Consider an infinitely repeated partnership game between two players. In each period, the players select actions in the stage game, with common knowledge of the outcomes in all previous periods. In the stage game, player 1 selects a number x and player 2 selects a number y, where x and y are required to be in the interval from 0 to 10. Player 1's stage-game payoff is u1(x, y) = xy + 4x -x2
and player 2's stage-game payoff is
u2(x, y) = xy + 4y - y2
The players discount the future and have the same discount factor 8, which is strictly between 0 and 1.
1. Find the Nash equilibrium of the stage game.
2. Suppose that the players are interested in coordinating to select actions x = y = 10 in each period.

Consider a two-firm industry. firm 1 (the incumbent) chooses a level of output q1. firm 2 (the potential entrant) observes q1 and then chooses its level of output q2. the demand for the product is p = 100 - q, where q is the total output sold by the two firms which equals q1 +q2. assume that the marginal cost of each firm is zero. a) find the subgame perfect equilibrium levels of q1 and q2 keeping in mind that firm 1 chooses q1 first and firm 2 observes q1 and chooses its q2. find the profits of the two firms-? 1 and ? 2- in the subgame perfect equilibrium. how do these numbers differ from the cournot equilibrium? b) for what level of q1 would firm 2 be deterred from entering? would a rational firm 1 have an incentive to choose this level of q1? which entry condition does this market have: blockaded, deterred, or accommodated? now suppose that firm 2 has to incur a fixed cost of entry, f > 0. c) for what values of f will entry be blockaded? d) find out the entry deterring level of q1, denoted by q1b, as a function of f. next, derive the expression for firm 1

Needs to schedule the staffing of the center. it is open from 8am until midnight. larry has monitored the usage of the center at various times of the day and determined that the following number of computer consultants are required: time of dayminimum number of consultants required to be on duty8 am-noon4noon-4 pm84pm-8pm108pm-midnight6 two types of computer consultants can be hired: full-time and part-time. the full- time consultants work for eight consecutive hours in any of the shifts: morning (8am- 4pm), afternoon (noon-8pm) and evening (4pm-midnight). full-time consultants are paid $14 per hour. part-time consultants can be hired to work any of the four shifts listed in the table. part-time consultants are paid $12 per hour. an additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty. larry would like to determine how many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost. formulate this as an lp problem. you must define your variables clearly

Warner inc. sells a high-speed retrieval system for mining information. it provides the following information for the year. budgeted actual overhead cost $965,700 $905,000 machine hours 58,570 49,200 direct labor hours 107,300 104,200 overhead is applied on the basis of direct labor hours. compute the predetermined overhead rate. predetermined overhead rate $ per direct labor hour link to text determine the amount of overhead applied for the year. the amount of overhead applied $