Game Theory In Terms Of Reporting Tax and Auction Strategies Assignment Sample

Introduction to Game Theory In Terms Of Reporting Tax and Auction Strategies Assignment Sample

The report is about two different types of games played in economics. The first game deals with submitting and reviewing tax documents by the ATO. Renee needs to figure out if she should give the truth about her earnings or hide some of the information. After that, the ATO decides whether to scrutinize her report. The following game is centered on the strategy of auctions. Two persons are interested in the same thing and they both try to guess how much it costs. Since they do not know everything, they have to choose what is best. This paper clearly describes each game in common language and illustrates the options taken by each player.

This Game Theory Assignment Sample explores tax reporting decisions involving Renee and the ATO, alongside auction strategies where bidders make choices under uncertainty. An Assignment writing helper can support students in understanding strategic interactions, incentives, and decision-making in economic scenarios.

Discussion

Question 1: Income Reporting and Random Audits of Tax

a) Renee’s Consequences and those of ATO after Lying and Getting Audited

In the course of the year, Renee earns enough to pay $5,000 in taxes at the end of the year. She deceives the authorities and claims to make less than the required income to reduce her taxes. It is decided by the ATO to carry out an audit on Renee (Paccagnan et al. 2022). Whenever she is audited, she will have to pay the complete $5,000. Moreover, her time and effort total $1,000 during the audit. Overall, Renee’s loss amounts to:

If tax is $5,000 and audit costs $1,000, at that time the total expense will be - $6,000

The ATO, after reviewing the records, pays $1,000 for the audit and ends up being refunded the $5,000 owed in taxes (Tang and Liang, 2023). Thus, their total gain comes from both the interest and the treasury balance.

Since I paid $1,000 for the audit and $5,000 for the tax, I still made $4,000.

As a result, Renee receives a payoff of -$6,000 while the ATO receives a payoff of $4,000.

b) The person Might Play the Bluffing Game

When someone bluffs, they pretend that something is true which not the case is (Chremos and Malikopoulos, 2024). There is a reason for Renee to try to fool others in this game. She has full knowledge of what she realizes, yet the ATO does not (Zheng et al. 2022). Even if she enjoyed a good year, she could end up with low income. This is an example of bluffing.

Renee pretends that this was her worst year when she really had a lot to be happy about (Nwogugu, 2025). Taking this action, she intends to reduce the tax she must pay by $5,000. Renee’s report is something that triggers the ATO to take any action.

c) In extensive form, a game is played out step-by-step and each player makes their move at a particular stage

There are just two parties in the game: Renee and the ATO. The game is carried out by taking these actions:

1. Nature has decided the kind of story Renee should write.

• It will be a good year (chance is 60%).
• The chances that 2023 will be a bad year are 40%.

1. Renee identifies her type and picks what she needs.

• Inflate the company’s reported income (H).
• Check off low income in the section where it is asked (L).

1. Renee’s report is the only one that the ATO can review. If Renee submits high income on her return, the ATO will not look into her return (Yan et al. 2024). There will be no adjustments made to the amount of personal allowance if her (L) declares no further income.

• Audit means to conduct an investigation (A)
• To avoid having an internal audit (N)

It is important to know that when ATO chooses, they cannot determine if Renee had good or bad earnings that year. The only detail they have is that she claims she has little income.

d) Total number of Pure Strategies

A pure strategy refers to an entire plan that covers every action.

There are 4 strategies that Renee can use:

• Write H if sales were examined in a good year, write H if sales were analyzed in a bad year.
• When the economy is strong, choose H as the rating and use L when it is weak.
• Select L if the year was good for the economy and choose H otherwise.
• If the year has been good, put down an L and if not, report an L too.

There are 2 pure strategies that ATO might use.

• Check the records of everyone reporting Levit.
• Never have auditors check the reports of someone who reports L.

As a result, Renee is using 4 strategies and ATO is using 2.

e) Game matrix and Nash Equilibria

Here is the matrix. Rows are the strategies used by Renee. The strategies used by ATO are columns.

Renee’s Strategies:

1. (H, H)
2. (H, L)
3. (L, H)
4. (L, L)

ATO’s Strategies:

1. Audit all the provided data in the form of L reports.
2. It is crucial not to perform an audit on L reports.

The payoffs are indicated as (Renee, ATO).

Yes, the company has completed an audit (A) and a new one is not required (N).

The curve belongs to the family with parameters (H, H), having values (-5000, 0) along the x-axis and y-axis.

The settlement on the points (H, L) is (-3600, 2000).

(L, H) (0.6×-1000 + 0.4×-5000: 0.6×-1000 + 0.4×0 = (-2600: -600: 0: 0)

In the (L, L) site, multiply by 0.6 for the minus and then by 0.4 for the plus and left is -3600 and right is 2000.

Now looked for the Nash Equilibria.

1. i) When Renee gives low numbers (L, L) all the time and ATO does not make any audits, then:

• Renee is given 0 points (the best for her).
• ATO does not have to bear any cost due to GST.
• Changing is not something most people want. That situation illustrates what is called a Nash Equilibrium.

1. ii) Renee takes deductions using (H, H) and then they are audited for a low-income return

• Irrespective of results, Renee’s cost is always 5000.
• ATO gets a score of 0 because they are never required to check and audit.
• However, the payoff Renee gets from having machines with low benefits is higher than the payoff she gets from having machines with medium benefits (Dütting et al. 2024). All of this shows that a stable balance has not been reached.

