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Let A = (aij ) and B = (bij ) be two n × m matrices representing two-player zerosum games in strategic form. Prove that the difference between the value of A and the value of B is less than or equal to
maxni=1 maxmj=1 |aij - bij|.
Prove that every 2 × 2 game has a Nash equilibrium. - Do this by considering the following general game and breaking the analysis:
Write down the payoff table for this game, and find the equilibrium when the two firms move simultaneously. Write down the game tree for this game, with Coke moving first and Pepsi following.
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.
An injection molding machine produces golf tees that are 20.0% nonconforming. Using the normal distribution as an approximation to the binomial, find the probability that, in a random sample of 360 golf tees, 65 or less are nonconforming. Show you..
What is the payoff of a person whose number is the highest of the three? Can she increase this payoff by announcing a different number?
Find the subgame perfect Nash equilibria of this new model and compare it/them with the subgame perfect equilibrium of the original model.
Show that army 2 can increase its subgame perfect equilibrium payoff (and reduce army 1's payoff) by burning the bridge to its mainland, eliminating its option to retreat if attacked.
First, player 1 selects a real number x, which must be greater than or equal to zero. Player 2 observes x.- Then, simultaneously and independently, player 1 selects a number y1 and player 2 selects a number y2, at which point the game ends.
The following payoff matrix represents long run payoffs for 2-duopolists faced with the option of purchasing or leasing buildings to use for production.
problem 1a in the game from the previous problem set old lady crossing the street identify all pure strategy nash
Give examples to show that neither of the above properties necessarily holds for a game that is not strictly competitive.
Calculate and graph each player's best-response function as a function of the opposing player's pure strategy.- Find and report the Nash equilibria of the game.
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