, as China’s actions vary, then opt to act in the direction of this worst outcome is best, i.e. maximizing the minimum.

Game theory has the strength to analyze past behavior and past outcomes, and by no means attempt to predict behavior, and future outcomes in the process of China's engagement with Mozambique. In this case, when both countries simultaneously reveal their strategies as model one shows, both will be better off if Mozambique disagrees and China consents with the decision taken by Mozambique. The extensive form model only strong equilibrium is when China responds with agreeing twice, no matter the decision taken by Mozambique. This game shows that Mozambique maximizes its utility by deviating. When it comes to playing the repeated game, China chooses to agree whilst Mozambique chooses to rebel. Repetition then does not assure reputation building, and it does not change the strategies that are being played in the constituent games of the repeated game.

We strongly believe that during past public tendering processes in Mozambique, to a project financed by China, granting of surplus benefits to China was not imperative for Mozambique to get its surplus benefit from these deals; China would have always followed its plan to deliver development assistance to Mozambique in exchange to political backup internationally. The Chinese have the assistance, Mozambique has natural resources, they benefit from the alliance, so leverage for negotiation is not in total disequilibrium between them.

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