Is political economy a game?

Based largely on the works of Shubik and Kreps, but also from numerous internet sources, I am going to investigate the recent behavioural theory of the institutions - the game theory. Then I will consider its relevance and applications to the political economy. I will try to establish many links between the political economy and the game theory, like the voting mechanisms and the party ideology theory. In the last part of my essay I will look at some evidence of games in politics, namely the purchase of votes by wealthier institutions through the pressure groups, the tendency for the bureaucracies, like government, to grow over time and the case for regulating the externalities and providing public goods.

First I like to give a brief overview about the theory and the definitions of the game and the political economy. A group of people are engaged in a game if the fate of each depends upon the actions chosen by all. A game must include a set of strategies for each player I call the players in the politics as institution later on as they can be firms, parties, government, financial institutions or bureaucracies. A strategy is a description of what a person can feasibly do in given situations and in what conditions will s/he carry out the actions. I must also include the disposition of each institution (its tastes and preferences), and the information it possesses (about the others and outside world) to the game. Information is very important issue in the game theory - namely that it is usually imperfect and that all decisions of the institutions depend heavily on the availability of information. In competitive markets people do not have to know everyone else - they will just need the market price to determine their strategy.

There can be 0-sum games, with losers and winners being in equal number. But a majority of the games are not 0-sum. That means that depending on the strategy, the total gain of the system can be larger or smaller. Furthermore, this implies that a rational decision made by an institution can turn up to be bad as a consequence to all participants (like in the prisoners dilemma explained later). Games that are not 0-sum can be divided to co-operative and non-co-operative.

Co-operative games are the ones that have usually larger utility outcomes for the participants as a whole, but many of the players might not be maximising their individual revenues, or might not play according to their dominant strategy. Co-operative games are usually found in macroeconomy where there are few players. In non-cooperative games all individuals choose their dominant strategies without considering the others. Here people are completely rational and the if the game reaches an equilibrium it will be a Nash equilibrium - a point where no party can be better off when they change their strategy, but they could be better of if all of them would change their strategy. Non-cooperative games are the substance of public choice theory - a part of political economy. There are, however, ways by which external forces can affect the game, so that the non-co-operative games, that produce a non-Pareto efficient outcome (i.e. not maximising the returns) are changed to ones that will produce a Pareto efficient outcome. This is the task of the political economy in many sense. The game will still be a non-cooperative one, but the payoffs and conditions will be changed so that the Pareto optimal output will also be a Nash equilibrium.

The simplest example is the prisoners dilemma. Without going into much detail, basically both players will have dominant strategies to cheat (they will be better off cheating irrespective of other person's choice), but the payoff will be greater for both of them if they will not cheat. Table below gives an example of this game, numbers denote years in prison (bad things) and left numbers are for player one and right for player 2:

Person 1 \ Person two	Cheat	Do not Cheat
Cheat	5,  5	0,  6
Do not cheat	6,  0	1,  1

Nash equilibrium will be in cheat, cheat. But best strategy for both would be for not to cheat. Now if the external agency (the 'gang') punishes the cheater with imprisonment of 10 years in the event of cheating the payoff matrix will change to:

Person 1 \ Person two	Cheat	Do not Cheat
Cheat	15,  15	10,  6
Do not cheat	6,  10	1,  1

And a Pareto optimal outcome of Do not cheat Do not cheat will emerge as a Nash equilibrium.

Political economy can be viewed much as a science determining how groups of individuals allocate their scarce resources to provide an equilibrium outcome of production, wealth etc. So in this sense the game theory can be applicable to the political economy as a "distinct and interdisciplinary approach to the study of human behaviour." The disciplines most involved in game theory are mathematics, economics and the other social and behavioural sciences. This type of game theory was founded by John von Neumann and later it was developed by Morgenstern to include the neo-classical ideas.

