Game Theory Questions and Examples

Question 1: Evaluating the Statement on Dominant Strategies

1.Evaluate this statement:  “If a player has only two available strategies, if one strategy is a dominant strategy then the other strategy MUST be dominated.”

2.Evaluate this statement:  “If a player has more than two available strategies, if one strategy is a dominant strategy then it is not necessarily true that there exists a dominated strategy.”

3.Please provide a unique and original example of a game with multiple Nash Equilibrium.  Describe the game completely, draw the payoff matrix, identify the Nash equilibria, and discuss which outcome is most likely (and why).

4.Suppose that there are two firms, A and B, which have joined together to take advantage of a business opportunity.  Each firm is called on to make an investment in an asset that is entirely worthless outside of the joint venture.  To keep matters simple, suppose that the project requires that each party make an initial investment of $2 each, and the gross return from the investment is 8; yielding a net benefit of $4.  Suppose that the division of the gross benefits between the two firms can be affected by costly actions that each takes.  Specifically, suppose the possible actions are “grab” or “don’t grab,” where grabbing costs 3.  Assume that when both firms choose “grab” they split the gross return.  Further, if both firms choose “don’t grab” they also split the gross returns.  Finally, assume that grabbing works fully – so that the firm that grabs gets the entire gross return.  Please draw out a payoff matrix for this game and discuss its outcome.  What type of game is this?  Explain.