Occurrence of Deception Under the Oversight of a Regulator Having Reputation Concerns

The pioneer work that shows the disappearance of noncredible reputations in a class of games that encompasses the same payoff structure of the current paper with different signalling technology is [6] (see Sect. 1.1 for further discussion).

For instance, Bernard Madoff, a prominent investment manager, was arrested and found guilty to several offenses including securities fraud and making false statements with the Securities and Exchange Commission (SEC). He began the Ponzi scheme in the early 1990s, yet he was arrested in late 2008 even though the SEC had previously conducted several investigations since 1992. SEC has been criticized for failure to act on Madoff fraud. The SEC inspector confessed that “Despite several examinations and investigations being conducted, a through and competent investigation or examination was never performed” (see “SEC criticized for failure to act on Madoff” at http://​business.​timesonline.​co.​uk by Seib and “Madoff Explains How He Concealed the Fraud” at www.​cbsnews.​com). Another investment fraud charge was against Robert Allen Stanford in 2009. A report of investigation by the SEC Office of the Inspector General shows that the agency has been following Stanford’s companies for much longer and reveals lack of diligence in the SEC enforcement (see the Report of Investigation at http://​www.​sec.​gov/​news/​studies/​2010/​oig-526.​pdf). The negligence of regulation may also have fatal consequences. For instance, there was a mine accident that took place in Soma, Turkey, which caused loss of 301 lives on May 13, 2014. In the response to a parliamentary question in the aftermath of the accident, it is understood that The General Directorate of Mining Affairs of Turkey—GDMA (that is connected to Ministry of Energy and Natural Resources), who is in charge of reviewing the conditions of mine fields, could only afford to audit less than one fourth all the mine fields annually. Yet, GDMA claimed that this particular mine had been reviewed many times. Although minor fees had been charged for infringement of some rules, an extensive audit of the field and mandatory safety measures had never been done and fatal mistakes went unnoticed according to the reports.

For an extensive overview of the reputation literature, we refer to [18].

These findings are likely to change when the regulator faces a long-lived agent having future objectives. Some other structures (such as stochastic replacement of the regulator or reform in the regulation system) would be needed to obtain recurrent reputation then. Cripps et al. [6] suggest that to obtain non-transient reputations other mechanisms should be incorporated into the model. One string of literature attains recurrent reputations by assuming that the type of the player is governed by a stochastic process through time. The reader is referred to [8, 12, 15, 17, 21, 23].

See [10] for games with perfect monitoring, [11] for games with imperfect public monitoring, and [13] for games with imperfect private monitoring.

These studies include: [22] (for games of conflicting interests with asymmetric discount factors); [4] and [1] (for games with imperfect monitoring and asymmetric discount factors); [7] (for games of strictly conflicting interests with equal discount factors); [3] and [2] (for games of locally nonconflicting or strictly conflicting interests with equal discount factors); [5] (for games with equal discount factors where the commitment action is a dominant action).

The results of [11] and [6] differ because [11] fixes the prior belief of being the commitment type and selects a threshold discount factor depending on this prior above which the player is sufficiently patient for their results to hold; whereas [6] fixes the discount factor while allowing the posterior belief to vary which eventually becomes so low that makes the required threshold discount factor (for [11]’s result to hold) to exceed way above the fixed discount factor.

The proof is along the lines with [9]. However, in their model, the long-lived agent’s concern for differentiating himself from his bad counterpart results in the loss of all surplus and market collapse since the short-lived players choose not to participate the game.

Take any Nash equilibrium in which the agents have been truthful with probability one until date s > t. In these periods, the reputation of the regulator will stay the same regardless of her behavior. Thus, it is a best response for the regulator to be lazy during these periods, thus her payoff is zero. Then the continuation play starting from date s is a Nash equilibrium with the same prior γ whose payoff can be no more than the original game.

When the agent is truthful with probability σ _A, t (h ^t ), choosing lazy is superior to diligent. Thus, the constraint involves an inequality rather than an equality.