Political economy has also received much attention recently as a tool that could describe the real world more accurately than the classical models of leadership and economy. Public Choice is one of the radical strands of political economy. It defines the world and bureaucracy to be completely rational and self interested. In this theory, "the single-minded elected official will attempt to appease and provide services to well informed and influential voters, and will rationally concentrate on particularised legislation that quickly provides constituency appreciation (Anthony Downs)". Thus, the general problems plaguing society will be overlooked - politicians are only "in it for themselves". Downs claims that this self-interested ideology breeds catastrophe as budget maximising bureaucrats, well-organised interest groups, and rationally ill-informed voters will act collectively in creating a political chaos. If public choice theory is correct, then a governmental bureaucracy should have little interest in efficiency. In reality, the theory may be guilty of being too extreme.

Since the work of John von Neumann, "games" have been a scientific metaphor for a much wider range of human interactions in which the outcomes depend on the interactive strategies of two or more persons, who have opposed or at best mixed motives. Among the issues discussed in game theory is rationality. What does it mean to choose strategies "rationally" when outcomes depend on the strategies chosen by others and when information is incomplete? Or in "games" that allow mutual gain (or mutual loss) is it "rational" to co-operate to realise the mutual gain (or avoid the mutual loss) or is it "rational" to act aggressively in seeking individual gain regardless of mutual gain or loss? Rationality was the key link between neo-classical economics and game theory. Specifically, the assumption is that each person maximises her or his rewards - profits, incomes, or subjective benefits - in the circumstances that she or he faces. This hypothesis serves a double purpose in the study of the allocation of resources. First, it narrows the range of possibilities somewhat. Absolutely rational behaviour is more predictable than irrational behaviour. Second, it provides a criterion for evaluation of the efficiency of an economic system. If the system leads to a reduction in the rewards coming to some people, without producing more than compensating rewards to others (costs greater than benefits, broadly) then something is wrong. Pollution and inadequate resources committed to research can be examples of this. Game theory was intended to confront the problem of individuals outside markets and their interactions with individuals. It provides a theory of economic and strategic behaviour when people interact directly, rather than "through the market." The theory can be developed to incorporate all the institutions. For example, the general elections can be thought of as a game with very many participants and which, in fact as I prove later, turns out to be a non-cooperative game.

A major problem in defining the political economy as a game is the inherent uncertainty which dims the borders of the choice space and also makes participants ignorant of their rational choice. So the individuals might not always behave fully rationally, because they would have to acquire more information to act rationally. But this acquisition requires resources and we have a paradox - one will need information to find out how much information he or she needs to acquire.

 Now I would like to talk a bit about the applications of the political economy that have links to game theoretic models. Politics is a very complicated game with several player, it very hard, but not impossible task to filter out individual sub-games and institutions that participate in the game. Furthermore, the rules of the game (like constitution) can change over time which makes the strategies very hard to construct.

Voting is presented as one of many parts of political economy with direct links to games. There are different voting systems adopted across the world by different institutions, although only one of them is used at a time. Different systems will lead to different strategies. It is usually the case that smaller electorate groups can reach a co-operative agreement in voting, whereas in general elections, for example, the game is often uncooperative. Still, in the United Kingdom there are signs of co-operation called vote trading. People will, for example, not vote for Liberals as they have very little chance to get into power. So their vote would be wasted. They instead vote for the second best alternative.

There is also a problem with election in determining the winning outcomes and the restrictions that have to be imposed on winners to protect minorities. Unanimity cannot certainly be used in General Elections, whereas it might be appropriate in some cases. Sometimes just a majority of votes is sufficient, sometimes a third of the votes can be enough to impose a veto. When we use the backward reasoning (starting to account decisions from the end) we can find that the order of the things that are elected on can change the outcome. But can a winning party impose a tax on the others? Or not call anymore elections? Is it actually legal to buy votes? These normative questions are left unanswered at present by the game theory.

Another link with the game theory arises from the study of party ideology. In a simple example, when electors make their decisions according to a single measure (i.e. left or right) then in a simple two party system the winner party is the one that is appealing to the median voter as it will get the median and everyone else in the half (i.e. left or right) were the other party is not, plus it will get half of the people who are in between the two parties in the half where the other party is. However in real life things are complicated, because the distribution of votes is likely to be bimodal, and when a party is too far away from an individual preference, the individual will not vote at all (i.e. there are more people in the left and right than in the centre and a left minded individual will not vote for the centre parties). So positioning of the parties can be looked as a complicated game, rather than a set of competing ideologies.

