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1. Explain how you would formulate a strategy for playing the paper–rock– scissors game on a repeated basis.
2. Explain why it makes a difference in a repeated game if the end of the game can be foreseen.
3. Explain why in ultimatum bargaining games the result is often a fifty–fifty split between the players. Does this contradict the predictions of game theory?
4.Let’s have fun with game theory, which can shed some light on the outcome of the monetary policy dispute between Prime Minister Thaksin Shinawatra and former Bank of Thailand governor MR Chatu Mongol Sonakul.
Many might be perplexed by Chatu Mongol’s abrupt dismissal after he refused to cave in to the government’s demand to raise interest rates. But by applying game theory to analyse the jostling between the two, one may find a surprising answer and become more aware of the usefulness of the tool. We know that Thaksin and Chatu Mongol took polar positions on the issue and are by nature rather proud and stubborn. So let us begin by constructing what the payoff matrix for the interest rate policy would have been before Chatu Mongol was sacrificed.
Faced with Thaksin’s command to ‘review’ the central bank’s longstanding low interest rate policy, Chatu Mongol could do one of two things – concede to Thaksin, or not give way. Similarly, Thaksin had two options in dealing with the obstinate governor – either fire him or keep him. In order to keep the game simple, we rank the preferences for the possible outcomes from worst to best, and assign the respective payoffs the numbers 1 through to 4. Chatu Mongol had made it perfectly clear that he had no intention of changing the low interest rate policy. Therefore, the worst outcome for Chatu Mongol was to concede but then get fired, so that outcome would have a payoff of 1 for him.
The second worst outcome was to concede and not be fired, but that would leave Chatu Mongol with his integrity bruised and the central bank with its independence impaired.
The third worst outcome was not to concede, and get fired. Though he might lose his job, he could still maintain his integrity and time could prove his stance correct.
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Chatu Mongol’s strongest preference was not to concede, but still keep his job. This outcome would have a payoff of 4 for him. This would mean he had beaten Thaksin in their two-way gamesmanship. Meanwhile, the worst outcome for Thaksin would be for Chatu Mongol to defy his demand, but to keep the maverick as central bank governor.
The second worst option was for Chatu Mongol to make a concession, but for the PM to have to fire the governor anyway to avoid future trouble. The next worst scenario was for Thaksin to fire Chatu Mongol for his defiance. Thaksin’s highest preference was for Chatu Mongol to fully agree with his demand so that he would not have to get rid of him as governor.
a. Describe the type of game that is involved in the above situation.
b. Draw a game tree of the situation, with the appropriate payoffs.
c. Using the backward induction method, analyse the game tree and explain the result observed.
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