This is a two-person game where Player 1, the plaintiff, alleges that Player 2, the defendant, is guilty of not providing adequate safeguard at an industrial plant. The plaintiff has no way of being certain that this is the case, whereas the defendant knows whether he is guilty as charged. The plaintiff can either Sue or take No Action. In return, the defendant can either Hold Out or Offer to settle out-of-court. If the defendant offers to settle, then the plaintiff can either Settle or he could Refuse, in which case the proceeding goes to Trial. If the defendant holds out, then the plaintiff can Try the case, resulting in the proceeding going to trial, or he can Drop it.
The extensive form of the game is displayed in the tree diagram over the next page. Note that the root of the tree is a move by Nature, labelled 0, who determines whether the defendant is guilty or not guilty of the charge of negligence.
The following are the costs associated with this game.
• S = settlement amount
• W = damages
• δ = court cost for defendant
• π = court cost for plaintiff
Also, we let Pr(defendant guilty) = q and therefore Pr(defendant is innocent) = 1 − q.
It will be assumed that if the case reaches the court, justice is done. In addition to his legal fee δ, the defendant pays the damages W only if he is guilty.
(a) Explain the information sets surrounding Player 1′s nodes.
(b) Display the strategic (normal) form of the game.