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How Sequential Games Can Be Solved By Backward Induction Economics Essay

Game theory has been widely acknowledged as an important tool in many fields. Its attraction is prominent and its importance is explained by Robert Aumann and Oliver Hart in the following way:
“Game theory may be viewed as a sort of umbrella or ‘unified field’ theory for the rational side of social science…it develops methodologies that apply in principle to all interactive situation” (Aumann and Hart, 1992).
It is not difficult to understand the enthusiasm towards theories of games developed from various game types and game-solution analyses. This essay will focus on a particular sort of games, namely, sequential game and the solving method of backward induction.
Sequential games are those in which players take turns moving or make moves at different times. This means that players moving later in the game have additional information about the course of others’ actions. This also means that players who move first can often influence the game. Each player makes decisions conditional on what other players have done.
Consider a sequential game where there is an incumbent (Macrosoft) and an entrant (Microcorp). Macrosoft decides on a marketing strategy for its new software game. It can choose either a slick campaign or a simple campaign. Macrsoft faces potential competition with “legal clones” of its game from Microcorp. It moves first and Microcorp observes its action. Regardless of what Macrosoft chooses, Microcorp then has two options: entering the market, or staying out of the market. The two firms’ payoffs are displayed in table 1:
Table 1: The payoffs for software game
Macrosoft’s ad campaign Slick Simple
(-$250, $380)
($100, $400)
($0, $430)
($0, $800)
Payoff (in $1,000s)
Microcorp’s entry decision Stay out
Figure 1: The game tree for software game
($380,000, -$250,000)
($430,000, $0)
($400,000, $100,000)
($800,000, $0)
Microcorp’s entry decisionIn order to establish the set of strategies for either firm, it is important to identify clearly not only the players’ moves but also the order in which these moves are chosen and the information available to players when they make decisions. An effective way of organizing this information is by using a game tree. A game tree will depict a path of play in addition to the players, actions, outcomes and payoffs. The game tree for the software game, thus, appears as follow:
(Macrosoft, Microcorp)
stay out
stay out
Macrosoft has two strategies: choose slick or choose simple. Microcorp, however, has four strategies since there are two nodes to consider, b and c, and two possible actions at each node, enter or stay out. These strategies are:
Choose to enter regardless of which campaign Macrosoft chooses (enter, enter).
Choose to enter if Macrosoft chooses slick, otherwise choose to stay out (enter, stay out).
Choose to stay out if Macrosoft chooses simple and vice versa (stay out, enter).
Choose to stay out in both cases when Macrosoft chooses slick or simple (stay out, stay out).
Table 2 shows the strategic form of the game:
Table 2: Strategic form of the software game
Macrosoft slick simple
(- $250, $380)
($100*,$400*) (- $250, $380)
($0, $800*)
($0*, $430*) ($100*, $400)
($0*, $430)
($0, $800*)
(Payoffs in $1,000s)
(enter, enter)
Microcorp (enter, stay out)
(stay out, enter)
(stay out, stay out)
There are two pure strategy Nash equilibria to this game which are {slick, (stay out, enter)} and {simple, (enter, enter)}. These are the optimal outcomes of the game as no player would wish to deviate from his chosen strategy given the other’s choice. However, the question is which of these equilibria is more reasonable. The best outcome can be found through a procedure called backward induction. This process assumes that players act rationally at each node. This means that they will act in their own best interests. Knowing this, a player working to solve a game tree can confidently remove suboptimal actions to his rivals until only the most likely path remains. By doing this, an opponent’s possible moves from the initial node to the payoff can be depicted; allowing the player to devise a strategy for each of those probable moves and eventually finds the equilibrium. The software game can thus be solved using this method of reasoning:
Figure 2: Game tree of the software game
($380,000, -$250,000)
($430,000, $0): A
($400,000, $100,000): B
($800,000, $0)
(Macrosoft, Microcorp)
stay out
stay out
At node b, entering the market gives Microcorp a loss of $250,000, while staying out gives it a zero-payoff. Therefore, Microcorp would rationally choose to stay out. Similarly, the possibility that Microcorp will stay out at node c can be eliminated since its payoff for enter is higher than that for stay out. Therefore, of the four strategies available to Microcorp, backward reasoning indicates that its only optimal strategy is to choose enter at node b and stay out node c.
