**ECON3534. Developments in Advanced Microeconomics**

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**Ruben Martinez Cardenas**

**Assessment 1 Part a**

**Submission deadline: Wednesday 16 December, 11:59 AM**

Answer the following questions using the theoretical concepts reviewed in the lectures and seminars. Be formal, clear and tidy when presenting your answers. If you are using a result you should clearly state what result you are using. Plain answers without the corresponding procedure that produced the result will be penalised.

**Problem 1. Users’ data game problem**

There are two social network platforms, *FB* and *SC*. Both platforms generate revenues from advertisement and by selling user’s data to third parties. Users do not care much about their data being used to generate revenues by the firms as long as the level of exploitation is moderate. However, users experience dissatisfaction as their information is more commercialised, leading them to abandon the platforms if the use is too excessive. Therefore, firms face a tradeoff between exploiting users’ data, and keeping their user base. The two firms have the same strategies available, they can either choose low (*L*), medium (*M*), or high (*H*) level of data exploitation, that is, the set of strategies available to *FB* is , and for SC is . The payoffs perceived by each firm are represented by , the payoff are the payoff perceived by FB when FB follows strategy and SC follows strategy . Similarly, the payoff are the payoff perceived by *SC* when *FB* follows strategy and SC follows strategy . The specific payoffs for each firm for each pair of strategies followed by the firms are, for *FR*, , , , , , , , , ; and for SC, , , , , , , , ,

Assume for the first part of the problem set that the players play a simultaneous game, with both moving at the same time

- Construct the game representation in strategic form, where the first element of each pair of payoffs in any of the cells indicates the payoff to firm
*FB*and the second element indicates the payoff to firm*SC*, that is (FB’s Payoff, SC’s payoff) (5 marks) - Indicate the best responses of each player in the following form: , where is one of the players, say
*FB*, and if the other player, say*SC*. (5 marks) - Find all dominated strategies, either weakly or strictly dominated, and indicate each of them. Using iterated elimination of dominated strategies, construct a reduced form game and show this new game in its strategic form. Indicate any equilibria for this game. (10 marks)
- Find the Nash equilibria, if any, for this game, and show why the proposed equilibria are in fact Nash equilibria. (5 marks)
- If the government would like to observe as a Nash equilibrium outcome, how can it modify the payoffs? Explain your answer and construct the new game in strategic form, and show that the strategies are in fact a Nash equilibrium. (10 marks)
- Consider the original game and assume now that platform
*FB*moves first, and then, after observing*FB*’s move, platform*SC*chooses its strategy- Express this new game in its extensive form (5 marks)

- In this case, with
*FB*moving first and*SC*second, What equilibrium is more likely to emerge in this game? Use backward induction to find the equilibria, if any. (10 marks)

- Are the results in the extensive form game different from does in the strategic game? Explain why? (5 marks)

**Problem 2. Mixed strategies**

Consider the following game

- There are two players: and
- The action sets for each player are: for , for

- Players and choose strategies and respectively

- The payoffs are given by , for

- The specific payoffs are the following: , , , , , , , and .

- Specify this game in its strategic form (5 marks)
- Are there any equilibria in pure strategies? Justify your answer clearly (5 marks)
- Find a mixed strategy equilibrium for this game. Assume that assigns a probability equal to to playing strategy , and a probability to playing strategy . Similarly, assume assigns a probability to playing strategy , and a probability to playing strategy . (15 marks)

**Problem 3. Utility maximisation and competitive market equilibrium**

The firm you work for, Coxtech, is asking you to determine which price should the company set for product *x* in a new location called market *N*, where the firm is planning to enter next year. You don’t have data available for the new market, what you have is an estimated utility function for market *E *where Coxtech is already operating. The estimated utility function for a tipical consumer in market *E *is .

Recent studies show that the preferences of consumers in market *N,* for goods that are similar to good *x*, are more sensitive in comparison to consumers in market *E*, where the company is already present. These estimates indicate that consumers’ valuation for products similar to *x* in market *N* are valued 20% more than what consumers in market *E* value them. Studies also show that in market *E, *even if they don’t consume the good, consumers value the fact that good *x* is available in the market in an equivalent of 3 utils, you can identify this in the utility function. In contrast, the studies show that in market *N* consumers only get satisfaction from consuming the good and they don’t get any satisfaction from the mere fact that the product is available.

Finally, both markets have the same supply function: , there are a total of 100 identical consumers in each market *E* and market *N*, and the firms are price takers.

- Obtain the marginal utilities for market
*E*and market*N*. What is different in the two cases in terms of valuations for good x? (10 marks) - Find the equilibrium price and quantity for both market
*E*and market*N*assuming perfect competitive markets and that both markets have 100 consumers each (10 marks)

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