I have released this EMA to help future OU students who are studying on the same course. It received a mark above 70% and will hopefully be of use as an example or guideline for DU301 students to look at.
Outline and evaluate the game theory explanation of the difficulties faced in solving collective action problems.
In this essay I shall outline and evaluate game theory itself and its relationship with collective action problems and the difficulties in working through such complications. As part of this I shall examine game theory matrix representations and explore empirical examples.
Before we begin, we should ask just what game theory is. Well, “Game theory provides conceptual tools to analyse situations of strategic interaction” (Mehta & Roy, 2004, p.421). In clearer terms, it can be used to not only analyse strategic interaction but study all manner of situations; whether these be real-life situations, parlour games, economic agreements or, as in this case, political negotiations and international affairs.
Game theory can assist matters by providing models to place given problems in to, and then used to help formulate a solution. Game theory has its limitations, as we shall see, and it may not always be possible to determine which the appropriate model for a particular problem is. It works on the assumption that the participants are rational beings, with the ability to consider and rank various outcomes and work towards goals or targets.
But due to the fact that it strips complex problems down to the bare bones, some critics have argued that game theory models are too far removed from real strategic situations and the abstract models serve to, “…reduce actors to hyper-rational players or bloodless automatons that do not reflect the emotions or the social circumstances of people caught up in conflicts” (Brams, 1994). The same critics also state that game-theoretic models are, to a degree, difficult to test empirically due to the reason that they rely on assumptions that do not accurately reflect or consider the hard facts.
These criticisms are countered by exponents of game theory who claim that it brings a thoroughness to the study of strategic situations that other theories cannot contend with and even if the players are not hyper-rational they are at least rational and would mostly, “…choose better over worse means, even if the goals that they seek to advance are not always apparent” (Brams, 1994).
And when we view this in the context of collective action it is apparent that the difficulty of solving collective action problem lies in the fact that reaching a multiple agreement on matters –even for something which you would think was relatively clear cut- is often very difficult to achieve. Even though all players are likely to benefit from certain actions, and it is impossible for one alone to combat the given issue, the costs must be spread across all the players involved and share the cost as a collective action.
Tragedy of the Commons
For example, in the Tragedy of the Commons scenario (Mehta & Roy, 2004, p.418) where it is perceived that all nations would benefit from ensuring that open-access resources -whether they are the oceans’ stocks of fish or acres of land used for grazing cattle- were not over-exploited. Such blatant exploitation of natural resources is unsustainable, where self-interest prevails over co-operation.
All parties must be made aware of the implications of this and each country is required to act to stop the abuse of reserve. But each nation (or ‘player’) has their own agenda, and a resolution is needed to solve a collective action problem. Simply put, “A collective action problem exists when it is not in an individual player’s unambiguous private interest to do their part in an outcome which is in the common good” (Mehta & Roy, 2004, p.453).
We now turn to the game theory matrix representations themselves and firstly we shall examine the Prisoner’s Dilemma model, which is often loosely based around the hypothetical example of two partners in crime who are caught, arrested and questioned in separate rooms. The game here centres on the options each prisoner has, with regards to confessing, implicating his partner, holding silent etc, with each option assessed in the payoff matrix to help decide which strategy each should adopt.
The Prisoner’s Dilemma model can be applied to political and economic situations, such as the nuclear arms race during the Cold War for example where the prisoner’s confession could be substituted for the deployment of a missile, the prisoner’s denial substituted for not deploying the missile and so on.
The thinking behind a Prisoner’s Dilemma model is that it strips collective action problems to the bare bones and we can see the idea by looking over the diagram below.
This example relates to the outbreak of a disease (in this case SARS) and how two countries, Canada and China, should respond when dealing with the epidemic and whether to admit and disclose to the world that they have this disease. We should bear in mind that the result could be extremely harmful to the economies of each country, with tourism potentially being affected and other nations being reluctant to import from them, amongst other reasons. If both China and Canada comply (and each admits to the SARS outbreak) then both stand to lose -1 (which in reality could be billion, trillion or other).
