Question

A firm and its supplier are going to negotiate a deal. Since the supplier’s cost is $10 million per quarter and the value to the firm is $13 million per quarter, there is $3 million per quarter to split between the two. However, they can each hire a negotiation consultant for $500,000 per negotiation. If neither hires the consultant, each expects to get half of the $3 million pot. If only one hires the consultant, it expects to get three-fourths of the pot minus the consultant costs, leaving the other firm to gain 0 (and incur in 0 cost as well). If they both hire consultants, their consultants suggest additional expenditures that erases the potential gain of $3, leaving the firm and the supplier with the cost of hiring the consultants.

What is the equilibrium of this simultaneous move game? Hint: set up the 2x2 table and fill in the pay-off values in the cells, then determine the Dominant Strategies (if any) and Nash Equilibrium (if any)? Explain your reasoning.

Show Work.

Answer 1

Payoff are in millions.

Given supplier action of hiring consultant , best response for firm is to not hire consultant and earn zero payoff.

Given supplier action of not hiring consultant,best move for firm is to hire consultant and earn 1.75 payoff.

So firm don't have any dominant strategy .

By same reasoing supplier also doesn't have any dominant strategy.

The nash equilibrium is when one is choose to hire consultant and other choose not to hire consultant.

So there are two possible nash equilibrium .

The payoff at nash Equilibrium is : 1.75 for , who hire consultant and zero for ,who don't hire consultant.