# Discussion on Introduction to Game Theory

Game theory questions
Looking for help with some game theory questions.BOOK BEING USED:Osborne, Martin. (2004). Introduction. An Introduction to Game Theory. Oxford, New York: Oxford University Press. (IGT)

Problem 1:

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Consider a situation in which each of two economic agents chooses whether to join (J) efforts in a business project or not (N), and neither agent, when making his or her decision, knows the action chosen by the other agent. If both agents decide to work together (J), agent 1 gets a profit of \$2,000,000, and agent 2 receives a profit of \$1,000,000. If each agent decides to work as a sole investor (N), agent 1 earns \$1,000,000, while agent 2 earns \$2,000,000. If one agent is willing to join (J) for a common investment, and the other agent does not (N), each agent earns zero profits.

1. Draw a game-tree that represents this situation.
2. Describe the situation as an extensive form with imperfect information. Identify players, terminal histories, player function, information sets, chance, and preferences.
3. Provide a behavioral strategy for player 1 and a behavioral strategy for player 2.
4. Determine the Nash and subgame-perfect equilibria in pure strategies of the game.

Problem 2:

Consider the situation described in Figure 1 below

1. Represent the strategic form of the game.
2. Determine all Nash equilibria in pure strategies of the game.
3. Determine the subgame-perfect equilibria in pure strategies of the game.
4. Is it plausible or credible to have the situation (R, R’) as an equilibrium in this game? Explain.
5. Assume that player 2 believes that history L occurred with probability p, and history M occurred with probability 1-p.
1. Given player 2’s belief, calculate player 2’s expected payoff from playing R’ and player 2’s expected payoff from playing L’ ?
2. Given the belief, what action should player 2 choose between R’ and L’? Explain.
3. Requiring that each player has a belief and acts optimally given this belief, would any change occur in the subgame-perfect equilibria found in question 3.?

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