By pruning the non-optimal moves from Microcorp’s decision nodes, Macrosoft’s choices now look as follows:
Figure 3: The new game tree of software game
(Marcrosoft, Microcorp)
($430,000, $0)
($400,000, $100,000)
Macrosoft’s optimal strategy is obvious-choosing slick as this yields a payoff of $430,000 instead of $400,000 from adopting simple campaign. Therefore, by looking ahead and taking its opponent’s entry decision into account Macrosoft can avoid making a mistake of $30,000. Consequently, the strategy profile – {slick, (stay out, enter)} is called the sub-game perfect equilibrium (SPNE); it is also a Nash equilibrium (NE) of the game. Since backward induction holds that players will play their optimal action at each decision node, the resulting strategies will thus lead to a NE. However, it is important to note that a NE is not always a SPNE. In particular, the other NE of the software game – {simple, (enter, enter)} is not a SPNE. This is because it violates the rules of backward induction which assumes that Microcorp would never choose enter at node b.
On the other hand, Microcorp may want to arrive at the NE – {simple, (enter, enter)}. Since Microcorp prefers outcome B of ($400,000, $100,000) to outcome A ($430,000, $0) (figure 2), but it cannot get there unless Macrocorp adopts the simple strategy. Microcorp may, therefore, threaten to always choose enter. If Macrosoft were to believe the threat, it would believe that it would earn only $380,000 by choosing slick and $400,000 by choosing simple. However, Microcorp’s threat to enter is not credible and Macrosoft knows that once it chooses slick, Microcorp will choose stay out regardless of its commitment as stay out is simply its best move at node b. In this case, Macrosoft has the advantage by becoming the first mover and can therefore induce its rival to stay out of the market. While Microcorp suffers the disadvantages of a second mover unless it could credibly commit to always adopt the strategy (enter, enter).
Figure 3: Centipede game
I II I Payoffs to (I, II)
(8, 19)
(0, 0) (-1, 10) (9, 9)
Effective as it is, backward induction has revealed some limitations. One of these has been disclosed in the well-known centipede game. Figure 3 illustrates the game in which two players alternate in choosing between stopping and continuing the game. If a player stops the game, each will receive a zero payoff at that point. But if a player chooses to continue, he is fined £1 while the other is rewarded with £10. The game continues until one of the players stops or both reach the final payoffs of £8 and £19 respectively.
Stop St
Backward induction suggests that player I should stops the game at the very first move and gets a zero payoff. Suppose that the game has reached the final decision node where player I makes the last move. At this point, player I has to choose between Stop and Go. The only rational choice here is to stop and pocket £9 rather than deciding to continue and receiving a less payoff of £8. This means that at the previous decision node, player II will choose to stop the game, taking into account that player I, who is rational, responds by choosing Stop on the next move. This in turn implies that player I, at the first decision node, now effectively considers between Stop and receiving a zero payoff or Go and losing £1 when player II rationally stops the game at the succeeding node. Player I, therefore, should stop the game immediately. This outcome is the unique SPNE. However, it would be better if player I continues the game until he can get £9 by stopping at the penultimate node, or, as a second best, until the final round where he gets £8. The question is that if player I, in practice, really chooses to stop the game at the first decision node.
Experimental evidence by Kelvey and Palfrey (1992) and El-Gamul et al. (1993) shows that the logic of backward reasoning is seldom followed by decision-makers. In particular, in a four-legged centipede game experimented by Kelvey and Palfrey, only 7% of players stopped the game at the very first move with a maximum payoff of $6.40 at its head. When the payoff was increased to $25.60, 15% chose Stop at the first decision node. Even at the final node, only 69% of players (in the high-payoff centipede) and 85% of players (in the low-payoff centipede) chose to end the game.
