ECON 20005: Competition and Strategy
Assignment One
Semester 2, 2025
Question 1: AI Chip Wars – Nvidia vs. StarSilicon
Nvidia is the dominant incumbent in the booming AI chip market, supplying GPUs for everything from gaming to AI data centers. A new startup, StarSilicon, is considering entering the market with a next-gen chip design. The potential reward is high—but so are the risks.
StarSilicon decides whether to Stay Out (O) of the market or enter the market with Cautious R&D (C), costing $2, or Ambitious R&D (A), costing $4. If StarSilicon chooses to Stay Out (O), StarSilicon’s and Nvidia’s payoffs/profits are $0 and $10, respectively.
If StarSilicon chooses to enter the market, after seeing StarSilicon’s entry and R&D choice, Nvidia subsequently chooses whether to run a marketing campaign—either Market (aggressive marketing and discounting, M) or Do Nothing (N). The cost of Market (M) is $3.
StarSilicon’s R&D yields Success (S) or No Success (NS) with probabilities p and 1 - p.
If StarSilicon enters the market with Cautious R&D (C), then p = 0.3; if StarSilicon invests in Ambitious R&D (A), then p = 0.9.
If Nvidia chooses Market, then Nvidia’s and StarSilicon’s revenues are $8 and $4 if StarSili- con’s R&D is successful, and $12 and $0 if not successful. If Nvidia chooses Do Nothing (N), then Nvidia’s and StarSilicon’s revenues are $5 and $5 if StarSilicon’s R&D is successful, and $10 and $0 if not successful.
The outcome of StarSilicon’s R&D is determined by Nature after Nvidia and StarSilicon make their choices.
1.1 What is StarSilicon’s payoff/profit (revenue minus cost) if it chooses Ambitious R&D (A), Nvidia chooses Do Nothing (N), and the R&D is not successful? What is Nvidia’s pay- off/profit if it chooses to Market (M), and StarSilicon chooses Cautious R&D (C) and the R&D is successful?
1.2 Determine whether information is perfect or imperfect in this game. Briefly explain.
1.3 Present this game using a game tree (i.e., in extensive form).
1.4 List all the possible strategies of the sequential game for Nvidia and StarSilicon.
1.5 Predict what will happen in the game by characterizing the SPNE. In particular, what are the SPNE strategies for each player, as well as the SPNE path and payoffs?
1.6 Present the game in normal form.
1.7 Find the PSNE using the normal form (from 1.6) and compare it with the SPNE that you found in (1.5). Briefly explain why there is a difference.
1.8 If the cost of Market (M) is $2.4, do you expect the game outcome to change? If so, what are the new SPNE strategies, path, and payoffs? Briefly explain what will happen in the game and why.
1.9 Now go back to the original game where the cost of Market (M) is $3. Suppose the order of moves changes so that Nvidia chooses Market (M) or Do Nothing (N) before StarSilicon’s choice of Stay Out (O), Cautious R&D (C), or Ambitious R&D (A). Note that the order of moves does not change the R&D success probability. Draw the game tree. Given the expected payoffs, what do you expect will happen in the game? What are the SPNE strategies, path, and payoffs if Nvidia moves first? Does Nvidia prefer moving first or moving second?
2+1+3+3+3+2+2+3+5=24 Marks
Question 2: Harry Potter and Ron Weasley’s Magical Adventure
Harry and Ron, two friends who respectively live at 4 Privet Drive and The Burrow, are consider- ing taking a last-minute adventure together on Harry’s birthday. They consider using Floo Powder to travel to either Godric’s Hollow (GH) or the Quidditch World Cup Final (Q). Unfortunately, Harry’s uncle, Vernon Dursley, forbids Harry from contacting his friends at Hogwarts, so there is no direct communication with Ron. That means they must decide where to go simultaneously.
Another complication is that Harry loves visiting Godric’s Hollow, his birthplace, while Ron loves supporting his favorite Quidditch team at the World Cup Final. If Harry and Ron go to Godric’s Hollow together, they respectively get happiness of 8 and 1. In contrast, if they go to the Quidditch World Cup together, they respectively get happiness of 3 and 5. If they end up in differ- ent places, they will both be miserable and receive happiness of -1 regardless of where each ends up.
2.1 Draw the normal and extensive form of the game. (The row player is Harry in the normal form game.)
2.2 Find all PSNE.
2.3 If there are multiple equilibria, which equilibrium do you think Harry and Ron are more likely to choose? Briefly explain.
2.4 Now suppose all payoffs remain the same, except that Harry makes his choice of destination first, and then Ron chooses where to go upon seeing Harry’s choice. Draw the extensive form of this new game.
2.5 Characterize the SPNE (i.e., state the SPNE path, each player’s SPNE strategies, and the SPNE payoffs).
2.6 Does this game have a first or second mover advantage? Briefly explain.
2.7 Keeping with the same sequential game from 2.4, now suppose that before Harry or Ron make their destination choices, Ron has the option to first purchase a special Quidditch pack for a cost of 5. If he buys the Quidditch pack, Ron will receive a Omnioculars at the World Cup, giving Ron a happiness of 15. Assume all other payoffs remain the same as before from part 2.4 (for example, if Ron buys the Quidditch pack and ends up in the World Cup alone, his net payoff is 15-5-1=9). Draw the extensive form of this game and characterize its SPNE (i.e., state the SPNE path, each player’s SPNE strategies, and the SPNE payoffs).
2.8 Can the Quidditch pack be seen as a sort of “commitment device” for Ron to ensure they end up at the Quidditch World Cup? Briefly explain.
5+2+1+2+3+3+4+2=22 Marks
Question 3: Backward Induction
Three rational kids, Alice, Bob, and Charlie, find 5 bars of chocolate. Each kid would like to get as many bars as possible. The kids decide to distribute the bars as follows: Alice proposes a distribution of bars. The three kids then vote on whether or not to accept this distribution. If two or more of the three kids vote to accept this distribution, the bars are distributed according to Alice’s suggestion. Otherwise, Bob can decide how to distribute the bars (and there is no vot- ing). Find the equilibrium distribution of the bars of chocolate using backward induction. Briefly explain each necessary step of reasoning.
4 Marks