Equality is much of an issue of a game. But this is more like a 0-sum game as there are always winners and losers. One can find several games in inequality policy, but in general the policy is more based on normative issues. Although public choice can offer normative solutions as well as positive, game theory is essentially concerned with rationality and at present there is no adequate measure of “rational inequality”.

The last two links to games I would like to discuss about are the externalities and the money. Externalities are goods where the private costs and benefits are different from the social ones. So there should be a political intervention into the production of these goods in order to maximise the social welfare. However the social costs are not easily defined, people will tend to exaggerate them as they know there will be a compromise anyway. Same applies to the provision of public and merit goods. First ones are goods that are collectively consumed and cannot be charged for easily. Furthermore, the charging would occur a dead-weight lost as the marginal cost of producing public goods is zero, but when a price is put on them some people cannot use them, whereas the MC=MR condition of optimum allocation would mean that everyone who wants should be able to use them. One example is the street-lighting. Problems arise in bargaining and pricing also because there is a tendency to free ride and not to pay.

Merit goods are goods that could be produced by the free market but not in sufficient quantity (health). Again social benefits of a healthy nation exceed the private ones (spread of epidemics is avoided). Money and stock markets are also associated with very complicated games in the modern society with the state as the biggest producer playing a major role in the money markets. These games are, however, too complicated to go into much detail at this level.

I will now move on to explore some evidence from the real world with relevance to previous examples. First example I will explore is the growth of bureaucracies. It was suggested that as the politicians are “in it for themselves”, they would like to make their departments grow, so that they could have more power etc. The considerable inefficiency within government agencies has become a common characteristic. Economists often point to the monopoly possessed by many of the government agencies that provides no incentive to operate at cost efficient levels. Also, the allocative wisdom of government is quite dubious as they have often caused harmful misallocation effects. Optimism by economists for the effectiveness of government is diminishing, and "even when economists believe that a good case can be made for government intervention, they have come to realise that the intervention will not necessarily be the kind they envision or could defend." This phenomenon was observed until 1979 when government sector was growing as a proportion of the GDP. With conservatives, however, the trend has been slowly reversed.

Another evidence is the ignorance and the falling participation in the voting process. People will rationally think that it is not worth acquiring the information to vote, but this will have detrimental collective effect, when no-one votes. Proportion of the people voting has been falling in England. Similarly the two major parties in England have been approaching each other in their views quite rapidly to get more votes.

Pressure group activity has also increased. These are set up by institutions effectively to "buy" votes, because in simplistic terms, they spend money to acquire popularity. Games arise as it is hard to actually persuade the people that are in power, and the pressure group activity is often ineffective.

Externalities are often politically regulated. They are often a political question involving uninformed public opinion (“pollution is bad”) and thus there is a tendency for the government for not to correct the externalities always like is socially optimal, but like is most beneficial for the bureaucracy or most popular among the voters. This issue relates directly to the bargaining and pressure groups, as there are people to bargain for and against  pollution. National Health Service, being an example of a merit good, is now been highly de-regularised. The situation can be viewed so that the NHS was put out of the bureaucratic games arising with state control and into market environment. However, in market conditions the profitability is all-important, whereas in bureaucracy, according to public choice, the popularity of bureaucrats were most important. Bureaucrats rose their popularity also by making the NHS more equal, which is probably socially more beneficial, but not necessarily effective or Pareto optimal. So one cannot say for sure that the bureaucracy outcomes are beneficial only to bureaucrats themselves. Bureaucrats do have to make popular decisions to get themselves re-elected.

The general equilibrium theory determining the microeconomic behaviour of the economy has been know to the society for long. Similarly macroeconomics is explained by co-operative games (because of small numbers of participants), or from the other angle neo-classical and Keynesian models. Political economy has classically been the co-ordinator or link between the two theories. Despite its limitation due to its complexity, it is trying to view the whole state system with microeconomic institutions as participants. As there are a number of small players the political economy can be viewed as a non - cooperative game with its outcomes not directly dependent on the individual choices. The game theory, although hard to implement, is a very useful tool in this situation in describing the political economy.