But if China complies and Canada cheats (fails to disclose the outbreak) then China serves to lose -3 and Canada goes even at 0. And in return, if China cheats and Canada complies then Canada will lose -3 and China stays level at 0. So in this case it is in the best interests of both nations to respond to one another by cheating and the payoff to this combination is -2 (billion) to each country. This is known as a Nash equilibrium and seeing as this is a one-shot game and each nation is unaware of each other’s choices, it is in the interest of both to cheat.
Whatever China does it has to make sure that it does not regret it and China wants to avoid the so-called ‘sucker’s payoff’, which would happen if they complied and Canada cheated –or vice versa from Canada’s point of view. If each nation were looking to maximize their total benefits, then each would have chosen to comply and lose only -1, which in a collective action game is known as the social optimum. But can they take that chance? In international relations there is no government, or supranational power to enforce things and neither nation can be sure as to what the other will do.
As we mentioned before, collective action games and the likes assume that the players are self-interested and that as a consequence, “…the social optimum is not automatically realized” (Mehta & Roy, 2004, p.429). Therefore, if China’s choice is optimal, given Canada’s choice and Canada’s choice is optimal given China’s, then the Nash equilibrium is reached.
In simple terms, if China complies then the best response for Canada is to cheat, because 0 is better than -1. It makes sense for China to cheat if Canada complies. But if China cheats then Canada’s best response is still to cheat, because -2 is better than -3. China basically wants to avoid the sucker’s payoff. So the outcome is that both countries will cheat and the social optimum is not the one that’s reached (comply -1,-1).
There’s a lot of so-called cheap talk and a lack of trust in international relations and so the outcome is that both will cheat! As we have seen, the Nash equilibrium dictates that when each player follows a certain set of strategies the equilibrium is attained when none of the players can change strategies and expect a larger payoff as a result.
We shall now move on and assess another matrix, called the Chicken Game. The basic idea behind the Chicken Game looks at two teenagers driving towards one another on an apparent collision course. As they approach, each are given choices to make. If one swerves he loses face while his opponent gains prestige for continuing to drive straight and if both swerve then each suffer mild embarrassment. If neither swerves then each suffers the extreme consequences of a head on collision.
We apply this concept to the Cuban missile crisis as the US and USSR faced a very real Cold War collision and their own game of Chicken. American reconnaissance planes had discovered missiles on Cuba and the Americans demanded that they be removed and they subsequently blockaded Cuba. The Soviet Union had a convoy heading for Cuba and the issue remained: was the USSR going to break the blockade as their tough strategy or turn their ships around?
And were the Americans going to maintain the blockade (their tough strategy) or remove the blockade? There were other options available to the players, but the stripped down, ultra rational nature of game theory means we get to deal with what we have. We refer to the diagram below.
In this case we see that there is a different relationship between the numbers. If the USSR breaks the blockade and the USA maintains the blockade, then it will be -3, -3. That would be like the two cars colliding and a strategy that both countries would be keen to avoid. If the USSR turns their ships away they will get 0 and the US will get 2 in terms of the game but a great victory in terms of prestige and standing in the world.
If the USSR breaks the blockade and the Americans remove the blockade then the USSR will get 2 and the USA will get 0. In the final, both ships remove or turn away and end up with 1,1. In the Prisoner’s Dilemma case there was one possible outcome, and in this case there is two, and the USSR would prefer 0,2 and the USA would prefer 0,2. Both want to avoid (or in the car analogy, swerve) option 1,1 (which means USA remove and USSR turn ships away).
Therefore, the game looks at the options and in this case one side backed down – which happened to be the USSR who turned their ships around. So the USA achieved their preferred option. The USA played a tough strategy won out as a result. They had forced their opponent to make a move.
