Proposition cuatro means the strategy regarding RA1 hinges on their own as well as competitor’s character
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 three, RA1’s approach has a tendency to raise which have RA2’s character. Given that informed me prior to, race enjoys a couple of reverse consequences into the behaviour out-of RA1: the newest disciplining perception and also the market-discussing impact. In the event the reputation for their enemy grows, RA1 are able to find they less appealing to boost its own character provided a smaller expected future share of the market, thus have a tendency to act way more laxly. As well, RA1 may have bonuses to do something really whenever RA2’s reputation grows to steadfastly keep up their industry frontrunner condition. Our our teen network very own investigation suggests that the market industry-discussing feeling can control the new disciplining feeling. One to possible reasons is the fact that the market share regarding a rating department is set not just by the the character prior to you to of the opponent, plus by absolute number of its character. That’s, even good monopolistic RA dont respond completely laxly, since the otherwise its reputation carry out getting too lower in order to credibly rates really ideas. Ergo, the brand new incentives away from a beneficial RA to steadfastly keep up an effective character, despite absence of battle, provide the fresh new disciplining effectation of competition weakened. We think it is practical because the in reality, offered rational people, a beneficial monopolistic RA would not have unbounded sector vitality.
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 Unlimited-Horizon Options
We now present the brand new numerical solution of design inside infinite opinions. The newest mathematical solution is once more determined using backwards induction, that’s, i very first solve brand new model on finite period case, and improve the amount of episodes so that the balance means converges into unlimited-vista service.
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 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.