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Equilibria of a variant of BoS with imperfect information:-
Show that there is no pure strategy Nash equilibrium of this game in which player 1 chooses S. If you have studied mixed strategy Nash equilibrium (Chapter 4), find the mixed strategy Nash equilibria of the game. (First check whether there is an equilibrium in which both types of player 2 use pure strategies, then look for equilibria in which one or both of these types randomize.)
We can interpret the actions of the two types of player 2 to reflect player 2's intentions in the hypothetical situation before she knows the state. We can tell the following story. Initially player 2 does not know the state; she is informed of the state by a signal that depends on the state. Before receiving this signal, she plans an action for each possible signal.
After receiving the signal she carries out her planned action for that signal. We can tell a similar story for player 1. To be consistent with her not knowing the state when she takes an action, her signal must be uninformative: it must be the same in each state. Given her signal, she is unsure of the state; when choosing an action she takes into account her belief about the likelihood of each state, given her signal. The framework of states, beliefs, and signals is unnecessarily baroque in this simple example, but comes into its own in the analysis of more complex situations.
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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