For all t < T ? 1 , the strategy of the RA depends on its own and its competitors' reputation
When A is large, RA1 always gives a GramsR to a bad project. Conversely, when A is small RA1 behaves honestly and gives NR to bad projects. In the intermediate range, RA1 has a mixed strategy, with 0 < x1 < 1 . Note that the lower threshold for A is increasing with RA1's reputation.
The results imply that RA1 tends to lie less as its reputation increases (Corollary 3). The intuition behind this result is straightforward. Since we assumed pG = 1 , the reputation of RA1 goes to zero immediately after a project fails. This means that the cost of lying increases with RA1’s reputation while the benefit of lying stays constant. Hence, it is not surprising that RA1 prefers to lie less as its reputation increases. 18 18 Our results in Section 5 show that this is no longer true if pG < 1 . The penalty on reputation will be smaller as the reputation of RA increases, that is, the cost of rating inflation can decrease with reputation, resulting in a “u-shaped” relationship between strategy and reputation.
Additionally, considering Corollary step 3, RA1’s means does boost that have RA2’s reputation. As the told me before, competition has actually a couple of opposite consequences towards the behavior regarding RA1: new disciplining effect plus the markets-revealing impact. If the reputation for the adversary develops, RA1 discover it reduced appealing to improve its very own character offered a smaller sized asked upcoming business, so because of this commonly behave far more laxly. At the same time, RA1 have bonuses to do something truthfully when RA2’s character grows in order to maintain their field commander position. Our very own analysis implies that the market industry-revealing impression tends to dominate the fresh disciplining perception. You to definitely possible cause is the fact that share of the market off a get department is determined not simply from the its profile according to one of the competition, also because of the sheer amount of their reputation. That is, even good monopolistic RA don’t act entirely laxly, since if not its profile carry out be as well low in order to credibly speed extremely plans. Ergo, the fresh incentives regarding an effective RA in order to maintain an excellent profile, even yet in absence of race, promote the fresh new disciplining effectation of battle weakened. We think it is sensible because indeed, provided rational buyers, a monopolistic RA don’t have unbounded industry powers.
However, the results above are based on a three-period model with the assumption that pG = 1 , that is, the strategic RA is caught immediately after the project fails. The results may be driven by the fact that the RAs only live for three periods, and hence have limited potential gains associated with higher reputation. In order to capture the long-term benefits of reputation under a more general setting, we move on to the next section, where we relax parameter assumptions and compute numerical solutions in an infinite-horizon case.
5 Infinite-Horizon Settings
We now establish the mathematical service of one’s design inside the infinite horizon. The brand new mathematical solution is again calculated playing with backward induction, that’s, i first solve brand new model regarding the finite period instance, after which increase the number of periods so the harmony method converges to the unlimited-panorama services.
We assume that the model ends at period T and solve the model backwards. We know that the strategic RA will always lie at period T and T ? 1 , according to Corollary 2. We solve for the equilibrium strategy of the RA described in Section 3. We look at the pay-offs from lying and being honest and determine the strategy. As long as for xt = 1 , RA1 will always choose to lie. Conversely, if for xt = 0 , RA1 will always tell the truth. In teenchat free trial all other intermediate cases, there exists a unique xt states that at which RA1 is indifferent between lying or not. Hence, we deduce inductively the equilibrium strategies of RA1. As T goes to infinity, we approach the infinite horizon solution. Since ? < 1 , the Blackwell conditions are satisfied.