In conclusion, the rationale of applying backward induction seems strong since it can help narrow the number of possible Nash equilibria. By looking forward and reasoning backward, each player can predict what other players will do at subsequent stages of the game. Therefore, he can judge the consequences of his possible moves, assuming that players are rational, and therefore; decides on the optimal move. However, backward induction exhibits some limitations as discussed in the centipede game where the argument rests on the prediction of behaviour off the equilibrium path. This arguably leads to the challenge of rationality assumption of game theory which needs further justification.
Word count: 1499

Outward Foreign Direct Investment By Malaysian Transnation Companies Economics Essay

This paper tries to understand trends, patterns and determinants of outward foreign direct investment (OFDI) by Malaysian transnational companies. It shows that Malaysian OFDI had taken a massive leap since 1993 and the number of Malaysian transnational companies making investments abroad since the 1990s has increased radically.
The factors that influences the outflow of FDI is evaluated into considerations. The OFDI is focused mainly in services industry (finance, banking, insurance and tourism) and natural resources (oil and gas) with also manufacturing sector. This also includes the emergence of offshore financial centres and developed countries as the most important host region for trans-border activity although investments in developing countries especially within ASEAN have shown tremendous growth. The key drivers of OFDI have been to increase efficiency, to access resources and to access markets.
Keywords: Outward FDI, Malaysia, Economic Growth, Transnational MNC
Globalization has attracted increasing attention among researchers in international business. In an international business context globalization finds its roots in the increasing trade and investment flow between countries. Trade growth continuously exceeded the growth in both world commodity output and world Gross domestic product (GDP).
The World Investment Report (WIR2006) noted that the stock of outward foreign direct investment (OFDI) from transition and developing economies in 2005 reached USD1.4 trillion, up from USD335 billion 10 years ago.
As an emerging market, Asia is one of the regions in the world in which FDI activities are prevalent. Some developing countries especially in Asia also emerged as important sources of FDI. Malaysia is among the developing countries that involves in OFDI. It also stated that TNCs from Malaysia are extending their global reach [WIR2006: pp. 103]. More impressive is that Malaysia’s inward and outward flows are converging.
South, East and South-East Asia continued to register strong growth in FDI inflows in 2008 (17%), to reach a new high of $298 billion. Inflows into the major economies in the region varied significantly; they surged in China, India and the Republic of Korea; continued to grow in Hong Kong (China); dropped slightly in Malaysia and Thailand.
FDI outflows from other major economies (Malaysia, Singapore) in the region generally slowed down in early 2009, as the crisis has largely reduced the ability and motivation of many TNCs from these economies to invest abroad [WIR 2009: pp:24].
Outward FDI of Malaysia was nearly non-existent prior to 1970s. Nonetheless, recently Malaysia has not only been able to sustain FDI inflows position, but also emerged as the fifth largest investor among the developing economies in Asia region (UNTACD, 2005).Malaysian companies have been investing abroad since the mid-1970s.
However, Malaysian OFDI became significant in the early 1990s with the changes in the global economic order that came about with end of the Cold War. Internationally, the completion of the GATT/WTO Uruguay Round that began in 1986 and completed in1994, regionally, the formation of the ASEAN Free Trade Area (AFTA) in 1992 and domestically, the economic liberalization processes beginning in the mid 1980s were sign of the changing global economic order that prompted OFDI. Recession has strictly affected the OFDI from transnational MNC’s from Singapore and Malaysia during the last financial year.
Research Question
“Foreign direct investment re¬‚ects the objective of obtaining a lasting interest by a resident entity in one economy (”direct investor”) in an entity resident in an economy other than that of the investor (”direct investment enterprise”).
The lasting interest implies the existence of a long-term relationship between the direct investor and the enterprise and a signi¬cant degree of in¬‚uence on the management of the enterprise. Direct investment involves both the initial transaction between the two entities and all subsequent capital transactions between them and among affiliated enterprises, both incorporated and unincorporated” (OECD, 1999).
The study is conducted to find the outward foreign investment by Malaysian transnational firm abroad. The research paper tries to find the factor that influence outward flow of FDI from developing nations. The paper tries to evaluate what factor triggers the outward flow of FDI, the factor that triggers the outflow of FDI can be critically evaluated so that it assist to a improved perspective of the theme.
