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Prove that every 2 × 2 game has a Nash equilibrium (in either pure or mixed strategies). Do this by considering the following general game and breaking the analysis into two categories:
(a) one of the pure-strategy profiles is a Nash equilibrium, and
(b) none of the pure-strategy profiles is a Nash equilibrium.
What are the solutions to this game and how much is it worth to you to get your casino building permit first
Adapted from the battle game "Bowser's Bigger Blast" from Nintendo's "Mario Party 4"- Is this a fair game?- Or, is one player more likely to lose than the others?
Determine the critical discount factor above which cooperation between the two firms can be sustained (i.e., playing grim trigger strategy by both firms is an equilibrium in the repeated game).
A survey of 356 local drivers reveals that 18.7% of them car pool. Is there evidence that the actual proportion of local commuters car-pooling is less than national level. Also find and interpret the p-value of this test.
A 40 year annuity due has level annual payments of $1000 except for the m-th payment which is $2000. When using an annual effective interest rate of 5%, the value of the annuity four years after the first payment is $22,722.53 Find M.
Critical Thinking: Suppose you and a friend each take different random samples of data pairs (x,y) from the sample population. Assume the samples are the same size.
Assume two competitors every face important strategic decisions where payoff to each decision depends upon reactions of the competitor. Company A can select either row in the payoff matrix defined below,
Examine the common price setting strategies of airlines that use game theory. Predict the potential effects of such pricing strategies on the demand for seats, and conclude the resulting impact on the profitability of the airlines
What is firm 2's optimal quantity as a function of q1, conditional on entry? - Compute the subgame perfect Nash equilibrium of this game.
A poll by Louis Harris and Associates of 1249 adult Americans indicated that 36% believe in ghosts and 37% believe in astrology. Can you compare the proportions using inferential methods for independent binomial samples? If yes, do so. If not, exp..
Assume you are one of two manufactures of tennis balls. Both you and your competitor have zero marginal costs. Total demand for tennis balls is
In a two player, one shot simultaneous move game each player can select strategy A or B. If both players select strategy A, each receives a payoff of $500.
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