Game Theory Of Cheating

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Why I Let My Students Cheat On Their Game Theory Exam. Teaching people game theory is good. Making them live it is even better, says UCLA professor Peter Nonacs. The other perspectives consistof the conflict theory and the interactionism approach. This theory of functionalism examines the society based on a functional framework. Functionalism stresses the importance of all the societal components. The theory lays down the major components of an ideal society in terms of how such a society functions. Index Terms—game theory, Kuhn poker, cheating I. INTRODUCTION Poker is one of the most popular games studied among game theory researchers. The complex nature of the game provides challenging problems, however its complexity and size also make poker a difficult game to study. Kuhn poker, a toy poker game, can pose theoretical challenges at a. Game theory helps us to understand strategy, which is an omnipresent aspect of the human condition since we are rational and social beings. It might even explain the “honesty” – or “corruption” – in different cultures. Game theory, the study of strategic decision-making, brings together disparate disciplines such as mathematics, psychology, and philosophy. Game theory was invented by John von Neumann and Oskar.

A controversial blog post from an NYU Stern School professor has been circulating. The original has been removed but it is available here. From reading it, I can’t understand why the original was taken down. It is a solid tale and, in the end, the cheaters were caught.

Let me recap the story. Professor offers assignment to class that is the same as previous years. This is the first year the Professor has had easy access to Turnitin; a copying detection tool which is extremely effective. This is also the first year the Professor has tenure (but I think that is secondary). The Professor first notices lots of students just coping and pasting from the Internet (direct plagiarism). He decides to admonish rather than punish. Then he discovers copying of past assignments. Much hilarity ensues as the offenders try to talk themselves out of it (using the old “mixed up files from roommate trick”) and then — and this is the good part — copies the same assignment again when correcting the “error.”

I want to pause here to reflect on what is going on. First, this kind of cheating is not new. I suspect there are long-standing institutions within most universities that trade in past assignments. What is new is the ease of that process coming at the same time as a step-up in easy of detection. The problem is that the detection and enforcement is still not often used so students, playing out an equilibrium, cheat. So solid is this equilibrium that students do not appear to revise their beliefs when cheating is detected — forecasting (correct for some equilibrium) that the Professor won’t bother checking again. In this particular case, the students were wrong about the Professor’s behaviour.

But they weren’t too far off. The post is about the Professor telling the world that this was personally too costly and he wouldn’t do it again. And it was personally costly — right down to reduced teaching evaluations and the consequences of that. Detecting any crime is a public good and we expect too little of it to be done. The problem is that we end up in an equilibrium with too much cheating and too little enforcement.

The Professor actually did do the right thing and that was change the next assignment. He didn’t do it in a major way, however, which would have killed his problem dead. Instead, he did it in a sneaky way that — on my reading — was almost designed to catch up more cheaters. /mafia-2-game-cheats-codes.html. And it did. And hilarity ensued. And the Professor met with the costs of that including those flowing from a clever “turn yourself in” mechanism.

After all this, the Professor reflected on what he could do and decided that he could modify how he assessed students. But as he pointed out, it is not always a good idea to change assignments year on year and some assignments work and are valuable learning tools. My point here is that the Professor shouldn’t have to change his behaviour to minimise cheating. It is a public good for the School and the School should solve it.

So what should the administration do to change the equilibrium? First, take the enforcement of cheating out of the Professor’s hands. Employ a policing person who is the one who receives the Turnitin results and decides what to do about it. Make it their job and you solve the free-riding problem right away. You also allow cross-course, repeat offender detection. And you change the cheating equilibrium to one where enforcement is expected. Finally, the Professor has their hands clean and so suffers no conflict over teaching evaluations.

Actually, I wrote ‘first’ here, but that is The Solution.

Now, for those academics whose School does not employ The Solution, here is how I do it. You have to learn to love the whole forensic grading process. I love it the same way I love dreaming up imaginative and ironic punishments for my children. Nothing pleases me more than to detect cheating and to find ways of “dealing” with it.

Let me give you an example from, now 25 years ago. I was tutoring first year undergrads at the University of Queensland on the History of Economic Thought. I set an assignment for the students on Karl Marx — something I had enjoyed reading about myself when I was in High School. Two instances of cheating turned up. The first was identical assignments handed in by two students. Examining them, it was clear who had cheated — the one who had corrected the typos. Anyhow, the assignments had two different tutors — myself and another. We deployed the “confront individually” strategy and weeded out a confession. It turned out that the non-cheater’s was completely oblivious to what had happened as it was lifted from a common computer in their college. I recall that I tortured the cheater — my usual approach is a grade of 0 and you have to still write and pass the assignment to pass the course.

The second one was better. I read an assignment that had a ring of familiarity. It turned out that the reason for that is that it was mine. The very assignment I had written in High School. The student had gone to the same High School and, somehow, had a copy of my assignment. I have no idea how. Anyhow, they were not sensible enough to actually have checked the names of the assignment’s author and their tutor. They were punished but I had to admit, at least they had taste. It is one thing to copy a bad assignment. Copying a clearly excellent one demonstrates some feel for the material of the course.

Anyhow, let that be a message to all my future students. I enjoy detecting cheating and punishing cheaters. I let all my students know it. But, sadly, for some reason, I don’t get that many cases to play with.

