# 1. Evaluate this statement: “If a player has only two availa...

## Question

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 colled 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.

## Solution Preview

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1. Yes. Dominated strategy is a strategy that yields a lower payoff than any other strategy regardless of what strategy is chosen by all other players. If one strategy is a dominant strategy, it gives the player a higher payoff than any other strategies whatever move the opponent takes than the other strategy. It implies that the other strategy gives a lower payoff than the dominant strategy whatever move the opponent makes.

2. The same line of though can be constructed even if a player has more than two strategies in which one of them is a dominant strategy. There must exist a dominated strategy by...

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