게임이론과 경쟁전략

소개

3,4,5,6,7,9,11 문제 해석과 정답 해설입니다.

목차

3. Two computer firms, A and B, are planning to market network systems for office information management. Each firm can develop either a fast, high-quality system (High), or a slower, low-quality system (Low). Market research indicates that the resulting profits to each firm for alternative strategies are given by the following payoff matrix:
3. Two computer firms, A and B, are planning to market network systems for office information management. Each firm can develop either a fast, high-quality system (High), or a slower, low-quality system (Low). Market research indicates that the resulting profits to each firm for alternative strategies are given by the following payoff matrix:
5. Two major networks are competing for viewer ratings in the 8:00-9:00 P.M. and 9:00-10:00 P.M. slots on a given weeknight. Each has two shows to fill this time period and is juggling its lineup. Each can choose to put its “bigger” show first or to place it second in the 9:00-10:00 P.M. slot. The combination of decisions leads to the following “ratings points” results:
6. Two competing firms are each planning to introduce a new product. Each will decide whether to produce Product A, Product B, or Product C. They will make their choices at the same time. The resulting payoffs are shown below.
7. We can think of the U.S. and Japanese trade policies as a prisoners’ dilemma. The two countries are considering policies to open or close their import markets. Suppose the payoff matrix is:
9. You play the following bargaining game. Player A moves first and makes Playter B an offer for the division of $100. (For example, Player could suggest that she take $60 and Player B take $40) Player B can accept or reject the offer. If he rejects it, the amount of money available drops to $90, and he then makes an offer for the division of this amount. If Player B rejects this offer, the amount of money drops to 0. Both players are rational, fully informed, and want to maximize their payoffs. Which player will do best in this game?
11. Three contestants, A, B, and C, each have a balloon and a pistol. From fixed positions, they fire at each other`s balloons. When a balloon is hit, its owner is out. When only one balloon remains, its owner gets a $1000 prize. At the outset, the players decide by lot the order in which they will fire, and each player can choose any remaining balloon as his target. Everyone knows that A is the best shot and always hits the target, that B hits the target with probability .9, and that C hist the target with probability .8. Which contestant has the highest probability of winning the $1000? Explain why.
12. An antique dealer regularly buys objects at hometown auctions whose bidders are limited to other dealers. Most of her successful bids turn out to be financially worthwhile because she is able to resell the antiques for a profit. On occasion, however, she travels to a nearby town to bid in an auction that is open to the public. She often finds that on the rare occasions in which she does bid successfully, she is disappointed the antique cannot be sold at a profit. Can you explain the difference in her success between the two sets of circumstances?
13. You are in the market for a new house an have decided to bid for a house at auction. You believe that the value of the house is between $125,000 and $150,000, but you are uncertain as to where in the range it might be. You do know, however, that the seller has reserved the right to withdraw the house from the market if the warning bid is not satisfactory.

본문내용

3. Two computer firms, A and B, are planning to market network systems for office information management. Each firm can develop either a fast, high-quality system (High), or a slower, low-quality system (Low). Market research indicates that the resulting profits to each firm for alternative strategies are given by the following payoff matrix:




Firm B


H
L



H
50, 40
60, 45

Firm A
L
55, 55
15, 20



a. If both firms make their decisions at the same time and follow maximin (low-risk) strategies, what will the out come be?
→ Maximin전략에서는, 한 기업이 각각의 옵션에 대해 최악의 산출을 결정한다. 그리고 최악의 산출물들 중에서 결과를 최대화한 옵션을 선택한다. 만약 기업 A가 High를 선택한다면, 최악의 결과는 기업 B가 High를 선택할 경우에 발생할 것이다. A의 결과는 50일 것이다. 만약 기업 A가 Low를 선택한다면, 최악의 결과는 기업B가 Low를 선택할 경우에 일어날 것이다. A의 결과는 15일 것이다. Maximin전략을 따르면, 기업 A는 결과적으로 High를 선택한다. 만약 기업 B가 Low를 선택한다면, 최악의 결과는 기업 A가 Low를 선택한 경우에 일어날 것이다. 즉 결과는 20일 것이다. 만약 기업 B가 High를 선택한다면, 최악의 결과 40은 기업 A가 High를 선택할 경우 일어날 것이다. Maximin전략을 따르면, 기업B는 결국 High를 선택한다. 그래서 A와 B 모두 Maximin전략 하에서 고품질 시스템을 생산한다.

b. Suppose both firms try to maximize profits, but Firm A has a head start in planning, and can commit first. Now what will the outcome be? What will the outcome be if Firm B has a head start in planning and can commit first?
→ 만약 기업A가 처음으로 실행한다면, 기업A는 기업B가 합리적으로 Low를 선택할 것과 Low가 이 기업B에게 높은 결과를 줄 것(45, 40)이라는 것을 알기 때문에 High를 선택할 것이다.

참고자료

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