In other words, the main Nash Equilibrium is:

Renee plays (L, L), and No Audit is played by ATO

Both kinds of Renee behave identically which creates a pooling equilibrium.

f) The Situation does Renee regularly report findings as negative

Let p stand for the chance that Renee has a good year. It is known when a taxation review by ATO can happen.

The planned outcome for ATO when auditing is:

p times 4000 plus (1 – p) times (-1000) is equal to or greater than zero

Solve it:

4000p - 1000 p plus 1000p ≥ 0

Having a resolution of 5000p means 1000 or more pixels is not an issue.

p needs to be more than 0.2 to be significant.

Because of this, if p is less than 0.2, the ATO will opt out of an audit since the loss is too high (Burgess, 2022).

Consequently, she understands that she cannot be selected for an audit (Naidu et al. 2023). On that basis, she will report her income as being low.

Anytime the probability, p, is smaller than 0.2, Renee will not be truthful and will just keep lying.

It consists of all the following:

Whenever the result for p is less than 0.2, Renee claims that she receives low income.

g) Probability Renee is saying a good year is true, if she says her year was bad

This involves someone’s beliefs. Renee reports low income. People in the ATO are well aware:

• If Renee is honest, it shows that low income is a bad sign for the year.
• Renee could lie if she makes deliberate attempts to avoid telling the truth.

When Renee’s income is always low, regardless of whether she is an S or an M, the information in the report is useless (Pool et al. 2023). She saying she had a bad year still gives her a chance of having a good one, which means:

Still, 0.6 as it was before.

If this happens, it would probably indicate that Renee’s reporting was inaccurate in that year.

Bayes’ Rule in this situation can be used.

Imagined that Renee reports she earns only a little money.

This graph shows that the chances of getting a good year and lie work out to 0.6 × 1 = 0.6

When the chance of bad year is 0.4, the probability that truth is false = 0.4

The sum of all chances is 1.

So the changed probability that Renee had a great year given she said she made low income is:

0.6 divided by the sum of 0.6 and 0.4 gives 0.6

Sixty percent of them are in their places of origin.

Sometimes, in separating or semi separating equilibrium states, the level may be different.

Question 2: Private and Common Value Auctions

Question 1: The First-Price Auction model uses Bayesian Nash Strategy

In these auctions, people try to evaluate the other bidders to guess their bids (Zhang and Qin, 2021). The person who placed the highest bid is the winner and they need to cover their own bid.

All bidders know which card they received, yet not what the other person has been dealt. The value that Bidder 1 gets from the item is:

V₁ means taking the average of S₁ and S₂.

Therefore, Bidder 1 considers the worth of the object by considering their signal and what they think the other bidder might bid. In the same way, Bidder 2 loses.

People in this game believe their opponents are using a signal that is 50 on average.

So:

• Bidder 1’s expected value = the sum of S₁ and 50 divided by 2
• Bidder 2 is expected to win with a value of (S₂ + 50)/2

Most bidders try to bid an amount lower than what the item is worth to keep from paying too much.

This kind of game finds the best bidding function as being:

b(S) = S divided by 4 and then increased by 50

So:

• Bidder 1 submits the bid value of b₁(S₁) = (S₁ + 50)/4
• Bidder 2 bids b₂(S₂) = (S₂ + 50)/4

This is when the Bayesian Nash Equilibrium occurs.

Question 2: Second-Price Auction – Strategic Thinking

In this type of auction, the winner is the person with the second-highest bid and they pay for the item.

In this format, the best move is to put in a bid equal to how much the item is worth.

So:

• Bidder 1 bids V₁ = The number halfway between S₁ and S₂
• Still, the value of S₂ is not known. For this scenario, Bidder 1 picks the expected value of S₂ to be 50.

So:

• Bidder 1 offered (S₁ + 50) and then divided it by 2
• Bidder 2’s bid = (S₂ + 50)/2

That is a good way to address these challenges. There is no benefit for the bidders to bid below their highest value because they keep all the profit they make.

Question 3: Planned revenue and standard revenue

Revenue Equivalence Principle means that, when certain conditions exist, the auction types end up giving the same revenue to the seller.

Still, these factors make up the following:

• A bidder usually values their offer at a specific level.
• There is no shared value between them
• Bidders do not care about risks.

The values in this game are affected by the other person’s signal (Ara and Northcote, 2023). This is a typical aspect of values.

It goes against one of the main points of the principle.

In this case, revenue equivalence principle is not a perfect match.

As a result, in first-price auctions, people tend to bid a bit low which means the seller’s earnings may be slightly less on average than when there are second-price auctions.

Conclusion

It covers two key concepts found in game theory. Initially, discovery is done regarding how Renee might fool the tax office and it explains why the tax office might pick or avoid auditing her account. It is also found out that game theory helps determine if someone will act honestly or dishonestly depending on what they can gain.

During the following part, it is observed how bidders in these auctions use their own pieces of information as well as what the other party does not reveal. The discussion is done in this regard those strategies for bidding and the number of sales an auctioneer makes rely on what each bidder knows about the auction. The parts rely on easy concepts like “who knows what,” “who moves when,” and “what happens next” to solve tough issues.

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Reference List

Journals

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