Chapter 13, Problem 1TY

Examine the payoff matrix below which involves two beverage companies: “Pepsi and Coke”. The dollar values within the cells represent profit values from advertising strategies under different scenarios. Determine Pepsi’s “dominant strategy”.

Using only numbers 0 and 1 for payoffs, construct a 4x4 game that has a solution through iterated dominance in themaximal possible number of steps.

Suppose that the following prisoner's dilemma game (stage game) is played repeatedly and players discount future payoffs with the common discount factor δ <1.  a)    Carefully specify the strategy spaces for both players, draw the extensive form game and find a subgame perfect Nash equilibrium when the stage game is played twice, and both players observe the outcome of the first play.

Burger Doodle, the incumbent firm, wishes to set a limit price of $8 (rather than the profit-maximizing price of $12) to prevent Designer Burger from entering its profitable market. The game tree above shows the payoffs for various decisions. Burger Doodle makes its pricing decision, then Designer Burger decides whether to enter or stay out of the market. If Designer Burger chooses to enter the market, then Burger Doodle may or may not decide to accommodate Designer’s entry by changing its initial price to the Nash equilibrium price of $10. If Burger Doodle canNOT make a credible commitment to maintain its initial price should Designer Burger decide to enter the market, then Burger Doodle will set price equal to $________ at decision node 1 and the outcome _____________(is, is not) a Nash equilibrium.

Normal-Form GameFind all Nash equilibria of the following two-player game. Provide necessary computation.

A typical centipede game has (A) many pure-strategy Nash equilibria; (B) a unique Nash equilibrium that can be found by backward induction; (C) a dominant strategy equilibrium; (D) none of the above.

Demonstrate the nature of the chain store paradox by constructing, solving and discussing a suitable game theoretical example with at least three players

Is the set of SPE of any extensive form game with perfect information is identical to the set of Nash Equilibria of the induced normal form game? If yes, provide a proof. If no, provide an explanation by illustrating a game. [Maximum word limit for this question is 80 words.]

Two firms are considering simultaneously developing a new product for a market.  The costs of developing the product are $10m but there will only be revenue in the market of $40m if only one of the firms develops the product.  If both firms develop the product then earnings/revenues will be competed away. a) Capture this entry game in a payoff matrix.          b) What is the Nash equilibrium and why? Please provide explanation.  c) Does either firm have a dominant strategy? Please provide explanation.