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Ronald and Jimmy are betting on the result of a coin toss. Ronald ascribes probability 1/3 to the event that the coin shows heads, while Jimmy ascribes probability 3/4 to that event. The betting rules are as follows: Each of the two players writes on a slip of paper "heads" or "tails," with neither player knowing what the other player is writing.
After they are done writing, they show each other what they have written. If both players wrote heads, or both players wrote tails, each of them receives a payoff of 0. If they have made mutually conflicting predictions, they toss the coin. The player who has made the correct prediction regarding the result of the coin toss receives $1 from the player who has made the incorrect prediction. This description is common knowledge among the two players.
(a) Depict this situation as a game with incomplete information.
(b) Are the beliefs of Ronald and Jimmy consistent? Justify your answer.
(c) If you answered the above question positively, find the common prior.
(d) Find a Bayesian equilibrium in this game (whether or not the beliefs of the players are consistent).
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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