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Game
Theory: a Refinement or an Alternative to Neo-classical Economics? © Copyright 2005 Matthew
McCartney This
paper1 is not intended to say much that is new, rather it takes
issue with the traditional manner in which economics has presented game theory.
In particular this paper emphasises that game theory has some quite radical
implications; these are however smothered by a heavy emphasis in textbooks
and in teaching on what is neo-classical about game theory rather than
presenting game theory as a very different way of modelling economic life. As
in a previous paper2 I take for my texts three books that form the
core of many masters programmes in microeconomics. Neo-classical economics, Game Theory and General Equilibrium The
intellectual centrepiece of neo-classical economics is general equilibrium.
“The view of the economy central to microeconomics is that it is an
interrelated system of markets through which one particular resource
allocation is achieved out of infinitely many which are possible. Until now3
we have been considering the constituent elements of this system: households,
firms, goods markets, and factor markets. We now have to synthesise all these
elements into a model of the equilibrium of the economy as a whole.” (Gravelle and Rees, 1992, p438). There
is nothing inherently neo-classical about general equilibrium. For example
Keynesians postulate that an economy may become stuck in an underemployed
equilibrium. An equilibrium in game theory may be equivalent to one in
general equilibrium. In the example (fig one) below (Up, Left) represents a
Nash Equilibrium, a Dominant Strategy Equilibrium and we could suggest, a
General Equilibrium of a simple two-person economy. Figure One
The
key assumption that distinguishes a game theory world from a neo-classical
economy is that of interdependence. In game theory the payoffs or utilities of
any strategy depend on the strategy of the other player(s), or even the
expectations of the strategy of the other player. In the above example the
possibility of player one getting a payoff of 3 from choosing Up is
contingent on the choice of Left by player two. There
are a variety of assumptions in the neo-classical version of general
equilibrium necessary to prove the existence,
the uniqueness and stability of
equilibrium. Important among those assumptions is independence. For the stability of
equilibrium, “if all goods in the economy are gross substitutes, then the
time path of prices, p(t), determined by the tatonnement
adjustment process…converges to an equilibrium.” (Gravelle
and Rees, 1992, p450). An equilibrium may not exist in the case of goods that
are complements. If there is excess demand for a particular good such as CDs
the price in a Walrasian type economy will rise.
This will have the undesirable (from the perspective of equilibrium) effect
of reducing the demand for CD players. Such complications from interdependent
markets may prevent the economy converging to a stable equilibrium. For uniqueness the neo-classical version of
general equilibrium likewise demands that choices be independent. What
happens otherwise can be best illustrated by another example of a game. Figure Two
In
this example (fig two) there are multiple equilibria4. Once the utility
from a strategy or choice by one individual depends on the strategy or choice
of another individual, any presumption of uniqueness of equilibrium breaks
down. This then is the crucial difference. Game theory drops the assumption
of independence. The implications of this are profound: they open the door
for a completely different way of analysing the stability and efficiency of
an economy, the role of the state, expectations, and the role of conflict in
economic exchange. I will return to this later. First I will try to make the
case that so completely has game theory been colonised and smothered by
neo-classical economics that these implications may escape us. Is Game Theory a Theory?
I would argue that game theory is perfectly entitled to stand alone as a theory of how economies behave in a situation of interdependence in decision making. Game theory is though commonly presented as an appendage. “Game theory by itself is not meant to improve anyone’s understanding of economic phenomena. Game theory (in this book) is a tool of economic analysis, and the proper test is whether economic analyses that uses the concepts and language of game theory have improved our understanding.” (Kreps, 1990b, p6). Kreps (1990b) further argues that game theory comprises “formal mathematical models that are examined deductively” (p6), and “a taxonomy for economic contexts and situations” (p37), to “ask questions about the dynamics of competitive interactions” (p87).
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Firm Two
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Not Invest |
Invest |
Firm One
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Not Invest
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(1,1) |
(0,-5) |
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Invest |
(-5,0) |
(3,3) |
The
problem was theorised by Rosenstein-Rodan, Scitivsky in the 1940s and 1950s as the ‘Big Push’
approach to economic development. With interdependence change
(industrialisation) would not be automatic. Only simultaneous investment
across a wide range of industries would be viable. It could be possible for
investors in a complementary project to agree to a contract though this will
be costly to draw up and monitor, (Chang, 1999). Such transactions cost
considerations would be particularly relevant in the case of a large upstream
industry supplying inputs to a large number of firms. This could be the case
with a railway system that would then be used by a host of small firms,
(Murphy et al, 1989). The takeover mechanism could provide a solution but
profound capital market imperfections during the early stages of development
are likely, (Bardhan, 1999). Foreign investment in
crucial sectors may be seen as an unacceptable loss of domestic economic
sovereignty. In East Asia the state played an important role in resolving
this kind of co-ordination failure. Such interventions can be simply modelled
using game theory. Intervention in the capital market to subsidise credit,
changes the payoffs in the game to make (Invest, Invest) more likely9.