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Game theory is concerned with predicting the outcome of games of strategy in which the participants (for example two or more businesses competing in a market) have incomplete information about the others' intentions

  • Game theory analysis has direct relevance to the study of the conduct and behaviour of firms in oligopolistic markets – for example the decisions that firms must take over pricing and levels of production, and also how much money to invest in research and development spending.
  • Costly research projects represent a risk for any business – but if one firm invests in R&D, can a rival firm decide not to follow? They might lose the competitive edge in the market and suffer a long term decline in market share and profitability.
  • The dominant strategy for both firms is probably to go ahead with R&D spending. If they do not and the other firm does, then their profits fall and they lose market share. However, there are only a limited number of patents available to be won and if all of the leading firms in a market spend heavily on R&D, this may ultimately yield a lower total rate of return than if only one firm opts to proceed.

The Prisoner's Dilemma

  • The classic example of game theory is the Prisoner's Dilemma, a situation where two prisoners are being questioned over their guilt or innocence of a crime.
  • They have a simple choice, either to confess to the crime (thereby implicating their accomplice) and accept the consequences, or to deny all involvement and hope that their partner does likewise.

Confess or keep quiet? The Prisoner's Dilemma is a classic example of basic game theory in action!

  • The 'pay-off' in this game is measured in terms of years in prison arising from their choices and this is summarised in the table below.
  • No communication is permitted between the two suspects – in other words, each must make an independent decision, but clearly they will take into account the likely behaviour of the other when under-interrogation. This highlights the importance of uncertainty in an oligopoly.

Nash Equilibrium

Nash Equilibrium is an important idea in game theory – it describes any situation where all of the participants in a game are pursuing their best possible strategy given the strategies of all of the other participants.

In a Nash Equilibrium, the outcome of a game that occurs is when player A takes the best possible action given the action of player B, and player B takes the best possible action given the action of player A

Two prisoners are held in a separate room and cannot communicate

They are both suspected of a crime

They can either confess or they can deny the crime

Payoffs shown in the matrix are years in prison from their chosen course of action

Prisoner A

Confess

Deny

Prisoner B

Confess

(3 years, 3 years)

(1 year, 10 years)

Deny

(10 years, 1 year)

(2 years, 2 years)

  • What is the best strategy for each prisoner?
  • Equilibrium happens when each player takes decisions which maximise the outcome for them given the actions of the other player in the game.
  • In our example of the Prisoners' Dilemma, the dominant strategy for each player is to confess since this is a course of action likely to minimise the average number of years they might expect to remain in prison.
  • But if both prisoners choose to confess, their 'pay-off' i.e. 3 years each in prison is higher than if they both choose to deny any involvement in the crime.
  • In following narrowly defined self-interest, both prisoners make themselves worse off
  • That said, even if both prisoners chose to deny the crime (and indeed could communicate to agree this course of action), then each prisoner has an incentive to cheat on any agreement and confess, thereby reducing their own spell in custody.

The equilibrium in the Prisoners' Dilemma occurs when each player takes the best possible action for themselves given the action of the other player.

The dominant strategy is each prisoners' unique best strategy regardless of the other players' action

Best strategy? Confess?

A bad outcome! – Both prisoners could do better by both denying – but once collusion sets in, each prisoner has an incentive to cheat!

Prisoner A

Confess

Deny

Prisoner B

Confess

(3 years, 3 years)

(1 year, 10 years)

Deny

(10 years, 1 year)

(2 years, 2 years)

Applying the Prisoner's Dilemma to Business Decisions

  • Game theory examples revolve around the pay-offs that come from making different decisions.
  • In the prisoner's dilemma the reward to defecting is greater than mutual cooperation which itself brings a higher reward than mutual defection which itself is better than the sucker's pay-off.
  • Critically, the reward for two players cooperating with each other is higher than the average reward from defection and the sucker's pay-off.

Consider this example of a simple pricing game:

The values in the table refer to the profits that flow from making a particular output decision. In this simple game, the firm can choose to produce a high or a low output. The profit payoff matrix is shown below.

Firm B's output

High output

Low output

Firm A's output

High output

£5m, £5m

£12m, £4m

Low output

£4m, £12m

£10m, £10m

  • Display of payoffs: row first, column second e.g. if Firm A chooses a high output and Firm B opts for a low output, Firm A wins £12m and Firm B wins £4m.
  • In this game the reward to both firms choosing to limit supply and thereby keep the price relatively high is that they each earn £10m. But choosing to defect from this strategy and increase output can cause a rise in market supply, lower prices and lower profits - £5m each if both choose to do so.
  • A dominant strategy is one that is best irrespective of the other player's choice. In this case the dominant strategy is competition between the firms.
  • The Prisoners' Dilemma can help to explain the breakdown of price-fixing agreements between producers which can lead to the out-break of price wars among suppliers, the break-down of other joint ventures between producers and also the collapse of free-trade agreements between countries when one or more countries decides that protectionist strategies are in their own best interest.
  • The key point is that game theory provides an insight into the interdependent decision-making that lies at the heart of the interaction between businesses in a competitive market.

Potential Benefits from Collusion – A Game Theory Example

An industry consists of two firms, X and Y. The Profit-Payoff Matrix in the table below shows how the profits of X and Y vary depending on the prices charged by the two firms

Price charged by Business B

Price Business A = £20

Price Business A = £8

Price charged by Business A

Price Business A = £20

£12m A, £12m B

£16m A, £-2m B

Price Business A = £8

£-2m A, £16m B

£0m A, £0m B

If both businesses chose to collude on price rather than act competitively, the two firms would be able to increase their joint profits by £10m. However, if they agree to collude at the higher price of £20, then there is then an incentive for one business to under-cut the other, charge a lower price of £8 and inflicts a small loss on the other business.

Game theory - 2018 revision update:

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Geoff Riley

Geoff Riley FRSA has been teaching Economics for over thirty years. He has over twenty years experience as Head of Economics at leading schools. He writes extensively and is a contributor and presenter on CPD conferences in the UK and overseas.

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Game Theory Of Cheating

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