PS3F07 - Name:_ SID:_ _ GAME THEORY IN THE SOCIAL SCIENCES...

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Name:_____________ SID:______________ _ G AME T HEORY IN THE S OCIAL S CIENCES Problem Set 3 (Due in Lecture Tuesday, October 16) Question 1. Final-Offer Binding-Arbitration: Many contract disputes in business as well as sports are no longer being settled by going to court. Litigation is just too expensive. A typical way that the disputes are settled is that a neutral arbitrator is selected. Then each of the two parties to the dispute proposes a settlement. (When deciding what to propose neither party knows what the other is proposing.) The arbitrator then chooses the proposal which she thinks is closer to the “fair” outcome. Consider the following situation of final-offer binding-arbitration. Player A has just had a fire and has put in a claim with its insurance company. But the insurance company disagrees with A ’s estimate of how much it will cost to repair the damage and refuses to pay. Unable to reach agreement, A and I go to arbitration. To keep things manageably simple, assume that A and I can propose a settlement in the amount of 2, 4, 6, 8, or 10 thousand dollars. The arbitrator’s estimate of how much damage was done is 6, and both A and I know this. So if A were to propose 4 and I were to propose 2, the arbitrator would find in A ’s favor because A ’s demand is closer to 6 than I ’s offer. The payoffs in this case would be 4 for A and -4 for I . In the event of a tie, the arbitrator goes with the firm’s proposal. If, for example, A were to propose 8 and I were to propose 4, then arbitrator goes with I ’s proposal, leaving A with 4 and I with -4. (a) What is the strategic form for this game? (b) Are there any strictly dominated strategies? (c) Solve the game by iterated deletion of strictly or weakly dominated strategies. Be sure to identify the order of deletion and what dominates what. As you know, the order of deletion may affect the solution when weakly dominated strategies are deleted. Do not worry about checking all possibilities. Only solve it one way. (d) What are the Nash equilibrium/a of this game? If so, do some seem more plausible than others. Be sure to explain why or why not.
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Name:_____________ SID:______________ _ Question 2. Consider the market interpretation of the basic threat game (although you can also think of the international-crisis interpretation as well). A potential enterant E can either enter a market or not, after which the local monopolists, M , can decide whether to fight by engaging in a price war or acquiesce by sharing the markets. The game below illustrates the situation. EM (-1,-1) (0,2 (1,1) As we have seen in class, the backwards-programing solution to that game is that there are is no price war: E enters and M 1 acquiesces. This, however, does not seem consistent with empirical observation – there are price wars in the world. We might then ask what is going on in the world that we are not capturing in the model. One idea is “reputation”. Perhaps costly price wars take place so that the monopolist can establish a reputation for being tough and thereby deter others from challenging in the future .
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PS3F07 - Name:_ SID:_ _ GAME THEORY IN THE SOCIAL SCIENCES...

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