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Zero Sum Two Player Games

Spine creases, wear to binding and pages from reading. 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.

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Figure Four. The chicken game can illustrate an aspect of the second issue facing the developmental state noted by Fine and Stoneman 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 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.

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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 displaced 12 , but because new technology and economic change may simultaneously affect the distribution of political power.

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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.

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  5. 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 , 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 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 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 Without significant scale economies in farm production and problems of monitoring hired labour, the family farm is the most efficient institution for production.

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    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.

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    Keynes assigned an important role to expectations as an autonomous causal factor. Woodford 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. 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.

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    Negative expectations can become self-fulfilling without any change in the underlying economic fundamentals. A lot of the literature about the 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 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 s. 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 effectively removed the sell option. The IMF stand-by credits and loans would, it was hoped, mitigate this effect by reducing the cost of not selling early. 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? Many thanks to Alan for invaluable editorial assistance. This is chapter Number Theory and its History. An Adventurer's Guide to Number Theory. Here are five excellent elementary texts that last I knew are still in print. Silverman, Joseph H. Dudley, Underwood.

    Elementary Number Theory , 2 nd Ed.