Homework # 1 - ISyE 6230 – Economic Decision Analysis II – Spring 2007Due Tues Jan 30Grading: up to 10 points per problem for completing each problem; the remaining 50 points will come from grading one randomly selected problem for correctness. 1) Give an example of a business situation that can be modeled as a game: Find an article from a reputable journalistic source (e.g., NY Times, Wall Street Journal, Forbes) detailing a business situation. Identify the players involved, the set of actions, and a description of the payoffs. If you can identify the classic game to which the situation belongs (e.g., Chicken, Prisoner’s Dilemma, etc.), then make this argument. Predict the outcome of this game; if applicable, describe how the outcome would be different if there were not multiple players acting strategically. Make sure to detail your reference for this article explicitly. Be prepared to describe your business example in class the day homework is due. 2) There is a game called “Rock, Paper, Scissors”. (If you are not familiar with it, you can find more in details on the internet. In short, players simultaneously decide (or display) one of those three decisions: rock beats scissor, scissor beats paper, and paper beats rock. If the sameaction is chosen by both players then it is a tie and no one wins.) Assume two players are playing the game. The player who loses should give $1 to the winner. When the game ties, no player receives or gives a payoff. a) Write this game in normal form and identify all of the elements that comprise the game. b) Does a Nash Equilibrium exist for this game? If so, then identify it. c) Will the strategy remain the same if the payoff from winning with rock is $2? If not, how would it change? 3) There are three players: 1, 2, and 3; and three alternatives: A, B, and C. Players vote simultaneously for an alternative; abstaining is not allowed. The alternative with the most votes wins; if no alternative receives a majority, then alternative A is selected. The payoff or utility) functions based on then final selected alternative are: 1 2 31 2 31 2 3( ) ( ) ( ) 2( ) ( ) ( ) 1( ) ( ) ( ) 0u A u B u Cu B u C u Au C u A u B= = == = == = =.a) Write all of the actions, outcome, and payoffs for when player 1 chooses A. b) Identify the pure-strategy Nash equilibria. (Hint: There are a lot.) c) Does outcome A Pareto-dominate other outcomes?d) Identify any pareto optimal outcomes.4) A worker is hired by a company. The worker can either work hard or shirk, and the company can either monitor the worker or not. The company can penalize the wage only if it monitors worker shirking. If the worker puts in effort, it is at a cost of g. If the company monitors, it costs h. The payoff to the company from output is v. Assume g>h>0. The following is the payoff table.6230 Spring 2007 Page 1CompanyMonitor No monitorWorkerWork 0,-h w,-wShirk w-g, v-w-h w-g, v-wa) In what case does there exist a weakly or strongly dominated strategy?b) Assuming it’s not the case of (a), identify the Nash equilibrium.5) Consider the following bargaining game. Players 1 and 2 are bargaining over how to split a dollar. Both players simultaneously name shares they would like to have, s1 and s2, where1 20 , 1s s� �. If 1 21s s+ �, then the players receive the shares they named, but if 1 21s s+ >, both get none.(a) What are each player’s strictly dominated strategies?(b) What are each player’s weakly dominated strategies?(c) What are the pure strategy Nash equilibria of this game?6230 Spring 2007 Page
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