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In a more recent empirical example of the Chicken Game, William Brown discusses the December 2011 meeting of world leaders in Durban, December 2011, to discuss climate change and, who, after two weeks of intense negotiations, finally reached an agreement (Brown, 2011). Brown highlights the fact that a change in the European Union (EU) stance on CO2 emissions meant that for the first time developed and developing nations committed themselves to cutting emissions. Was the EU’s shift from a weak stance to a tough one a game of climate change chicken? Well, game theory models operate along the assumptions that each nation (player) will act in its own self-interest and indeed developing countries like China, India and Brazil argued that seeing as it was the developed nations who had caused so much of the climate change issues (through years of intense industrialisation) that they should not be subject to the same restrictions, as their role in causing the problems were far less. This seems like a fair argument.
Where the chicken game comes into play is in the fact that the EU initially (pre-Durban, at the Kyoto Protocol) played a weak stance or swerved, while the developing nations played tough and stayed on course (to stick with the aforementioned driving analogy). But, as Brown explains, this produced an undesirable outcome (known as a sub-optimal outcome) because the EU suffered a ‘sucker’s payoff’, enduring all the costs of cutting CO2 emissions while the other nations did not. At the Durban summit the EU stance changed – they were clearly determined not to get ‘suckered’ again!
This time they played tough and showed China and co that if they did not swerve then the EU would not swerve either, which would not only have lead to a collapse of the existing rules that had been built up, but would have caused a metaphorical head-on collision. China did not want this and neither did the lesser nations that lined up behind her, hoping that the developed countries would incur the necessary costs or ‘foot the bill’, as Brown puts it. “In game theory terms, if you’re involved in a chicken game then convincing the other players that you will play tough and not swerve is the key to persuading them to swerve (make your opponent do something)” (Brown, 2011). Anticipating what an opponent will do is no easy task and in chicken game scenarios, not only is cooperation often unstable but non-cooperation could easily lead to a disastrous outcome.
We now move on to the third game theory example and whereas previously we have analysed one-shot games like the Prisoner’s Dilemma, where each player knows nothing of his opponent’s decision making, is prone to being dealt a ‘sucker’s payoff’ and in which cheats do prosper, the assurance game is a little different. “One which still contains a collective action dilemma, but where the outcome depends on the confidence we have in the likely behaviour of the other player” (Mehta & Roy, 2004, p.431). This model relates to the building of nuclear weapons and refraining from building nuclear weapons.
Returning to a Cold War situation, we now see that if the USSR refrains from building and the USA refrains from building then it’s 4,4 and in that case it’s in the interests of both to do this. The social optimum here is actually one possible Nash equilibrium, whereas if the USA builds and the USSR refrain then they (the USA) stand to gain 3 and the USSR gets 1.
So each side doesn’t want to get into a situation where they refrain from building and the other side builds – they both wish to avoid this circumstance. If they both build then it’s 2,2. So there are two Nash equilibriums, in terms of both refraining and both building. So the Assurance Game models a situation where it is in the interests of both sides to cooperate, is built around trust and introduces the issue of co-operation or non-cooperation when dealing with international affairs. Will the players play a co-operative game and forge binding and enforceable agreements? Or fail to co-operate and ensure that any agreements are reached in equilibrium, where the player would be worse off if he violated the agreement.
Therefore, in conclusion, previous examples again highlight how difficult it can be to solve collective action problems. We have discovered that even by looking at game theory as a means of studying the complexity of finding solutions to collective action problems brings diverging issues. Game theory shows how the social optimum is not always the outcome that states prefer and it is not without weaknesses; the symmetrical nature of the game means there is a need for balance and for one to lose then the other has to gain.
However, taking this into account, even though game theory is not perfect and does not offer cast iron solutions to international and collective action issues, it is a powerful tool in modelling the problems and can help to strip down issues into an abstract and often more helpful manner for those using it.
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Mehta, J., Roy, R (2004) ‘The collective action problem’ In: Bromley, S Mackintosh, M, Brown, W and Wuyts, M (eds) Making the International: Economic Interdependence and Political Order, London, Pluto Press in association with The Open University.
Brams, S.J. (1994) Theory of Moves, New York: Cambridge University Press.
Brown, W (2011) Climate Change: Game Changer (podcast), The Open University. Accessed via: http://www.open.edu/openlearn/society/international-development/international-studies/game-changer