本文是数学专业的留学生作业代写范例，题目是“Using Game Theory to Predict Brexit Outcomes(用博弈论预测英国脱欧的结果)”，本文的论点是，由于英国脱欧，欧盟在谈判中会比英国实现更多的目的和目标。我的文章中包含的预测是，欧盟控制着这项协议，他们可以选择给英国一个好或坏的协议。因此，英国可以接受谈判达成的协议，无论这是好是坏，即使他们可能不得不支付500亿英镑，以保持进入单一市场，这是目前的新闻。(Boffey, Ramkin and Asthana, 2017)或者英国可以拒绝该协议并在没有协议的情况下退出欧盟。
The essay thesis is that due to Brexit, the EU will achieve more of its aim and objectives during negotiations than the UK will. The prediction which is encompassed within my essay is that the EU controls the deal and they can chose to give the UK either a good or a bad one. As a result, the UK can either accept the deal negotiated whether that be good or bad, even though they may have to pay £50 billion to maintain access to the single market which is in the news currently. (Boffey, Ramkin and Asthana, 2017) Or the UK can reject the deal and exit from the EU without one.
As reflected by McCulloch, (2017) game theory was invented by John Nash who using a mathematical strategy which could determine the likely outcome of 2 or more players with valuations assigned for the range of potential outcomes. According to the principles, a player will take action to try and secure the best deal to improve their bargaining power and therefore there no deal payoff to remain stronger than the other player. (Muthoo, and Benita, 2017).
正如McCulloch所反映的那样，(2017)博弈论是由John Nash发明的，他使用了一种数学策略，可以确定2个或更多玩家的可能结果，并对潜在结果的范围进行估值。根据这一原则，一个参与人会采取行动，试图获得最好的交易，以提高他们的议价能力，因此不存在比其他参与人更强的交易收益。(muthou和Benita, 2017)。
The prediction of negotiation is supported through the use of a pay off matrix which seeks to identify the pros and cons of accepting the deal based on the negotiations. However, Britain has more to lose than the whole of the EU so can be assumed that they will receive a worse deal as a consequence. The matrix is set up 2×2 as shown below, which helps identify the combinations that are dominate, and the ones being dominated. This ensures Nash equilibrium can be detected which is defined by Core (2017) as ‘A set of strategies, one for each player in the game, such that each player’s strategy is a best response to the strategies chosen by everyone else.’ In the negotiation this is the point when both the EU and the UK defect from their original course to observe and see what the opposing players are offering, as part of their negotiation. This would be the most favorable if both parties were to defect from the path allowing a stable outcome.
通过使用报酬矩阵来支持对谈判的预测，该矩阵旨在确定接受基于谈判的交易的利弊。然而，英国的损失比整个欧盟都要大，因此可以认为，他们将因此得到一个更糟糕的协议。矩阵如下所示2×2.这有助于识别占主导地位的组合和占主导地位的组合。这确保可以检测到纳什均衡，核心(2017)将其定义为“一组策略，针对游戏中的每个玩家，这样每个玩家的策略都是其他每个人选择的策略的最佳对策。”“在谈判中，这是欧盟和英国都背离原来的路线，观察对方提供了什么，作为谈判的一部分。”这将是最有利的，如果两党都偏离轨道，以获得一个稳定的结果。
The number present in the bracket illustrates the benefit to that player if the strategy is undertaken. As shown in the box on the matrix above, the first number is the result for the UK and the second is the EU. The relative size and comparison between the two numbers is important.
括号中的数字说明了如果采取这种策略，玩家将获得的利益。如上图方框所示，第一个数字是英国的结果，第二个是欧盟的结果。这两个数字的相对大小和比较很重要。
The top tight cell indicates the strategy that the UK has accepted a good deal offered by the EU. According to my game, the outcome is still negative, as in my opinion it is unlikely that the deal the UK accepts will give them the same full access to the single market which the UK currently has, this enables them to trade freely amongst each other without tariffs. (Cadman and Tetlow, 2017) However, as it is a good deal the loss cannot be that bad.
The top left cell displays the UK accepting a bad deal offered by the EU, hence the more negative number than the right cell as the UK will be worse off. In my opinion the payoff would be more negative, but it is the most negative for when the UK does not accept a deal yet leaves the EU regardless whether the deal offered was good or bad. This will detrimentally damage the UK, consequently the UK should accept whatever deal is offered as accepting no deal would damage the future for the country in an economic and a political sense.