The paper also tries to understand how trade promotes OFDI. Transnational companies do trade with a number of countries thereby enhancing the opportunity for investment to be made abroad. The paper try to discover does trade actually trigger an outflow of FDI from a country. OFDI helps in the flow of knowledge and know-how between the member countries, the research tries to estimate to what extend does the knowledge transfer happens and how does it help the home country to achieve a better state. Finally the paper tries to understand the relationship between the OFDI and economic growth. The research tries to understand the character and factor that influence the possible economic growth through OFDI.
Theoretical Rationale
There are a number of relevant theories on the growth and motivation of FDI explaining the outward FDI activities. One of the most popular theories is the OLI Eclectic Paradigms (Dunning, 1980) Ownership, Internalization and Locational. Firms make investment abroad due to certain ownership (O) advantages obtained by the firms.
These advantages enable the firms to utilize through a process of internalization (I) in countries that offer the essential locational (L) advantages. International Production Theory (Dunning, 1980 and Fayer weather, 1982) highlight on the affinity of a firm to open foreign production, depending on the particular lure of its home compared with resource implications and advantages of locating in another country.
Another popular theory regarding the FDI is associated to the income level of a country. Higher income of a country will leave vital proposition towards structural changes on the economy of the country. As pointed out by Chenery et al. (1986), firms are able to gain competitive advantage in term of economy of scale in the production despite adoption of new technologies.
Eventually, firms are able to acquire ownership advantages which become the driving force for establishing foreign production (Grubaugh, 1987). Meanwhile, higher degree openness is linked with greater level of outward FDI. Kogut (1983) stressed that the adoption of export-oriented policy eventually enable firms to acquire knowledge on the foreign market as well as skills in running operations abroad.
Eventually, the firms will decide to shift their strategy from exporting to make investment abroad.
On the other hand, they also revealed that exchange rate is an influential factor in affecting the outward FDI. Meanwhile, low interest rate in the home country relatively will lead to higher tendency of outward FDI (Prugel, 1987).
Investment made abroad require sound financial support and capital abundance in term of low interest rate enable firms to access to capital market. Therefore, firms can obtain necessary funding to finance their abroad investment. In related to that, exchange rate also has significant impacts towards the outward FDI.
Implication for Organisation
Since the amount of study prepared on this particular subject matter is fewer compared to FDI to the nation, the study would assist everybody to recognize the factor that influence the flow of outward FDI between two or more nation.
The amount of literature available on FDI to a country is comparative extra than the OFDI. The study would trigger more interest on the subject matter thereby increasing the number of study conducted on that subject matter. The paper tries to evaluate the difference between the export and outward foreign direct investment. The study would help companies to recognize the better option between investment and export.
Literature Review
Over the past two decades, FDI flows have grown at remarkable rates, with outflows averaging over 28 percent per annum from 1991 to 2000 (UNCTAD, 2004), greatly outpacing growth of exports.
Foreign Direct Investment (FDI) is always considered to be beneficial for the host countries economic growth, lot of studies on the impact of FDI on the economic growth and productivity domestic firm have also being undertaken. FDI which assist in the transfer of technology and knowledge help the firms to undertake their business actions in an improved approach.
Studies for developed home economies focus on a wide range of potential economic impacts of OFDI including impacts on domestic employment, wages, expenditures on research and development and innovation, trade flows and tax revenues, among others (Kokko, 2006).When we consider the factor that triggers the flow of Outward FDI economic condition prevailing in the nation play a vital role for the decision (Sanjaya Lall, 1997).
The growth of the Per Capita GNP also is an important characteristic that TNC’s consider while making these decision (J P Agarwal, 1980). The economic growth of the nation is the main character that attracts the companies to make investments in those particular countries.
As suggested above, the potential economic impacts of OFDI can best be appreciated in the context of how OFDI contributes to a nation’s international economic integration (Daniel Shapiro, Steven Globeman, 2006). It is important to note, however, that while there is a strong theoretical basis for expecting that OFDI will promote international trade, the causal linkage between the two is difficult to identify empirically (Duran and Ubeda, 2005).