The organisation of Chaebols in South Korea can be
thought of in a stylised manner as a merger of the two firms in this game.
The choice for the single firm would be straightforward Invest for a profit
of 6 or not invest for a profit of 210. The state itself may
undertake the investment, as in Taiwan, which largely retained crucial
large-scale upstream industries in the state sector. Indicative planning
exercises may provide a focal point for private sector co-ordination between
such complementary investment projects. (Chang, 1999)11.
b. Chicken Games
A
Chicken game is represented in Fig four.
Individuals can be aggressive or concede. The two positions that
optimise the social surplus (Concede, Aggressive) and (Aggressive, Concede)
require that one player concede. The worst outcome is mutual aggression,
which leads to a negative outcome for both players. There is an inherent
conflict because outcomes are unequal; for both to gain, one player must
resign himself to an inferior position.
Figure Four
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B
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Aggressive |
Concede |
A
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Concede
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(2,5) |
(0,0) |
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Aggressive |
(-2,-2) |
(5,2) |
The
chicken game can illustrate an aspect of the second issue facing the
developmental state noted by Fine and Stoneman (1996).
The political capacity of the state to identify and implement policies,
specifically that conflict over income distribution can prevent reforms or
perpetuate inefficient institutions over time.
This
game captures nicely the notion that development is an inherently conflictual process. Chang (1999) notes that development
is the process of shifting resources from low to high productivity areas.
Less mobile assets are likely to become obsolete, leading to unemployment and
income inequality. Those with a vested interest in the status quo will resist
such changes. The diffusion of technology may be blocked in order to protect
economic rents. This need not occur solely through opposition from those
likely to be displaced12, but because new technology and economic
change may simultaneously affect the distribution of political power. Acemoglu and Robinson (1999) propose a ‘political losers’
hypothesis - groups may resist technological change that would otherwise
erode their political power (rather than more typically economic rents). The
market failure is the lack of any credible commitment to compensate political
losers after economic changes have occurred. In the game above there is no
mechanism to allow a credible commitment to compensate the player who concedes.
In a dynamic political economy context, the resulting income inequalities may
be perpetuated over time. The wealthier player may be able to
institutionalise influence on the state and bias future changes to his own
benefit. This approach has been followed by Knight (1992), who explains the
development of institutions not in terms of responses to collective goals or
benefits but rather as a product of distributional gains. The main goal of
institutional development is to gain a strategic advantage over other actors.
This view of institutions introduces the concept of power. There are numerous
practical examples of this in the development literature. Sokoloff
and Engerman (2000) argue initial inequalities in
Latin America and the Caribbean in the early years of colonisation were
perpetuated over time, resulting in the slow spread of the voting franchise,
literacy and education. Harriss (2002) gives an
example of agrarian institutions in Eastern India as inefficient institutions
that have persisted over time. Usury and speculative trading in food grains
were privately profitable for a small class of landowners to the extent that
there was little incentive to make productive investments in agriculture.
These inefficient institutions supported and were supported by the power of
the landowning oligarchy with a strong vested interest in the reproduction.
The chicken game can also help explain the paradox of land reform, Bardhan (1999). Without significant scale economies in
farm production and problems of monitoring hired labour, the family farm is
the most efficient institution for production. Land reform has been fiercely
resisted by landowners despite possible efficiency gains. Landowners have
tended not to lease or sell land to family farmers to secure the surplus from
expanded production. There are problems of monitoring, insecurity of tenure
and fear the tenant will gain occupancy rights. Imperfect credit markets and
insecure property rights mean small farmers are frequently unable to afford a
market price. More generally we could consider the game as representing the
overall process of industrialisation. This requires the allocation of
property rights to form a class of capitalists, either player A or B must
concede and become a worker. Industrialisation will lead to an improvement in
aggregate income (2,5) or (5,2) but also to increased levels of inequality.
Political opposition to increasing inequality, especially if it is structured
on regional or ethnic lines, may lead to conflict and an outcome of (-2,-2)
instead.
Game
theory can easily model how expectations can have a fundamental impact on the
real economy and any efficiency properties of the market economy disappear.
Keynes assigned an important role to expectations as an autonomous causal
factor. Woodford (1991) shows that changes in beliefs become important in
generating fluctuations in circumstances in which they tend to become
self-fulfilling. A lot of the literature emphasises particular economic structures
which enable revisions of expectations to become self-fulfilling.