左上角的单元格显示的是英国接受了欧盟提供的一个糟糕的协议，因此负数比右下角的单元格多，表示英国的情况会更糟。在我看来，这样做的回报会更消极，但最消极的情况是，英国不接受一项协议而离开欧盟，无论该协议是好是坏。这将对英国造成不利损害，因此，英国应该接受任何提出的协议，因为不接受协议将损害国家的未来，在经济和政治意义上。
From the perspective of the EU, it would like to give the UK a good deal as it will benefit the EU economically in the future. However, it would want to punish the UK for deciding to leave and try and ensure that it puts off other countries from leaving too. This is further discussed by Maidment (2017) who quoted ‘that two of the EU’s top Brexit chiefs want to “punish” Britain to stop other countries trying to leave the bloc.’
In this situation, the dominant strategy for Britain which is defined by Core (2017) as ‘Action that yields the highest payoff for a player, no matter what the other players do.’ Is for them to be granted with a good deal for example maintaining access to the single market without having to pay the £50 billion, this has the potential to result in the highest pay off. In comparison, the EU has the dominant strategy if Britain are not part of the EU with a higher pay off.
在这种情况下，《Core》(2017)将英国的主导策略定义为“无论其他玩家做什么，为玩家带来最高收益的行动”。“对他们来说，如果能获得一笔不错的交易，比如不用支付500亿英镑就能继续进入单一市场，这有可能带来最高的回报。”相比之下，如果英国不是欧盟的一部分，那么欧盟拥有主导战略，并获得更高的回报。
The outcome is determined due to a combination of political as well as economic costs to the EU, the UK have limited control so in this case are being dominated by the EU. For the UK, if the deal is not worse than leaving with no deal it would be rational for the UK to accept it. (Muthoo, and Benita, 2017).
However, being rational acts as a major limitation which is drawn upon by Fairchild (2016.) who presents the case that as humans are not always rational so are not always unemotional and self-interested individuals who have no regard for others. As stated in Prisoners dilemma, the rational strategy is for each player in the game to gain the worst outcome possible. However, once empathy is added and individuals are not perceived as rational each player cares more about the others. Consequently, it can transform the game into a win-win situation for both players creating mutual cooperation. For this game the relationship amongst nations would improve creating more awareness and hence softer negotiating approaches with the potential of better deals for both parties.
Other limitations of game theory are explored by Maneesha, Vijay and Singh (2016) who quoted ‘we have only considered only two strategies per party.’p.4. This helps ensure simplicity and makes the whole scenario much easier to understand. Even though there are often many other strategies in place where more than 2 groups are involved with contrasting ideas.
Maneesha、Vijay和Singh(2016)探索了博弈论的其他局限性，他们引用“我们只考虑了每一方的两种策略”第4页。这有助于确保简单性，并使整个场景更容易理解。尽管有很多其他的策略，在这些策略中，有两个以上的群体有不同的想法。
Additionally, the pay offs which are the outcomes for each of the possible combinations of actions, can also be affected for both the EU and UK determined by the course of action taken and how long it takes for either player to change their mind and move from their original plan. If the EU were to swerve first, consequently it would be a more profitable outcome for the UK and vice versa.
When one applies an even value system to each successful outcome, Brexit deal negotiations can represent the ‘chicken game’ which is defined by Exton (2016. p.4.),’ If both parties in marital conflict choose escalation to full conflict in order to get their way (mutual defection) in the game situation a bad deal offered and hence the deal not accepted, this may be very harmful to both parties , so trying to reach a compromise (mutual cooperation) for example a good deal which is accepted is usually preferable over mutual defection’.
Each party has the ability to make threats before starting negotiating, so the more powerful party in this case the EU will intimidate the UK as they are deemed the weaker party in the game. In this situation, they would present them with a bad deal, for example implementing a cost to cultivate their access to the single market, in recent speculation a cost of £50 billion has the potential to be enforced.
In conclusion, it is predicted the UK will achieve less of their objectives during the recent Brexit negotiations. Through the use of game theory, it is attempted to prove that the UK will receive a worse deal than the EU. By assigning values to each strategy it is possible to create a pay off matrix showing all options available. Based on my findings I can conclude, that the UK should accept any deal given to them from the EU, however, the EU are dominant in this game, so it is likely that any deals will be unfavourable for the UK.
综上所述，在最近的脱欧谈判中，预计英国将实现更少的目标。通过运用博弈论，试图证明英国将得到比欧盟更糟糕的协议。通过为每个策略赋值，我们可以创建一个显示所有可用选项的回报矩阵。根据我的发现，我可以得出结论，英国应该接受欧盟给他们的任何协议，然而，欧盟在这个游戏中占主导地位，所以任何协议都可能对英国不利。
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