Host countries policies and strategies of the transitional corporation also influence the decision of outward FDI (Sanjaya Lall, 1997). Another major aspect that influence OFDI is the government policies, if the policies favour the FDI then the transnational companies will have invest in the nation.
Malaysia being the one of the front runner among the South East Asian Countries had significant economic prosperity from the early 90’s onwards with an average economic growth of 9 % (Malaysian Budget, 2001). This favourable economic growth had assisted Malaysian transnational companies to make investment abroad.
The outward FDI from the country was growing on a stable manner; only during 1998 and 2001 it had a sudden deterioration due to the financial crisis that has prevailing in the Asian economic market (UNCTAD). The Financial crisis of 1997 had a significant impact on the OFDI made by the TNC’s of Malaysia; there were a few firms that made a steady progress investing abroad, firms such as PETRONAS, YTL Corporation (UNCTAD 2006).
According to the United Nation Conference on Trade and Development (UNCTAD) report of 2006 the OFDI has seen tremendous increase over the last 15 years increasing to almost 34% by the end of 2005. FDI outflows from South, East, and South-East Asia rose by 7% to US$186 billion in 2008. The region´s outward FDI to developed countries has been growing as part of efforts by Asian firms to acquire strategic assets abroad.
However, due to the negative impact of the global crisis on Asian TNCs, FDI outflows from the region will inevitably slow in 2009, although to a lesser degree than in many other parts of the world (WIR, 2009). During 2009 GDP Malaysian economy was -3%, though a decline in the economy means the country is under-performing the Malaysian economy was considerably doing better off than they predicted GDP of -5% ( Malaysian Budget , 2010).
The recession may have affected the world economy drastically but when we consider the WIR 2009 report there was a 7% increase in OFDI made from these regions. So when we take into consideration whether OFDI help in economic prosperity of a nation, we can conclude that it certainly does helping in improving the environment of the economy.
The research is carried out to discover the one central aspect
“Does OFDI really lead to the economic prosperity of the nation?”
Data Source
The paper tries to comprehend outward foreign direct investment between two or more nation. Since the scale of subject matter is pretty enormous collecting first hand information making use of primary data collection method to evaluate the subject is a time consuming process. So the data relevant for the completion of the paper will be taken from secondary sources such as journal, books, and website and academic papers.
The information concerning to the paper can be accessed from official sources, this make the more accurate and precise. Secondary source of data is a better way to conduct to the study, since the element of time involved and also due to that fact that it would help to improve on the finding or to contradict any finding regarding the topic.
Academic papers and journals would help to understand the subject matter in a better point of view and so thereby helping to make the paper more accurate and informatics.
Resign Design
While taking into considering the number of available literature on the subject matter, it would be better off to include case studies done on TNC’s from Malaysia and other Asean Countries to give an idea about the present condition of OFDI from the region.
Literature from official source will be taken into consideration as they depict a true and fair view regarding the subject matter, other reliable sources such as the United Nations Conference on Trade and Development (UNCTAD) report and the World Investment Report (United Nations) give a better perspective of the prevailing condition.
Approval from the regulatory body and the government will be taken for the successful completion of the research. Recession of 2009 which played a imperative task in the by and large actions of the transnational companies will be taken into deliberation and will assist us to evaluate the critical factor the influence investing abroad.
The research undertaken by me involves use of secondary data sources as case studies, books, journals, websites and newspaper information regarding the pattern and factor that influence the flow of foreign direct investment from a nation. This method of collection information for the purpose of study is termed as Realist Research (Fisher, 2007). Both Quantitative and Quantitative approach will be applied so that depth knowledge and understanding of the subject, and make it easier to find out procedures that link one variable to another (Fisher, 2007). This would help to have a better outlook of the current situation. Since the research paper involves factor that influence the outflow and the growth the economy, statistical data regarding will be taken into consideration, thereby assisting the research for more accurate results. Ethical Issue The research paper is on outward foreign direct investment made by Malaysian transnational companies, proper care will be taken so that no ethical issue arise during the course of the study and if any ethical issue arise proper care will be given to take care about the issue.