Two countries, Alpha and Beta consider the construction of a bridge across a river that separates them. The bridge would increase commerce and trade in both countries. If they both contribute to the building of this bridge, then each receive a profit of $32 million. However, if they both fail to contribute, they are each left with a profit of just $30 million. If one country contributes and the other one does not, then the country that does not contribute is a “free rider” and will receive a profit of $35 million. The contributing player spends a lot of money building the bridge and is left with a profit of only $28 million.
Two countries, Alpha and Beta consider the construction of a bridge across a river that separates them. The bridge would increase commerce and trade in both countries. If they both contribute to the building of this bridge, then each receive a profit of $32 million. However, if they both fail to contribute, they are each left with a profit of just $30 million. If one country contributes and the other one does not, then the country that does not contribute is a “free rider” and will receive a profit of $35 million. The contributing player spends a lot of money building the bridge and is left with a profit of only $28 million.
5.1. Fill out the payoff matrix (below) for the game by including all the elements (players, their strategies, and their payoffs).
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5.2. Assume the players do not cooperate. Solve the game for the Nash equilibrium (find out the strategy played by each player in equilibrium). What is the payoff each gets when they play the Nash equilibrium?
5.3. Assume that players start with cooperate and play tit-for-tat strategy forever. Fill out the table below.
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Alpha |
Beta |
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Round 1 |
Strategy |
Strategy |
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Payoff |
Payoff |
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Round 2 |
Strategy |
Strategy |
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Payoff |
Payoff |
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Round 3 |
Strategy |
Strategy |
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Payoff |
Payoff |
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Round 4 |
Strategy |
Strategy |
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Payoff |
Payoff |
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Round 5… |
Strategy |
Strategy |
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Payoff |
Payoff |
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