Figure Five
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B
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Hold |
Sell |
A
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Hold
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(5,5) |
(-2,2) |
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Sell |
(2,-2) |
(1,1) |
Fig
five shows a situation in which the optimal social position is for both
players to hold (retain possession of a share, currency or other financial
asset). If either player has any expectation that the other is likely to sell
the best thing to do is to sell, avoid a loss and settle for a positive if
lower payoff. Negative expectations can become self-fulfilling without any
change in the underlying economic fundamentals. A lot of the literature about
the 1997 Asian Crisis is framed in just these terms. Herd-like behaviour can
be important; fund mangers would be faulted for not getting out when others
do but not for making losses when everyone else does. The effect will be compounded by imperfect
information, when entry or exit by one actor is interpreted as his having
access to superior information. As Krugman says:
“The
lesson for the real world is that your vulnerability to the business cycle
may have little or nothing to do with your more fundamental economic
strengths and weaknesses: bad things can happen to good economies.” (1999,
p10).
The
problem of multiple equilibrium is not a fault of game theory but a
justifiable reflection of how a real economy works. The particular structure outlined above was
created by financial liberalisation in East and South-East Asia in the early
1990s. Inexperienced domestic banks were able to take out large dollar
denominated loans from foreign lenders. Deregulation of the domestic economy
allowed these loans to be on-lent for construction and real estate investment
and speculation. The inflow of short-term capital created a game-like
scenario in which investors had to consider the decisions of other investors.
The reintroduction of capital controls by Malaysia in 1998 effectively
removed the sell option. Wade (1998a+b) criticises the IMF
for pushing for bank closure in countries without full deposit insurance - in
effect raising the cost of being caught holding when the other player sells.
The IMF stand-by credits and loans would, it was
hoped, mitigate this effect by reducing the cost of not selling early.
Conclusion
Game
theory can and should be a theory that stands on its own to model economic
processes that occur in a situation of interdependence. It offers a radical
alternative to neo-classical economics. Game theory illustrates just how
non-robust are the efficiency properties of neo-classical economic theory, it
provides a neat framework in which to model and justify a developmental role
for the state and can neatly illustrate how expectations can, contrary to neo-classical
economic theory have an important impact on the real economy. Game theory
deserves better than to be emasculated by the obsessions of neo-classical
economics, its formalism, rationality and its slavish devotion to
equilibrium. Perhaps there is a case
to be made for a heterodox Microeconomics text book that begins with game
theory as the standard case and introduces general equilibrium as a special
case?
Endnotes
1. Many thanks to Alan for invaluable
editorial assistance.
2. Matthew McCartney, “Dynamic versus Static
Efficiency: The Case of Textile Exports from Bangladesh and the Developmental
State”, post-autistic
economics review, issue no. 26, 2 August 2004, article 4, http://www.btinternet.com/~pae_news/review/issue26.htm
3. This is chapter 16.
4. More precisely three, two pure strategy and one mixed strategy equilibria. The latter are not considered here.
5. Kreps (1990a) is little different but does have
several pages dealing with ‘irrationality’ (p480-9). Such value-laden terms
in supposedly positive economics is evident. If players do not play the way
the equilibrium of the game says they should they are ‘irrational’. The
theory is correct by its by its own definition.
6. The “interested reader is directed to the more specialised
references at the end of the chapter for a fuller treatment” (p300).
7. See also Fine (1999
8. Grabowski (1994) attempts a synthesis of these two approaches using game theory,
Fine and Stoneman (1996) are not particularly
complementary about his efforts.
9. Gerschenkron (1962) emphasised
the importance of state supported development banks among late industrialisers in Europe.
10. The combined profits of the two independent firms.
11. An otherwise sterile analysis of ‘focal point equilibria’
can be found in Kreps (1990a, p554).
12. Most famously the Luddites, skilled weavers who attempted to block the
introduction of new machines.
References
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Economic Development’, September, mimeo.
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mimeo.
Chang, H-J
(1999), ‘The Economic Theory of the Developmental State’, in ‘The
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Fine, B. and
C. Stoneman (1996), ‘Introduction: State and
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A. M. D. Whinston and J. R. Green (1995), ‘Microeconomic Theory’,
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Rapoport,
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Wade, R.
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Wade, R.
(1998b), ‘The Asian Debt-and-Development Crisis of 1997-?: Causes and
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___________________________
SUGGESTED CITATION:
Matthew McCartney, “Game Theory: a Refinement or an
Alternative to Neo-classical Economics? ”,
post-autistic economics review,
issue no. 30, 21 March 2005, article 2, http://www.paecon.net/PAEReview/issue30/McCartney30.htm