1. Assume that two risk-neutral individuals i E N {1, 2} dispute over some property of value v > 0 and they appeal to court for resolution. The legal procedure is a two-period game.
In the first period of the game, litigants simultaneously decide whether to hire an attorney or not and the first period choices are made public. If a litigant does not hire an attorney, he represents himself in court.
The cost of legal expenses are linear with marginal cost of 1 for both litigants. If a player hires an attorney, in the second period, the litigant offers the attorney a limited liability contract, i.e., the litigant i chooses a representation fee, wi > 0, to be paid to the attorney if the attorney wins the case.
If the case is lost, the attorney is not paid. After observing the contract the attorney decides to accept or reject it.
If the attorney accepts the offer, she represents the litigant in court and pays the legal expenses herself. The outside option (payoff of not accepting the contract) of risk-neutral attorneys are normalised to zero. The cost of legal expenses of attorneys and the wage costs of litigants are linear with marginal cost of 1.
Advanced Microeconomic Theory
Formative Assignment Page 2 of 5
Probability of winning the case is a function of the legal expenses in court whether a litigant hires an attorney or not. Denoting the legal expenses by a player i E N (or player i’s attorney) by xi > 0, the probability of winning the case given the strategy profile x E ii82+ is given by the contest success function (CSF) 1/2 if x (0, 0), Pi(x) =otherwise. (1) xi +x3.
(a) Assume that both players are forced to hire an attorney in the first stage.
i. Formulate the expected payoff function of each attorney in the second stage given representation fees wi. (3 Marks)
ii. Determine the Nash Equilibrium legal expenses of each attorney. Show that the attorney accepts any positive wi. (5 Marks)
iii. Calculate the equilibrium probabilities of winning the case in the second stage as a function of attorneys’ representation fees. (2 Marks)
iv. Given the subgame decisions of attorneys in the second stage above, formulate the payoff functions of each litigant in the second stage as a function of wi. (5 Marks)
v. Show that there is no asymmetry in the representation fee choices in the Subgame Perfect Nash Equilibrium, i.e., 4 = W.
Determine the Subgame Perfect Nash Equilibrium representation fee choices of each litigant in the second stage. Calculate the expected payoff of each litigant under this equilibrium path. (10 Marks)
(b) Assume that both players are forced not to hire an attorney in the first stage. i. Formulate the expected payoff function of each litigant in the second stage. (3 Marks)
ii. Determine the Nash Equilibrium legal expenses of each player and calculate their equilibrium expected payoff in the second stage. (12 Marks)
(c) Assume that one player is forced to hire an attorney and the other forced not to in the first stage. i. Formulate the expected payoff function of each player (one litigant and one attorney) in the second stage. (3 marks)
ii. Determine the Nash Equilibrium legal expenses of each player and calculate their equilibrium expected payoff in the second stage. (12 marks)
iii. Determine the Subgame Perfect Nash Equilibrium wage choice of the player who is forced to hire an attorney. Calculate the equilibrium expected payoffs of each litigant in this equilibrium path. (10 marks)
(d) Assume that now decisions are not forced in the first stage and each litigant makes a choice on hiring an attorney or not.
i. Determine the Subgame Perfect Nash Equilibrium hiring decisions of each litigant. (10 Marks)
ii. Is there any Pareto improvement over the Subgame Perfect Nash Equilibrium hiring decisions of the litigants? Explain. (10 Marks)
iii. Is it recommendable for the state to include a mandatory law to hire attorneys? Would litigants be better off under this law? How do you explain this result? (15 Marks)
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