Hinge is a local company that has developed a dating application for mobile phones. Both men and women subscribe to the mobile application where they are matched. Besides people liking each other, the ‘value’ of likes has declined over time as many users like each other in the app but do not message each other, let alone meet face-to-face. The company is considering introducing an additional feature on the app, where a signaling mechanism is used. Complete the two tasks below based on the working paper ‘Soohyung Lee & Muriel Niederle

1. Hinge is a local company that has developed a dating application for mobile phones. Both men and women subscribe to the mobile application where they are matched. Besides people liking each other, the ‘value’ of likes has declined over time as many users like each other in the app but do not message each other, let alone meet face-to-face. The company is considering introducing an additional feature on the app, where a signaling mechanism is used. Complete the two tasks below based on the working paper ‘Soohyung Lee & Muriel Niederle (2015) Propose with a rose? Signaling in internet dating markets(No. 17340). National Bureau of Economic Research’.

• Discuss how the introduction of this new feature can improve the matching between both groups.
• Explain whether it makes a difference if the number of signals that each person can send is limited or unlimited? Explain your answer.

2. According to ‘Roth, A. E. (2007). What Have We Learned From Market Design? (No. w13530). National Bureau of Economic Research’ what are the three characteristics that marketplaces should have to work well? Briefly explain the role each of them plays on market performance.
3. Consider the matching problem for a marriage market. On one side we have women, and on the other one, men. In this market, women and men coincide in order to match with members of the other group. Assume there are 4 women: Maryam, Ada, Carmen, Esther; and 4 men: Alvin, Jean, Satoshi, and Abhijit.

Consider the following preferences:
Men

Women

Use the deferred acceptance matching mechanism to answer the following items:

• Present the Deferred acceptance algorithm (Gale-Shapley,1962), and explain clearly how it works.
• If the matching algorithm starts with men proposing, what pairs will result from the matching?
• Would a woman proposing matching render a different result? Which one benefits more men and which one woman? Why?

4. K technologies (K) and Maple digital (M) are deciding which programming language they should adopt for their new machine learning application in their respective platforms. They have users that are exclusive to each platform and other users that multi-home, that is users that use both platforms. There are three programming languages: Rattle, Cricket, and Nova. K’s platform is more compatible with Rattle, while M is more compatible with Nova. However, in terms of multi-homing, Cricket is more suitable for both firms and for the users. The payoff (profits) for each firm are shown in the payoff matrix below, in each cell, the first number in the pair corresponds to the payoff to player K and the second number to the payoff to player M, that is (Payoff for K, Payoff for M). These quantities are in millions of sterling pounds.

• Find all Nash equilibria for this game
• Researchers in the UK have found that users would benefit from both platforms using programming language Cricket. The estimated benefit is 4.5 million sterling pounds. The Government is willing to spend up to 2 .5 million sterling pounds in subsidies to incentivize K technologies and Maple digital to migrate to Cricket programming language. Modify the payoff matrix above in such a way that the firms find it optimal to migrate to Cricket. Verify these strategies are the only equilibrium and that it is actually a Nash equilibrium.

Now, the Danish company ICE has invited K technologies (K) and Maple digital (M) to start a new platform in Denmark. ICE can select only one programming language for the platform and has asked both K and M to report which language they will use for the new platform, once they report they stick to their choices, ICE will decide which one to use depending on the reports. K and M have information on the expected payoffs, for each company, depending on what language they use for this new platform. This information is the same for both companies. Again, K and M have three possible strategies: Rattle, Cricket, and Nova. The payoffs for each possible combination of strategies is summarized below in the payoff matrix

• Find the Nash equilibria for the game above. Assume both K and M choose their strategies simultaneously.
• ICE has decided K will submit its response first, then M will be informed of K response before submitting its response. Express this game in its extensive form.
• Find the subgame perfect equilibrium for the game above, if any.