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Three game theorists work on a team project. Assume they work independently, and it is not possible for them to monitor each other. No one likes working, and the cost of efforts is measured in dollars. Each player can work up to 5 hours, and the cost per working hour is $6. The quality and hence the profit of the project is determined by the joint efforts (total number of working hours) of the three players. For each additional hour that the team invests in the project, up to 10 hours, the total profit will increase by $15. After 10 hours, efforts will not increase profits. Assume players divide the profit equally among them. Hence, each player's payoff is his share of the profit minus his cost. There is common knowledge of rationality.
(a) What is the strategy space (the set of strategies) for each player?
(b) What is the payoff for each player as a function of the strategy profiles?
(c) Compute the set of rationalizable effort levels for each player.
(d) Suppose one player is kicked out of the team, and the remaining two players still share the profit equally. Compute the set of rationalizable effort levels.
Player 1 has the following set of strategies {A1;A2;A3;A4}; player 2’s set of strategies are {B1;B2;B3;B4}. Use the best-response approach to find all Nash equilibria.
A supplier and a buyer, who are both risk neutral, play the following game, The buyer’s payoff is q^'-s^', and the supplier’s payoff is s^'-C(q^'), where C() is a strictly convex cost function with C(0)=C’(0)=0. These payoffs are commonly known.
Pertaining to the matrix need simple and short answers, Find (a) the strategies of the firm (b) where will the firm end up in the matrix equilibrium (c) whether the firm face the prisoner’s dilemma.
Consider the two-period repeated game in which this stage game is played twice and the repeated-game payos are simply the sum of the payos in each of the two periods.
Two players, Ben and Diana, can choose strategy X or Y. If both Ben and Diana choose strategy X, every earns a payoff of $1000.
The market for olive oil in new York City is controlled by 2-families, Sopranos and Contraltos. Both families will ruthlessly eliminate any other family that attempts to enter New York City olive oil market.
Following is a payoff matrix for Intel and AMD. In each cell, 1st number refers to AMD's profit, while second is Intel's.
Determine the solution to the given advertising decision game between Coke and Pepsi, assuming the companies act independently.
Little Kona is a small coffee corporation that is planning entering a market dominated through Big Brew. Each corporation's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price.
Suppose you and your classmate are assigned a project on which you will earn one combined grade. You each wish to receive a good grade, but you also want to avoid hard work.
Consider trade relations in the United State and Mexico. Suppose that leaders of two countries believe the payoffs to alternative trade policies are as follows:
Use the given payoff matrix for a simultaneous move one shot game to answer the accompanying questions.
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